# Deal or No Deal 2/27/06



## atrac (Feb 27, 2002)

I swear the producers of the show read our previous thread -- No more sickening over-dubs from Howie.

The show felt a lot more polished tonight...I enjoyed it.

And the surprise visitor was just plain COOL. Sure, it was a nice lead-in for his returning show just afterward, but it was definitely a SURPRISE.

I really would like to spoilerize the above, but hey, it's not against the rules. 

I'm glad this show is back, but I don't see it lasting very long. Milk it while it's HOT though.


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## Amnesia (Jan 30, 2005)

Are all of the models new? Certainly my favorite from before is gone and at least some of the others are new as well...


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## lambertman (Dec 21, 2002)

Claudia (#1 this time) is a returnee. She's also formerly of Price is Right.

One other one also came back, but I don't recall her name right now.


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## Michelle5150 (Nov 16, 2004)

Watching his wife for the last few offers I could only think; _"dude, if you don't take the money, you're so divorced!"_


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## danielhart (Apr 27, 2004)

Michelle5150 said:


> Watching his wife for the last few offers I could only think; _"dude, if you don't take the money, you're so divorced!"_


Maybe that's why he kept saying "No deal!"


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## smak (Feb 11, 2000)

Um honey, we can buy 2 large pizzas with our winnings, ok?

Once he got it down to 3, i think mathematically it was correct to go all the way, but who can argue with taking the deal.

-smak-


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## Guindalf (Jun 13, 2001)

He stopped at exactly the right point. If he had gone on, the $500k would have lowered the offer considerably and he would possibly have felt compelled to take the 50-50 bet and ended up with $25.

Wow, I can't believe I'm actually discussing this mindless pap!


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## newsposter (Aug 18, 2002)

can't...stop ...watching..

they absolutely coach these people. No idiot would deal on turn number 1 with under 20K. Yet he spent a long time thinking about it. I hate that they took yet another 1st show to do one person. They did this last time too but it can't be rigged for that purpose because the girls have on the same outfits. Then again, I guess they could edit it 'up' to expand to the hour.

donald was pretty darn useless. I thought he'd come out with an abacus and figure out detail weighted odds or something. 

couldn't they get a fancier fake phone?


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## Dssturbo1 (Feb 23, 2005)

didn't nbc do some ads with new higher amounts like 2-3 million.

still the premise of a million $ winner is impossible without stupid risk.

the show can't last for more than 1-2 week runs without getting repetitive/boring.


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## Amnesia (Jan 30, 2005)

newsposter said:


> No idiot would deal on turn number 1 with under 20K. Yet he spent a long time thinking about it.


What I don't get is why the audience keeps screaming out numbers for him to pick? It doesn't make a difference!


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## Chunky (Feb 10, 2006)

Reminds me a lot of Who Wants to Be a Millionaire - long drawn out fluff. This show could be condensed to 15 minutes tops. That show lasted a little longer probably due to the trivial trivia element.


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## VegasVic (Nov 22, 2002)

Dssturbo1 said:


> didn't nbc do some ads with new higher amounts like 2-3 million.
> 
> still the premise of a million $ winner is impossible without stupid risk.
> 
> the show can't last for more than 1-2 week runs without getting repetitive/boring.


I believe the top prize is going up $500K each night, Friday night it will reach $3 million. I don't know if any of the other prizes are going up, or only the top one.

I think they should keep this as a weekly "event" 3 or 4 times a year. Once it goes to one night a week it will lose steam.


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## newsposter (Aug 18, 2002)

Amnesia said:


> What I don't get is why the audience keeps screaming out numbers for him to pick? It doesn't make a difference!


and they clap wildly like he's picked the right one no matter what he chooses!

didn't the guy yell like a girl? I'd be embarrassed. I guess they sort though and pick people like this for a reason though.

2 questions:

how did they work the contest for people who lived in the central or western time zones? I didn't follow or research it but swear they said live winner, which means 3 different zones right?

notice at the beginning they showed clips which inferred one woman picked the million? But i think it was up on the steps, not the one she was holding.


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## VegasVic (Nov 22, 2002)

Central and Eastern are watching at the same time. Pacific time zone would be different.


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## bruinfan (Jan 17, 2006)

The dude was married to Cheri O'Teri.

The only way anyone is going to win the top prize on this show is if somehow they picked ALL of the lower amounts in a row very early. 

I would like to see the behind the scene audition tapes. They must look for the most outrageous, lame, annoying people.

This show is so lame, but once you start watching, you just have to keep watching until it's done. Only solution, don't watch.


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## MikeMar (Jan 7, 2005)

stevieleej said:


> I don't see this lasting long. It's fun for a while but after watching it a few times you just get tired of it. Sort of like Weakest Link, Who wants to be a Millionaire, Trading Spaces, etc.
> 
> Here's an idea that would sink it quick - replace the girls with has-been stars and make the contestants banter with them before they open the briefcase.





Chunky said:


> Reminds me a lot of Who Wants to Be a Millionaire - long drawn out fluff. This show could be condensed to 15 minutes tops. That show lasted a little longer probably due to the trivial trivia element.


I Love millionare, still Tivo it every day (the day time version) Pefect show for tivo'ing.

Skip all the questions until you hit the $4,000 one, then you can skp til you see the answers and stuff. You can watch a 30min ep and get all the good stuff in less than 10 min. It's great.

That and price is right is awesome on Tivo


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## Lee L (Oct 1, 2003)

Dssturbo1 said:


> didn't nbc do some ads with new higher amounts like 2-3 million.
> 
> still the premise of a million $ winner is impossible without stupid risk.
> 
> the show can't last for more than 1-2 week runs without getting repetitive/boring.


Not necesarrily, but it would take a huge gamble or the right circumstances. I know I would definitely go if I had 3 amounts on the board, say $1, $500,000 and $1,000,000. Then lets say you pick the $1 leaving you with 500k and a million. All you have to do is chose and you win.

Now, if there were say $1, and $1,000,000 left, that would be a huge gamble and stupid risk, that is for sure.


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## MikeMar (Jan 7, 2005)

Lee L said:


> Not necesarrily, but it would take a huge gamble or the right circumstances. I know I would definitely go if I had 3 amounts on the board, say $1, $500,000 and $1,000,000. Then lets say you pick the $1 leaving you with 500k and a million. All you have to do is chose and you win.
> 
> Now, if there were say $1, and $1,000,000 left, that would be a huge gamble and stupid risk, that is for sure.


If you had 500k and 1Mill and the banker offered you 750k. WHat would you do?

I'd take the 750k personally.


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## newsposter (Aug 18, 2002)

VegasVic said:


> Central and Eastern are watching at the same time. Pacific time zone would be different.


then why do all the shows advertise as 8 eastern 7 central...or am i mixing it up


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## bruinfan (Jan 17, 2006)

Lee L said:


> Not necesarrily, but it would take a huge gamble or the right circumstances. I know I would definitely go if I had 3 amounts on the board, say $1, $500,000 and $1,000,000. Then lets say you pick the $1 leaving you with 500k and a million. All you have to do is chose and you win.
> 
> Now, if there were say $1, and $1,000,000 left, that would be a huge gamble and stupid risk, that is for sure.


But what if it were $25 and $1000000? That changes things!!


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## Lee L (Oct 1, 2003)

MikeMar said:


> If you had 500k and 1Mill and the banker offered you 750k. WHat would you do?
> 
> I'd take the 750k personally.


Well, all 3 outcomes are good but none of them are enough to quit your job though so I can see taking the 750 or going for it pretty much equally.


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## newsposter (Aug 18, 2002)

500*.3 for taxes = 350,000 cash in hand. times hopefully 10% after tax return =35K cash a year. I know a lot of folks that get by on less than that now.


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## Dssturbo1 (Feb 23, 2005)

yes, lee as discussed when the show first came on even under the perfect best case scenerio of having the $750K and $1M cases left and the banker offer of approx $875K your risking a minimum of $125K which is still a huge amount to give up simply by guessing even if it is a 50/50 shot.

risking a guanranteed $125K to win the $250K difference is stupid 

of course someone might do it since they would say hey I got the $750K no matter what so throw the dice


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## Guindalf (Jun 13, 2001)

newsposter said:


> then why do all the shows advertise as 8 eastern 7 central...or am i mixing it up


7 Central *IS *the same time as 8 Eastern. Therefore they are watching at the same moment in time. Clock time of course is one hour different.


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## lambertman (Dec 21, 2002)

Credit where it's due: Howie is actually very entertaining to watch in this role. I'm impressed how well he's been able to turn his shtick down. Seeing him on the Leno show last week reminded me what an irritating yutz he can be.


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## newsposter (Aug 18, 2002)

ok forget my mixup...how did they assure that east coasters didn't try to win during the west coast time?


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## smak (Feb 11, 2000)

I don't think they'd offer $875,000 if the two remaining cases were $750k and 1mil.

It would be less than the difference, probably $835,000 or something.

It's never been an exact average of the remaining cases.

The only way I see somebody winning 1mil is maybe if the last 3 cases are 500k, 750k and 1mil, and they just decide to go for it with 500k guaranteed.

With 3 left the deal would probably be something like $675,000 or something, and that would be worth a risk, and then if they didn't chose the million, maybe they'd try to go for it.

-smak-


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## brott (Feb 23, 2001)

Never watched the US version and I've only seen the show once. 

A good friend of mine in Australia, Stephen Frost (aka Frosty), was taped last December and the show was played about 2 weeks back (in Australia). Frosty's co-worker was actually on-stage picking the briefcases. In the Aussie version, multiple contestants each hold a briefcase (I think that models hold them in the US). Frosty held the last briefcase to be opened and was consulted often as the two of them were to share in the winnings. 

Long story short, the two of them managed to compile an all-time-record (at least for the Aussie version) by winning NOTHING . It was a hoot to watch and the max winnings were AUS$200,000 (~US$150,000). They had a Double or Nothing bit @ the end of AUS$2. Too classic. Odds are, they will get another shot as the losingest team.


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## n8. (Feb 26, 2006)

lambertman said:


> Credit where it's due: Howie is actually very entertaining to watch in this role. I'm impressed how well he's been able to turn his shtick down. Seeing him on the Leno show last week reminded me what an irritating yutz he can be.


Exactly... when he came on stage he thought it was the Howie Mandel show. Reminded me of that dummy who tries to make everyone laugh at your Thanksgiving dinner; starving for attention. He's good on Deal/no Deal but dont watch him on a talk show D:


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## SnakeEyes (Dec 26, 2000)

Australia has had a top prize winner.


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## alansh (Jan 3, 2003)

There are three prizes awarded for the play-at-home game, one for 8 ET/ 7CT, one for 7 MT (9 ET), and one for 8 PT (10 ET). Someone who wants a shot at a second chance can enter during the other time periods. This setup means those in the Mountain timezone have a better chance due to the fewer viewers.


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## DVC California (Jun 4, 2004)

MikeMar said:


> If you had 500k and 1Mill and the banker offered you 750k. WHat would you do?
> 
> I'd take the 750k personally.


I think the banker always offers just less than what would be a fair price. Instead of a straight 750k, the offer would be $744k. Just enough less to make contestant think the deal is not favorable.

The part that kills me is the final offer to "swap" cases when it's down to two. This really makes the decision tough because you could be trading for the $1M case...or trading away the $1M for teh lesser case.


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## Amnesia (Jan 30, 2005)

DVC California said:


> The part that kills me is the final offer to "swap" cases when it's down to two. This really makes the decision tough because you could be trading for the $1M case...or trading away the $1M for teh lesser case.


How is it tough? It's 50/50 and you have no reason to prefer one decision over the other. Just keep the one you have.


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## Lee L (Oct 1, 2003)

DVC California said:


> I think the banker always offers just less than what would be a fair price. Instead of a straight 750k, the offer would be $744k. Just enough less to make contestant think the deal is not favorable.
> 
> The part that kills me is the final offer to "swap" cases when it's down to two. This really makes the decision tough because you could be trading for the $1M case...or trading away the $1M for teh lesser case.


As far as I can remember, they have never offer more than 80% of the average value. In the early rounds, they are at like 15%.


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## Dssturbo1 (Feb 23, 2005)

well the lady made a stupid risk and lost big time last night.

the show was overboard stereotype with the choir and all.

howie has been a good host but those type productions aren't needed.


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## rich (Mar 18, 2002)

Dssturbo1 said:


> well the lady made a stupid risk and lost big time last night.


Too bad Trump wasn't there to talk some sense into her.


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## newsposter (Aug 18, 2002)

Dssturbo1 said:


> well the lady made a stupid risk and lost big time last night.
> 
> the show was overboard stereotype with the choir and all.
> 
> howie has been a good host but those type productions aren't needed.


The gospel stuff was overboard alright, even for this show. We dont need singing in a money game people! And I would have hated to be married to that 1st girl on the bench last night. She spinned so much after every turn that I couldnt imagine what she'd be like on a day to day basis. I could see it now, "honey, i found a penny on the ground" (super spinning ensues)

this show has more fake drama than a soap opera

i'm glad she only got 5 bucks. Greed is not a favorable trait and she learned it.



lambertman said:


> Credit where it's due: Howie is actually very entertaining to watch in this role.


It annoys the heck out of me. Every 1st phone call it's rarely more than 19K and even if the next 5 cases are all big amounts, you still get way more than 19K! So when he tells people 19K is a lot of money and they need to think about it, he pretty much lost me from that point. They expand things way to much here.


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## MasterOfPuppets (Jul 12, 2005)

One of my peeves about TCF is that so many people here are so ridiculously conservative...
If my choices were between $25 and $1,000,000...I'd probably go with the offer as well, but I can't say that with 100% confidence...
It's one of those once in a lifetime opportunities, plus you're guarenteed to leave with more than you came with...plus you'd be kicking yourself forever if you took the offer and had the $1,000,00 in your case...
Sometimes you just gotta take a few risks, especially when the entire premise is based on luck...
And I too think that Who Wants To Be A Millionaire is still entertaining, and wouldn't mind seeing Weakest Link make another run...then again, I try not to go by what the media tells me is hot at the moment, and when something's pop culture relevance has run its course...combine all that with the fact that most major and semi-major networks haven't developed a decent TV show in years...


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## Lee L (Oct 1, 2003)

I am definitely more risky than many here. I could definitely see doing exactly what she did. I would have probably stopped when she had the $187k offer, but once I have lost that and was down to $300k $5 and $1, I would have gone for it as well. Heck, you come on that show to win big money. $50 grand is nice, but in reality, it would just let me pay off my car and possibly have a nice vacation. It is just not that much.


They actually had open tryouts here in Raleigh for this show yesterday (not sure what the tryout would entail). I thought about going, but it was at 4:00 in the afternoon and I just did not have time to go all the way into Raleigh and wait in line with hundreds of people. Looks like they had quite a line and people even lined up yesterday morning at dawn. You would think they were giving away Xbox 360s or soemthing.


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## MasterOfPuppets (Jul 12, 2005)

Well, I'm glad that at least someone can see my same point of view...heh...
As for the choir being "overly stereotypical"...it's a game show, those aren't actors, they were just having some fun, I thought it was funny...I'm an athiest, and I really can't understand why people would be offended by that...as Bobby Knight says (sorta), must have been a rectal deposit...
If it's fake drama...where, exactly, are you people getting your "real drama"??? Hanging out in a lot of E.R's and courtrooms (untelevised ones, of course)??? Maybe the "real" drama from Lost or 24???
Mayhaps the drama from my sarcasm is enough to get you by...

I am somewhat curious as to what happens in a tryout...I'm sure that you have to at least appear to be a somewhat personable person, probably appear to be somewhat of a gambler (sorry, people)...and most likely have the uncanny ability to pick a random number between 1-26...you probably won't be on the show anytime soon if you show up at your tryout and say "I'd like case 28, Stone Cold Howie Mandel stand-in"...
And if they were handing out free Xbox 360's, I'm sure the line would have been longer, perhaps even with some "really cool" costumes...and fewer women...


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## verdugan (Sep 9, 2003)

newsposter said:


> couldn't they get a fancier fake phone?


Hey, that's a Bang & Olufsen phone. Pretty fancy and expensive. They're pretty awesome.


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## shelly40 (Nov 20, 2000)

Hasn't anybody here heard of the " Monty Hall problem" ?

They have the math all wrong.......

If they start with 25 cases, the chances of picking the correct case (the $1,000,000 one) at that point is 1 in 25.... 4%

And at the end, if there are 2 cases left.... one with $1,000,000 and the other with $1 you better bet your butt I'd be trading cases, as it is not a 50-50 chance....

You are MUCH better off swapping cases......
If you got to that point, you'd be an idiot not to swap..... (based on the odds)


Shelly


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## DancnDude (Feb 7, 2001)

shelly40 said:


> Hasn't anybody here heard of the " Monty Hall problem" ?
> 
> They have the math all wrong.......


This is under the assumption that Monty KNOWS what case is the "zonk" case. In this case, Howie doesn't know which cases are which, and he doesn't use that information to show a low dollar value. The odds don't change at all like in the Monty problem.

If however Howie said "I'll open 5 low dollar values for you" then yes, you would be better off switching at the end.


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## shelly40 (Nov 20, 2000)

It doesn't matter how they got to the final 2 cases.....
What IS important is they are.....

If they get down to the final 2 cases,
The original case has a 4% chance of containing the 1,000,000...... 
and the other case has a 96% chance.......(assuming you want $1,000,000)

Play it out with a deck of cards..... and you will see...

You would be a fool not to switch.......

Shelly


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## Guindalf (Jun 13, 2001)

shelly40 said:


> It doesn't matter how they got to the final 2 cases.....
> What IS important is they are.....
> 
> If they get down to the final 2 cases,
> ...


Sorry Shelly, but this logic does not compute.

The cases have two different amounts in them, one of which is the million, right? Therefore, it is a 50-50 shot. Either case can have either amount. Period.

Any choice of two random factors is 50%. There is no advantage to swapping whatsoever.


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## laststarfighter (Feb 27, 2006)

Amnesia said:


> How is it tough? It's 50/50 and you have no reason to prefer one decision over the other. Just keep the one you have.


It's tough because regardless of all previous decisions up to that point, this is the final choice to make. If you fail, you can pin point your failure to that one singular moment. One simple choice that changes your life: Win a lot of money or second guess yourself for the rest of your life. 

Yes you know the odds are a coin flip but, man, that is a lot of pressure.



shelly40 said:


> It doesn't matter how they got to the final 2 cases.....
> What IS important is they are.....
> 
> If they get down to the final 2 cases,
> ...


Sorry but that is faulty logic. That one last case does not represent the whole field. It only represents itself so the odds are 4% also. With each new case reveiled the odds change. If 15 cases are shown and 10 cases are left then the odds for each case becomes 10%, including the case you chose.

Now if the choice was pick either one case or the other 24 cases then yes you should pick the field every time. But there wouldn't be much drama in it now would there?


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## astrohip (Jan 7, 2003)

shelly40 said:


> It doesn't matter how they got to the final 2 cases.....
> What IS important is they are.....
> 
> If they get down to the final 2 cases,
> ...


Not in this case. The reason the Monty Hall scenario works is Monty *picks* which door to eliminate, so there is a 2/3 chance the remaining door is the winner, and only a 1/3 chance your door is the winner.

But on DOND, each case is eliminated randomly, so the odds of each case are identical. IF Howie eliminated 20 cases, guaranteed the $1MM was still there, and offered a switch, take it! But not when chosen randomly.


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## shelly40 (Nov 20, 2000)

so let me ask you this.....

lets say there are a million cases.....

The case picked is #2000....
Will you agree at this point that your chances are 1 in a million ?

I think you'll agree to that....

You randomly eliminate the 999,998 cases so that there are now 2 left....

Do you still really think it is a 50-50 shot ?

If you made your choice when there are 2 cases left, it's 50-50.....

But you didn't... you made your choice when there were a million cases....

Again... you'd be a fool not to switch..... 

or in the case of this show.....

Take their offer....for most likely, you're case will not contain the million....

Again.... do it yourself with a deck of cards....

The logic is 100% correct...

remember..... I'm not saying you'll win the million ALL the time....

I'm just saying by switching, you'll win it the vast majority of the time....


Once you get down to two cases, it doesn't matter how you got there.....
there are now 2 cases left...... Why does your original choice go from 1 in a million.... to 50-50 ?

And in fact, the one unchosen case DOES represent itself, and all the other cases that weren't picked , ....
and all the unchosen cases equate to 999,999 to 1 for one of them to contain the million..

Hey... people win the lottery... 
1 time in a million, on average.... you swapped to the wrong case....

But it's definitely better to switch

Shelly


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## MasterOfPuppets (Jul 12, 2005)

I seem to have wandered into some sort of special ed math class here...
The odds at the start of you picking the case with the top dollar amount is 26:1...
If, at the end there are 2 cases left, 1 of which contains the top dollar amount and one of which contains any other dollar amount, the odds are 1:1 at that point that you have the top dollar amount, which is 50/50...
The odds of not eliminating the top dollar amount up until that point are far greater...you have 24 chances to knock it out randomly...
I don't think anyone has said "yup, when you start out with all the cases out there, your odds are 50/50 of getting the top dollar amount"...
I'd argue that you're an idiot if you switch cases at the end...always go with your gut and never second guess yourself...you'd kick yourself far harder for giving away the top dollar case than you would for not switching...


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## astrohip (Jan 7, 2003)

I was a math major in college. Granted, that was back in the Jurassic, but statistics haven't changed much, I hope 



shelly40 said:


> lets say there are a million cases.....
> 
> The case picked is #2000....
> Will you agree at this point that your chances are 1 in a million ?
> ...


Here is the problem with your logic. Yes, your chances are 1 in a million at the first random selection. Then you say "randomly" eliminate 999,998 cases. At that point, the odds are 999,998 out of a million that you have already lost the million. So game over.

If they told you one of the cases had the million after randomly eliminating 999,998, it is still 50-50. If they picked the 999,998 cases knowing which was which, it is not random, and yes you want to switch. But since no one knows what is in the cases, it is random, and it is NEVER better to switch. Not worse either, but not better.

Clear as mud?


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## shelly40 (Nov 20, 2000)

Ummm.... no..... it's not clear.....

We're assuming you want to win the million, and you're right, there is a very good chance it will be eliminated before you get to 2 cases.....

But if it hasn't been eliminated.... you had better switch.....


and I'm not in special ed math............


you gotta see it to believe it...... do it with a deck of cards....

It's tough to convince people just explaining it here......
a demonstration works wonders....



surely I must have convinced at least 1 other person....


Shelly


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## Fl_Gulfer (May 27, 2005)

All I can say is thank God for TIVO I can watch the show in 20 min.


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## astrohip (Jan 7, 2003)

shelly40 said:


> Ummm.... no..... it's not clear.....
> 
> It's tough to convince people just explaining it here......
> a demonstration works wonders....
> ...


No, you haven't convinced anyone  . And let's do a demonstration:

Ok, let's simplify the other way. There are only three cases, A B C. Let's make A the winner. There are 6 scenarios.

* You pick A; B & C left. Get rid of B, C left. Switch. You lose. Don't switch, win.
* You pick A; B & C left. Get rid of C, B left. Switch. You lose. Don't switch, win.

* You pick B; A & C left. Get rid of A--game over (don't count this)
* You pick B; A & C left. Get rid of C, A left. Switch you win, don't you lose.

* You pick C; A & B left. Get rid of A--game over (don't count this)
* You pick C; A & B left. Get rid of B, A left. Switch you win, don't you lose.

There are six possibilities. With two, A (the winner) is eliminated, so no switch is possible. We won't count these. With the other four, if you switch, you win two, lose two.

If doesn't matter how many there are, switching has no affect on random selections. Remember, the Monty Hall offer is *not* random; Monty knows which one is the winner, and always eliminates one of the others.


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## Martyp (Jan 6, 2004)

Amnesia said:


> How is it tough? It's 50/50 and you have no reason to prefer one decision over the other. Just keep the one you have.


wouldn't it be 1 in 26 till you switched the case then it would be 50/50


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## shelly40 (Nov 20, 2000)

I'm saying that if you get down to 2 cases without the big jackpot being exposed, that you should switch...........

How you got to 2 cases doesn't matter......... you're initial choice was 1 in 26..... as it still is.......... 

you switch, and now you have a 25 in 26 chance of hitting the big one 


Shelly


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## Dssturbo1 (Feb 23, 2005)

no shelly,
with the intial 1 in 26 pick you have the first set of odds. 1:26 that's the odds you start with and the chance you had to pick the one winner.
So your right in it doesn't matter how you got to 2 cases BUT your fallacy is in the statment,....."as it still is"....

Because it DOES change with every eliminated case, (considering one case of the last 2 do contain the biggest/winner amount) all the way down to the last 1 in 2 shot = 1:2 = 50%= even odds = 50/50 shot etc...and obviously with a reality of the 50/50 shot there are no advantages to swap, simply luck of your 50/50 choice.

You do start with the worst odds 1:26 = 3.85%, it gets better with every case(s) eliminated and with 2 cases left you end up with the best odds you are going to get in the game 1:2 = 50%

1:26 start of game your one case pick
1:20 eliminate 6 cases
1:15 eliminate 5 cases
1:11 eliminate 4 cases
1:8 eliminate 3 cases
1:6 eliminate 2 cases
1:4 eliminate 2 cases
1:3 eliminate 1 case
1:2 down to last choice 1 in 2= 50/50 whether you switch or not.


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## fredo (Jan 26, 2006)

There is absolutely NO advantage to swap cases if down to the last 2 cases in Deal or No Deal.



Wikipedia said:


> The reason why Deal or No Deal isn't Monty Hall is that the cases to be opened in Deal or No Deal are chosen at random (by an uninformed player). In the Monty Hall gameshow, the host must know the location of the top prize and must actively reveal a door that does not contain the top prize. Thus in the Monty Hall problem, the host is forced to select non-randomly and thereby give information to the player. Contrast this with Deal or No Deal where the player chooses the cases, and does so essentially at random. This subtle difference changes the conditional probability completely. In fact, for Deal or No Deal with two cases remaining, there is no advantage to swapping the cases - it is equally likely that the top prize is in either of the two remaining cases. It is for this very reason that the Banker can offer the player the chance to swap cases because he knows there is no statistical advantage in doing so.


(Link to source in my next post)


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## fredo (Jan 26, 2006)

I can post URL's now...
http://en.wikipedia.org/wiki/Deal_or_no_deal#Comparison_with_the_Monty_Hall_Problem


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## Dssturbo1 (Feb 23, 2005)

and shelly it is the same with a deck of cards.

you start with a 1 in 52 chance of picking one specific card, 1:52 odds

IF your card is one of the two last cards after eliminating the other 50 cards then you still have the same 1 in 2 odds at the end and no reason to swap other than 50/50 chance


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## Marco (Sep 19, 2000)

shelly40 said:


> How you got to 2 cases doesn't matter......... you're initial choice was 1 in 26..... as it still is..........
> 
> you switch, and now you have a 25 in 26 chance of hitting the big one


*No!*

When you are down to two cases, you have the knowledge of what amounts the other 24 cases contain. Therefore, you know that the two remaining cases have, e.g., $1 and $1 Million.

Your odds of choosing the Million Dollar Case are 1 in 2.

You *cannot* improve your odds of winning by switching cases.


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## Dssturbo1 (Feb 23, 2005)

another theatrical night, they bring the guys coach and daughter in besides his 4 helpers.
then the girl gets husband with SEVEN kids and two cousins and two sisters.

28 with 7 kids, married with a nice BIG family but she shoulda been saying NO DEAL to her husband, LOL.


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## astrohip (Jan 7, 2003)

fredo said:


> I can post URL's now...
> http://en.wikipedia.org/wiki/Deal_or_no_deal#Comparison_with_the_Monty_Hall_Problem


Thank you Fredo, for that Wiki link. I didn't know wiki had a reference to DOND, but it confirms the exact same thing I have been trying to explain to shelly40. When the prior eliminations are random, switching is a non-event. When the eliminations are *not* random (ie Monty Hall), switching is a *must.*

Ok, let's move on to other, much more important topics. Like why the Others want Aaron


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## fredo (Jan 26, 2006)

astrohip said:


> When the prior eliminations are random, switching is a non-event. When the eliminations are *not* random (ie Monty Hall), switching is a *must.*


This is the key.

Also, just one more thing that I wanted to add. There is no way the producers of the show would allow you to switch the cases, when down to the last two, if there were any advantage to doing so.


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## astrohip (Jan 7, 2003)

fredo said:


> Also, just one more thing that I wanted to add. There is no way the producers of the show would allow you to switch the cases, when down to the last two, if there were any advantage to doing so.


Especially if it changed your odds from 1/26 to 50-50 !!!


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## Guindalf (Jun 13, 2001)

Shelly, we've hopefully explained that your logic is wrong and the choice is, indeed 50-50. But if you need one more thing to aid your thinking, maybe this'll help.

Remember that your logic applies to the LOWER amount as well as the million. In other words, you had that same 4% chance of picking the $1 as you did picking the million. The odds of your case containing the million are 1 in 26, but the odds of it containing just a dollar are the same 1 in 26. Therefore it is a 50% chance that either case contains the dollar OR the million!

Does that help?


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## laststarfighter (Feb 27, 2006)

shelly40 said:


> How you got to 2 cases doesn't matter......... you're initial choice was 1 in 26..... as it still is..........


This is the puzzle piece that you are missing. The odds are recalculated every time you change the variables. Take away one case and odds are now 1 in 25. Keep taking away and recalculating until you reach 1 in 2.

The problem with your scenario is that you never recalculated every time you found out new information.

This exact principle is the same as "counting cards" in blackjack or figuring the odds of winning in poker.


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## shelly40 (Nov 20, 2000)

laststarfighter said:


> This is the puzzle piece that you are missing. The odds are recalculated every time you change the variables. Take away one case and odds are now 1 in 25. Keep taking away and recalculating until you reach 1 in 2.
> 
> The problem with your scenario is that you never recalculated every time you found out new information.
> 
> This exact principle is the same as "counting cards" in blackjack or figuring the odds of winning in poker.


 I disagree.....

you made your choice when there were 26 cases.... so your odds of having picked the correct case are 1 in 26..... same as they were when you picked it.....

Those odds remain the same... you are not picking when there are 25 cases left....

the odds the million is in one of the unselected cases is 25 in 26....

Put out 25 playing cards and the joker......

pick one at random..... then look at it........

How many times did you get the joker ?

I would bet not many....

Shelly


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## jschuman (Feb 20, 2001)

Shelly,
You are thinking about/describing the Monty Hall problem. Deal or no Deal IS NOT the same!

Let's show how it works in both cases:
1) Monty Hall problem
Setup: 3 cases: A, B, C. One winning case.
- Contestant picks a case
- Monty opens a case that is not the winning case, showing it to the contestant.
- Contestant either stays with their original choice, or switches to the remaining unopened case.

Here are the possible scenarios (assume Case A is *always* the winning case):
Scenario 1) Contestant picks A. Monty shows B. *Contestant should not switch*
Scenario 2) Contestant picks B. Monty shows C. *Contestant should switch*
Scenario 3) Contestant picks C. Monty shows B. *Contestant should switch*
THEREFORE, Contestant should always switch. 2/3 of the time it is the right call.

1) Deal or No Deal problem
Setup: 3 cases: A, B, C. One winning case.
- Contestant picks a case
- _Contestant_ opens a case at random.
- Contestant either stays with their original choice, or switches to the remaining unopened case.

Here are the possible scenarios (assume Case A is *always* the winning case):
Scenario 1) Contestant picks A. Contestant picks B. *Contestant should not switch*
Scenario 2) Contestant picks A. Contestant picks C. *Contestant should not switch*
Scenario 3) Contestant picks B. Contestant picks A. *MOOT. Already eliminated winner.*
Scenario 4) Contestant picks B. Contestant picks C. *Contestant should switch*
Scenario 5) Contestant picks C. Contestant picks A. *MOOT. Already eliminated winner.*
Scenario 6) Contestant picks C. Contestant picks B. *Contestant should switch*
SO, in the scenarios where the Contestant is actually given a choice (1, 2, 4, 6) 1/2 of the time they should switch to win, 1/2 of the time they should NOT switch.

I hope this helps you understand.


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## SnakeEyes (Dec 26, 2000)

Disagree all you like but you are incorrect in your math. Your failure to look past the first pick and recalculate odds based on each random elimination is the flaw. If everything was chosen randomly and eliminated randomly with no one knowing the contents of the cases and you have two cases left it is indeed 50/50. Swapping will not increase your odds.


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## astrohip (Jan 7, 2003)

shelly40 said:


> I disagree.....


How about if we agree to disagree.  

I only watched the show once, Monday night. It was ok, but not enough to put on my SP list. The only reason I'm still hangin' round this thread is the math major in me refuses to give up.

Comes a time, when the blind man says, "Can't you see."


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## jschuman (Feb 20, 2001)

astrohip said:


> I only watched the show once, Monday night. It was ok, but not enough to put on my SP list. The only reason I'm still hangin' round this thread is the math major in me refuses to give up.


It's interesting, actually. We've had this discussion over at the Happy Hour several times (whenever someone brings up the Monty Hall problem). Of course, then it is people equally convinced that you should NOT switch.


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## MikeMar (Jan 7, 2005)

It is very simple as people have explained about

You are left w/ 2 cases. you KNOW that one of them has a million and the other a dollar. So you have a 50/50 shot of getting it right. If I walked in off the street and there were the 2 cases next to each other, I would have a 50/50 shot of getting the million. If you took case A and switched the spot w/ case B, they are still 50/50, the location has just changed.

If you have the winning lottery ticket and you mail it to a friend, it's still a winner right? just cause it's in a different location doesn't change what it is.


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## vman41 (Jun 18, 2002)

I want to see a contestant pick case 1 and then pick all the cases to eliminate in order (2, 3, 4...).


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## MikeMar (Jan 7, 2005)

vman41 said:


> I want to see a contestant pick case 1 and then pick all the cases to eliminate in order (2, 3, 4...).


What I would do is, regardless of the one i pick first, lets say #20. I would start my first 6 w/ 1-6.

I love the thing that Steve Jobs buys a lottery ticket w/ the numbers 1-2-3-4-5-6. why not, same odds as any other number. Not sure if it's true or not, but kinda funny.


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## shelly40 (Nov 20, 2000)

MikeMar said:


> If I walked in off the street and there were the 2 cases next to each other, I would have a 50/50 shot of getting the million. If you took case A and switched the spot w/ case B, they are still 50/50, the location has just changed.
> 
> QUOTE]
> 
> ...


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## jschuman (Feb 20, 2001)

shelly40 said:


> That is my point.... If you make your choice NOW.... with 2 cases left.... the odds are 50-50.......
> 
> But you made your pick when there were 26 cases........hardly 50-50.......
> 
> ...


Please read my 'scenarios' post and tell me where I am wrong. Switching neither helps nor hurts in Deal or No Deal.


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## MikeMar (Jan 7, 2005)

shelly40 said:


> That is my point.... If you make your choice NOW.... with 2 cases left.... the odds are 50-50.......
> 
> But you made your pick when there were 26 cases........hardly 50-50.......
> 
> ...


with the whole switch argument, if there are two cases left and you get to take your pick (via the switch) it's 50/50 which you just said.

If you had to pick 1 case and open it right there, yeah your odds are 1 in 26 of winning a million. But you get to pick 1 case and open others, and for every single case you open that's not a million your odds that you have the million increase a little. They even show the odds at the bottom of the screen!

So your odds increase a little at a time until you get down to your case and the other one, at that point the odds that you have a million are 50/50. So switching it just changes it from 50/*50 *to *50*/50

The 2 50's essentially switch, but your odds stay the exact same.


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## astrohip (Jan 7, 2003)

jschuman said:


> Please read my 'scenarios' post and tell me where I am wrong. Switching neither helps nor hurts in Deal or No Deal.


jschuman, she never replied to my scenario either (post # 54), so I think you are beating your head against the wall here. Notice that *no one else* is taking her side. We may just have to let it go.

Why it's even possible that she is actually a math major like me, and truly understands the statistical theory behind all of this, but just enjoys egging us on  . Maybe


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## jschuman (Feb 20, 2001)

astrohip said:


> jschuman, she never replied to my scenario either (post # 54), so I think you are beating your head against the wall here. Notice that *no one else* is taking her side. We may just have to let it go.
> 
> Why it's even possible that she is actually a math major like me, and truly understands the statistical theory behind all of this, but just enjoys egging us on  . Maybe


Agreed. I just couldn't sit idly by without adding my .02


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## shelly40 (Nov 20, 2000)

The little ABC scenarios just show that 1/3 of the time (given 3 choices ) you will pick the million dollar case....


If there were 10 choices, you would pick the right case 10% of the time.....

Those are the odds at the time you made your choice.....

Yes.... the odds change, but not for your case.......

They change for someone making a pick now....


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## SnakeEyes (Dec 26, 2000)

Shut up, just shut up. She doesn't get it, she will never get it. It's been twenty four hours, the cows can figure it by now.


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## MikeMar (Jan 7, 2005)

shelly40 said:


> The little ABC scenarios just show that 1/3 of the time (given 3 choices ) you will pick the million dollar case....
> 
> If there were 10 choices, you would pick the right case 10% of the time.....
> 
> ...


So by your logic, if you are down to 2 cases, your case has a 1 in 26 chance of having the million, and then the other case has a 1 in 26 chance of having the million, and apparently there is a 24 in 26 chance the world will then implode


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## jschuman (Feb 20, 2001)

shelly40 said:


> The little ABC scenarios just show that 1/3 of the time (given 3 choices ) you will pick the million dollar case....
> 
> If there were 10 choices, you would pick the right case 10% of the time.....
> 
> ...


I give up.


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## shelly40 (Nov 20, 2000)

Has anybody ever on this show actually had the $1,000,000 in the case they picked ?


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> Has anybody ever on this show actually had the $1,000,000 in the case they picked ?


doesn't matter. Anecdotal evidence will not change the math. Just let it go. We have no way to convince you, and everyone here is in disagreement with you and won't be convinced by your faulty logic. Please, let it die.


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## aarb00 (Mar 3, 2006)

While watching this show this week, I also figured the odds like Shelly is recommending. I believe she is correct and Ill try to explain it differently.

When you pick your case, you have a 1:26 chance that you picked the big money. We all agree on this. That means there is a 25:26 chance that one of the cases on the stage is the big money. I think we can all agree on that.

We get the opportunity to see up to 24 cases on the stage. If we make it that far, then we know that 24 cases on the stage didnt have the big prize, so that means that the one remaining case has a 25:26 chance of being correct.

I agree, statistically it would be better to switch if it came down to two. It is not a guarantee, but very statistically likely that the case on stage has the bigger value.

Saying you have a 50:50 chance seems true, but I dont think it is.


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## MikeMar (Jan 7, 2005)

If you flip a coin and it comes up heads 5 times in a row, what are the odds it will come up tails on the next toss?


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## MikeMar (Jan 7, 2005)

aarb00 said:


> While watching this show this week, I also figured the odds like Shelly is recommending. I believe she is correct and Ill try to explain it differently.
> 
> When you pick your case, you have a 1:26 chance that you picked the big money. We all agree on this. That means there is a 25:26 chance that one of the cases on the stage is the big money. I think we can all agree on that.
> 
> ...


So are you saying that the 2nd case has a 25:26 chance and the one you are holding is 1:26?? Just want to be clear on that.

Give me your odds on the 2 final cases of each one being the million


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## shelly40 (Nov 20, 2000)

I was just asking a question..........

If you don't want to answer.... fine.......

For no answer..... a post is not needed


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## MikeMar (Jan 7, 2005)

shelly40 said:


> I was just asking a question..........
> 
> If you don't want to answer.... fine.......
> 
> For no answer..... a post is not needed


I don't believe anyone has.


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## SnakeEyes (Dec 26, 2000)

aarb00 said:


> While watching this show this week, I also figured the odds like Shelly is recommending. I believe she is correct and Ill try to explain it differently.
> 
> When you pick your case, you have a 1:26 chance that you picked the big money. We all agree on this. That means there is a 25:26 chance that one of the cases on the stage is the big money. I think we can all agree on that.
> 
> ...


come on shelly, resorting to creating an alter to find support is lame.


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## aarb00 (Mar 3, 2006)

Your case still has 26:1; each of the two cases on stage is 12.5:1 each.


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## MikeMar (Jan 7, 2005)

aarb00 said:


> Your case still has 26:1; each of the two cases on stage is 12.5:1 each.


Umm the odds have to add up to 1, as in .5/1 and .5/1 as in 50/50. your's add up to 25/1 or something wacky like that.

This is my last post on this subject as my head will soon expload if i have to explain why it's not 50/50 again.


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## shelly40 (Nov 20, 2000)

MikeMar said:


> If you flip a coin and it comes up heads 5 times in a row, what are the odds it will come up tails on the next toss?


 I know I know

50-50


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## jschuman (Feb 20, 2001)

I'll just let Wikipedia do my talking:

*Comparison with the Monty Hall Problem*

When only two cases remain, Deal or No Deal might appear to be a version of the Monty Hall problem. This might seem to be true because there were (say) 22 cases, and suppose 20 of them have shown to not contain the major prize. At the start of the game, the probability that the player did not have the top prize was 21/22 -- if that probability still held true, then a player would almost surely win the top prize by swapping the originally chosen case with the other one remaining.

The reason why Deal or No Deal isn't Monty Hall is that the cases to be opened in Deal or No Deal are chosen at random (by an uninformed player). In the Monty Hall gameshow, the host must know the location of the top prize and must actively reveal a door that does not contain the top prize. Thus in the Monty Hall problem, the host is forced to select non-randomly and thereby give information to the player. Contrast this with Deal or No Deal where the player chooses the cases, and does so essentially at random. This subtle difference changes the conditional probability completely. In fact, for Deal or No Deal with two cases remaining, there is no advantage to swapping the cases - it is equally likely that the top prize is in either of the two remaining cases. It is for this very reason that the Banker can offer the player the chance to swap cases because he knows there is no statistical advantage in doing so. By contrast, a contestant repeatedly playing a 22-briefcase Monty Hall game will win the top prize more than 95% of the time by switching to the last unopened briefcase!

In Deal or No Deal, it is unlikely that 20 cases will be opened without revealing the top prize. In the rare cases where this happens, it is equally likely to be the player's initially chosen case or the last unopened case -- the probability of each outcome is 1 in 22.

Indeed, the Monty Hall problem may be usefully explained in terms of how it differs from Deal or No Deal. The reason that the Monty Hall problem produces an apparently counterintuitive solution is that it appears to work in the same way as Deal or No Deal, but is altered by the introduction of a non-random element.

_Source_: http://en.wikipedia.org/wiki/Deal_or_No_Deal

-----

Shelly/arb00: You may continue to argue your side but you are wrong. Have fun with that.


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## aarb00 (Mar 3, 2006)

Each of the two left on stage are 12.5:1, that makes 25:1. The one you have makes 26:1. 

To further explain, the two on stage are equally likely to have the big prize. The one you picked still has a 26:1 chance.


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## shelly40 (Nov 20, 2000)

SnakeEyes said:


> come on shelly, resorting to creating an alter to find support is lame.


 Thats not me..... but he did explain it better than I

I'm just glad to have a supporter....


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## shelly40 (Nov 20, 2000)

MikeMar said:


> Umm the odds have to add up to 1, as in .5/1 and .5/1 as in 50/50. your's add up to 25/1 or something wacky like that.
> 
> This is my last post on this subject as my head will soon expload if i have to explain why it's not 50/50 again.


 The odds add up to 1.....

the original pick is 1 in 26....

the case from the stage is 25 in 26..... as it represents the whole group....

and don't believe everything you read on the Wikipedia....


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## astrohip (Jan 7, 2003)

Let's try a different tack.

Bang your head against the wall 25 times. Hard. Really hard. To the point you are profusely bleeding, and concussed. Disoriented. Almost dead. Now you can choose whether to not bang your head against that same wall, or another wall across the stage. Either way, your head will feel better if you don't smack it on a wall.

See, it doesn't matter which way you don't bang against, it's still 50-50 you will feel better.


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## SnakeEyes (Dec 26, 2000)

When you open your first case there is no difference between any of the other unopened cases left on stage and the unopened case on your table. They are just randomly remaining cases. One is just place elsewhere. Same goes for each time you open a case. Eventually you are left with two randomly remaining cases and you have no idea what value is in either case and nothing prior to that to indicate which case has the higher amount. Therefore making it 50/50 and making swapping cases have no negative or positive effect on your chance to have the million.

Unless of course you can explain to me how a random unopened case on stage is any different than the random unopened case on your table.


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## aarb00 (Mar 3, 2006)

I gave this a lot of thought on this on my drive home and Ill take another stab at it.

First I need to correct myself on one point that MikeMar mentioned and my ratios are wrong.

If there are two cases on stage, then the odds are 12.5:26 that either case has the big prize and 1:26 that your case has the big prize.

Not that matters any more anyway.

It has been mentioned from the Wikipedia article that swapping your case would almost surely win the prize. This would agree with my argument. I dont recall on the show them being offered to switch. Why? Well they would statically lose. After the contestant makes a deal, they ask for remaining numbers to simulate what would happen, and when there is one case left, they dont ask if they want to switch. The reason they cant switch is that it wouldnt benefit the bank.

Someone correct me here, but I dont think you can switch. Perhaps I am not paying enough attention to the rules.

Also the article suggests that the fact the cases are random, eliminates my argument and the comparison to Lets Make a Deal becomes void where the host knows where the prize is. I dont see how this matters; in fact, it is because the cases are random, that I think my argument holds true. Because the cases dont change once selected, once selected they stay in the same case. It doesnt matter that no one knows where the top prize is because no one is trying to persuade you.

If you make it down to two cases, one on stage, one by your side. I am saying that the odds of your case having the top prize are 1:26, and the case on stage is 25:26. 

I would agree that if after each guess, they randomly change the money in each case, that when it came down to two, that you would have a 50-50 chance. How can your odds go from 26:1 to 2:1 if the cases dont change? Both statistics cant be true. The odds would have to be different in these two scenarios, but they dont change the values, they stay constant, and therefore the odds are not 50-50. 

I like the fact that such an interesting debate can come up from what appears to be a trivial show.


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## vman41 (Jun 18, 2002)

When you pick your case, there is a 25/26 chance that the million dollar case is in the unpicked pool. 24 out of 26 times though, the million dollar case will be opened before getting to the down to the last 2 cases, leaving 1/26 chance of the remaining unpicked case having a million dollars (the same odds as your initial pick being the million dollar case).


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## Amnesia (Jan 30, 2005)

aarb: You did not address the question raised by SnakeEyes: *Why are the odds for a random unopened case on stage any different than the random unopened case on your table?*

Let's make the math easier---let's say the game is only played with 5 cases. One random one has $1M and the others have 1 penny. OK?

So I pick case 1. What are the odds I have $1M? 1/5, right?
What are the odds that case 5 has $1M? 1/5, agree?

OK, so then I have Howie open cases 2, 3, and 4. They all have a penny. There is now one unopened case (case 5) on stage and 1 unopened case (case 1) on the table.

What are the odds that case 1 (my case) has $1M? 1/2. Two cases, so one chance in two.

You seem to believe that it's still only 1/5 and there's a 4/5 probabilty that case 5 has $1M.

But what makes case 5 so special? Just because it's on stage instead of one the table? The two cases are the same---how can one have 4 times the probability of having $1M than the other?


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## aarb00 (Mar 3, 2006)

Being in a different location doesnt make it special. We agreed that our case when we picked it had a 1/5 chance, and each of the remaining cases has a 1/5 chance.

But if our case has 1/5 chance, then it being on stage has a 4/5 chance.

If we opened all cases at the same time, I think we would agree that the odds of us picking the case are 1/5 and 4/5 that it is on stage.

The fact that we choose them one at a time doesnt actually change the statistics, just the presentation.


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## Amnesia (Jan 30, 2005)

vman brings up another good way of looking at the problem:

Let's stick with the 5 case game. There are 5 possibilites for how the amounts will be distributed among the cases.. Let's call them alternatives A, B, C, etc:

```
1 2 3 4 5
A: $ - - - -
B: - $ - - -
C: - - $ - -
D: - - - $ -
E: - - - - $
```
The $ represents the $1M and a - represents a penny.

So for alternative A, the $1M is in case 1, for alternative B, the $1M in in case 2, etc.
With me so far?

OK, and you agree that each alternative has an equal probability and that's why each case has an equal probability at the outset of holding $1M, right?

OK. So as I said, I pick case 1 and put it on the table.

I then have Howie open case 2, 3 and 4. Each holds only a penny.
Well, then we know that the cases were not layed out according to alternatives B, C or D---if they had, then the $1M would have been found in cases 2, 3 or 4 (respectively).

So the only remaining alternatives are A or E:

```
1 2 3 4 5
A: $ - - - -
E: - - - - $
```
There are two alternatives. In one, the money is in case 1. In the other, the money is in case 5. I have a 50% chance of having picked the money...


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## shelly40 (Nov 20, 2000)

Amnesia said:


> aarb:
> 
> But what makes case 5 so special? Just because it's on stage instead of one the table? The two cases are the same---how can one have 4 times the probability of having $1M than the other?


you picked case 1...... you have a 1 in 5 shot....

odds are, the million is in one of the other 4 cases....

I think you'd agree with that.....

That one case is part of a group that has a 4 in 5 chance of it being the million $ case.....when the others in the group are shown to not have the big prize.....the group as a whole still has that 4 in 5 chance...

Hence.. that one case now has a 4 in 5 chance of it containing the million.....


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## aarb00 (Mar 3, 2006)

If you could change your pick when there are two left, I agree that you have a 50-50 chance. But you picked it when there were 5 choices so the odds of your decision being correct are 1 in 5. I cant think of a better way to make my point. 

If I havent convinced anyone it is OK. I am just not convinced from anyone elses point either.

As I said before, interesting discussion.


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## Amnesia (Jan 30, 2005)

aarb00 said:


> Being in a different location doesnt make it special. We agreed that our case when we picked it had a 1/5 chance, and each of the remaining cases has a 1/5 chance.
> 
> But if our case has 1/5 chance, then it being on stage has a 4/5 chance.


Don't look at it as "on the table" vs. "on stage"---look at it as case 1 vs. case 5.

At the beginning case 1 has a 1/5 chance and case 5 has a 1/5 chance.

When it's down to 2 cases, why should case 1 have a lower probability than case 5? (Not some random case, but case 5 in particular?)


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## Amnesia (Jan 30, 2005)

aarb00 said:


> But you picked it when there were 5 choices so the odds of your decision being correct are 1 in 5.


You agree that there are 5 alternatives for how the money is laid out right? A-E?

Do you agree that if howie opens cases 2, 3 and 4 without finding the money, then money must have been laid out according to either alternative A or E?


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## Guindalf (Jun 13, 2001)

shelly40 said:


> you picked case 1...... you have a 1 in 5 shot....
> 
> odds are, the million is in one of the other 4 cases....
> 
> ...


No, Shelly, no, no no.

The FOUR cases TOGETHER have a 4/5 chance of containing the big prize. Each individual case has the SAME chance 1/5. Therefore, each case has an equal chance of containing the money.

OK, try it this way.....

Each case has a 1 in 5 chance of having the big prize, right?

YOUR case has a 1 in 5 chance, right?

Remove one case - it has a low amount.

You have a 1 in 4 chance of the money and so do each of the other three, so remove another case.

You now have a 1 in three chance, and each of the remaining two have the same 1 in three, right?

Remove one more case.

Now, you have a 1 in 2 chance and the other case ALSO has a 1 in 2 chance.

50/50

I rest my (very weary) case - pun intended!


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## aarb00 (Mar 3, 2006)

You have to look at it as on the stage vs. on the table because that is what is happening. We are discussing the odds of your case having the million vs. the million being on the stage. We are eliminating what is on the stage, and every time we eliminate a case on stage we are increasing the odds of any one of the remaining cases on stage going up, but not the odds of your cases going up.

Your cases odds dont go up, because when you picked it, there was a 1:5, or 1:26 chance of it being picked. On stage there was also a 1:26 chance of any one item on stage having the million, but as you eliminate each case it eventual goes down to a 25:26 shot.

You cant recompile statistics. 

Again, if we opened all of the cases at once, we would agree that the stage has a 25:26 shot while the player has a 1:26. Just because we open the cases one at time, doesnt change the odds of us having the correct case. 

That is why we are separating our case from the pool.

As I said in a previous post, when there are two cases on stage, each case has a 12.5:26 chance (almost 50-50).


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## shelly40 (Nov 20, 2000)

aarb00 said:


> .
> 
> Your cases odds dont go up, because when you picked it, there was a 1:5, or 1:26 chance of it being picked. On stage there was also a 1:26 chance of any one item on stage having the million, but as you eliminate each case it eventual goes down to a 25:26 shot.
> 
> ...


 Exactly.......


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## SnakeEyes (Dec 26, 2000)

aarb00 said:


> You have to look at it as on the stage vs. on the table because that is what is happening. We are discussing the odds of your case having the million vs. the million being on the stage. We are eliminating what is on the stage, and every time we eliminate a case on stage we are increasing the odds of any one of the remaining cases on stage going up, but not the odds of your cases going up.


Since your case came from the same pool of cases, opening a case that does not contain the million increases the chance that the case you chose from the 26 has the million.
Your case is part of the remaining cases that potentially could have the million. The only difference is it's sitting on a table instead of being held by a hot model.


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> Exactly.......


Please stop talking to yourself.

I'd love for an admin to IP compare these users


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## shelly40 (Nov 20, 2000)

SnakeEyes said:


> Since your case came from the same pool of cases, opening a case that does not contain the million increases the chance that the case you chose from the 26 has the million.
> Your case is part of the remaining cases that potentially could have the million. The only difference is it's sitting on a table instead of being held by a hot model.


 You only have the one case. It's on the table because you picked it......

Doesn't it increase the chances that one of the cases you DIDN'T pick contains the $$$ .... 
Yes it does.... and there are many more of them, as it is part of a group.......

Your case stays at the initial odds......... 1 in 26... as there were 26 choices...

on stage now ( the unpicked cases) odds rise to 1 in 24.... then 1 in 23 etc...... 
but as a group.... initial odds were 25 in 26.....

Shelly


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## shelly40 (Nov 20, 2000)

SnakeEyes said:


> Please stop talking to yourself.
> 
> I'd love for an admin to IP compare these users


 Let them compare....

It's not me...

Why would I do that... ?


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## Amnesia (Jan 30, 2005)

aarb00 said:


> You have to look at it as on the stage vs. on the table because that is what is happening. We are discussing the odds of your case having the million vs. the million being on the stage. We are eliminating what is on the stage, and every time we eliminate a case on stage we are increasing the odds of any one of the remaining cases on stage going up, but not the odds of your cases going up.


If I ever play the game, I would go in numerical order: 1, 2, 3, 4, 5.

So I would pick case 1 and the last one left would be case 5. No question.

That's why I want you to compare the odds for case 1 vs. the odds for case 5---not a random case on stage--case 5 and only case 5.

If there's 5 cases (1-5) and I choose case 1, what are the odds that case 1 holds $1M? 1/5.
What are the odds that case 5 (in particular) holds $1M? 1/5.

Now I open cases 2-4. They all have a penny. What are the odds that case 1 holds $1M? What about case 5?


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## aarb00 (Mar 3, 2006)

If you always picked 1, then two through 4, you would find that 1 only has a million in it 1/5 times. So would every other number. You are always saying that 2-4 dont have a million, so you are leaving only two possibilities. That is why you come up 50-50.

That is not the game, in the game 2-4 individually will all have the million 1-5 times. Which means again, that 1 will only win 1-5 times.

1 wont win 4-5 times irregardless of what you pick, the order you pick them, whether they are all picked one at a time, or all at once.

Therefore it makes sense, that if 1 doesnt have a million, that the remainders do, and number 5 only has a 1-5 chances of having it. 

If after each guess, they randomly change the money in each case, then at the last two, you would have a 50-50 shot. They dont so it is still 1-5.


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## Amnesia (Jan 30, 2005)

aarb00 said:


> If you always picked 1, then two through 4, you would find that 1 only has a million in it 1/5 times. So would every other number. You are always saying that 2-4 dont have a million, so you are leaving only two possibilities. That is why you come up 50-50.


OK, now we're getting to it.

If I appeared on the show, I would only get one crack at it. So I just told you that I would pick case 1 and the last case left would be case 5. And you agreed that it would be 50-50...if, of course, it came down to that. I hope you agree that most of the time the money would be in cases 2-4.

OK, so *I* would pick 1 for myself and open 2 then 3 then 4. You agreed that the odds would be 50-50 that I would have $1M.

But *everyone* has a particular order that they pick in.

Let's say you play the game. You might choose case 3 as your case and then open cases 5, 4 and 1.

Well, if my order leads to 50-50, then this order *must also* lead to 50-50. There's nothing magical about picking the cases in numerical order---any order is equally valid...


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## Amnesia (Jan 30, 2005)

aarb00 said:


> If you always picked 1, then two through 4, you would find that 1 only has a million in it 1/5 times. So would every other number. You are always saying that 2-4 dont have a million, so you are leaving only two possibilities. That is why you come up 50-50.
> 
> That is not the game, in the game 2-4 individually will all have the million 1-5 times. Which means again, that 1 will only win 1-5 times.


Yes, you're right---in the real game, 2-4 will have the million 3/5 times. Agree?

But we're discussing just the situations where the person gets down to 2. It's rare---it only happens in 2/5 times. But *in those situations*, then the odds are 50-50. Agree?


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## smak (Feb 11, 2000)

When i do the online version, i always have a theme. Either, 2,4,6,8... or 1,4,7,10,13...

I see 2 people saying that each case that is taken away increases the odds of each remaining case...

Increases the odds of what?

You don't know what the final 2 cases will be until there are 2 cases left.

The problem here, is that this isn't even a mathematical question.

You never have an equation. If you're talking about switching at the final 2, nothing you have done prior to that has any bearing on the situation, because there was never a question posed.

Monty Hall is easy. You either have Big Prize A, or Bad Prize B. You can do calculations based on that.

Since when you pick your case, you have no idea what the final 2 case amounts will be, there isn't even a way to start off an equation.

-smak-


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> Your case stays at the initial odds......... 1 in 26... as there were 26 choices...
> 
> on stage now ( the unpicked cases) odds rise to 1 in 24.... then 1 in 23 etc......
> but as a group.... initial odds were 25 in 26.....
> ...


Your cases initial odds is 1 in 26. The odds on your case does change as you open up each because you are revealing that the cases you could have chosen do not have the million. If the cases you could have chosen do not have the million, the liklihood your case has the million increases.


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## aarb00 (Mar 3, 2006)

I only said it was 50-50 because you said 2-5 dont have it. Then it is a given. We dont have that information so your selection is 1-5 and the remaining are 4-5. Everyones argument here is that it is OK to recompile the statistics after each selection. Shelly and I are saying it is not OK to recompile because the choice has already been made.

We are comparing the statistics when chosen to what we know now, and all we know now is what items on stage dont have it, increasing the odds of any individual case on the stage having it. 

My best argument is opening all the cases on the stage at once. It doesnt change your selection or the odds no matter how many cases on stage.

From a mathematical standpoint, it is either acceptable to recompile or not, I dont think elaborating our theories at this point is going to convince us either way.


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## smak (Feb 11, 2000)

See here's the problem. You say eliminating each case increases the odds?

Increases the odds of what???

-smak-


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## Guindalf (Jun 13, 2001)

smak said:


> See here's the problem. You say eliminating each case increases the odds?
> 
> Increases the odds of what???
> 
> -smak-


The odds increase all the way up to 50/50 or, to be fair, 100%. Each case you pick that does NOT contain the big prize increases the remaining odds that one DOES contain it...

1/26 becomes 1/25, 1/24, 1/23....all the way to 1/2 (or 50% or 50-50) All assuming that the big prize is not revealed in the process.

So, Shelly, you are right in that the odds at the START of the game are 25/26 that the million is on the floor, but when down to two cases, everything beforehand has no bearing on the final choice, so whichever way you want to look at it, there is a 50-50 shot that your case contains the million OR $1.


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## SnakeEyes (Dec 26, 2000)

aarb00 said:


> I only said it was 50-50 because you said 2-5 dont have it. Then it is a given. We dont have that information so your selection is 1-5 and the remaining are 4-5.


The remaining are each 1-5.


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## shelly40 (Nov 20, 2000)

It is not case 1 vs case 5............

it is case 1 vs case 2,3,4 and 5..........

or


1/5 vs ( 1/5 + 1/5 + 1/5 + 1/5 ) 

or 

1/5 vs 4/5 

your original pick will always have that 1/5 chance


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> It is not case 1 vs case 5............
> 
> it is case 1 vs case 2,3,4 and 5..........
> 
> ...


No it wont. It can't remain 1/5 because there isn't 5 cases left in the game at the end, there is only two that can have the million.


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## jschuman (Feb 20, 2001)

1/5 of the time you pick the winning case
3/5 of the time you don't pick the winning case BUT you open the winning case PRIOR to getting it down to only 2 cases
1/5 of the time you don't pick the winning case AND get down to only 2 cases

50/50 when you get down to 2 cases.


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## Regina (Mar 30, 2003)

Amnesia said:


> What I don't get is why the audience keeps screaming out numbers for him to pick? It doesn't make a difference!


That cracks me up too! And how Howie says things like, "Way to play! Way to play," or "Be careful.."   Umm...it's like totally random, how can someone play a certain way or be careful? 

..and I am a pharmacist, and I am very good at math--and all this discussion reminds me of a story. My (former job) boss was taking a statistics course and the prof announced the date of the final, what would be covered, etc and asked if there were any questions. Well, they had discussed playing cards quite a bit in the previous few weeks, and a woman in the class asked if she could bring a deck of cards to the final!  Sounds like it was too late for her!


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## SnakeEyes (Dec 26, 2000)

SnakeEyes said:


> How does a random unopened case on stage is any different than the random unopened case on your table.


In addition to finally answering this, can you please also answer this:

If the odds of your case never changes then why does the banker offer more money the longer the million dollars has not been revealed?

Don't you see, in arguing the position that you are arguing you are missing the whole point of the game?


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## shelly40 (Nov 20, 2000)

They do that for dramatic effect......

The money doesn't mean anything to NBC....

If the show gets the ratings... 1,000,000 isn't that much $$$ to them....

Besides, I don't think they have ever had to give $1,000,000 anyway.....

And even if they did, it is probably covered by insurance....


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## shelly40 (Nov 20, 2000)

The random unopened case on the stage is part of a group, with cumulative odds of 25 in 26 to have the 1,000,000 case within that group.....

the selected case on the table has the remaining 1 in 26 chance........


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## smak (Feb 11, 2000)

Guindalf said:


> The odds increase all the way up to 50/50 or, to be fair, 100%. Each case you pick that does NOT contain the big prize increases the remaining odds that one DOES contain it...
> 
> 1/26 becomes 1/25, 1/24, 1/23....all the way to 1/2 (or 50% or 50-50) All assuming that the big prize is not revealed in the process.
> 
> So, Shelly, you are right in that the odds at the START of the game are 25/26 that the million is on the floor, but when down to two cases, everything beforehand has no bearing on the final choice, so whichever way you want to look at it, there is a 50-50 shot that your case contains the million OR $1.


But when that big case is gone early, how do odds figure in after that?

If You have a 1/26 chance of picking the 1 million case, and you choose the 1 million dollar case in the 2nd set of 5 cases you choose, your whole odds calculations are out the window for the rest of the game.

Then you might have a 1/16 chance of having the 500,000 case.

That's a whole new set of odds.

So it's basically impossible to create any odds calculations for this show, escept for each case having no higher odds than any other case at all times.

-smak-


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## smak (Feb 11, 2000)

shelly40 said:


> The random unopened case on the stage is part of a group, with cumulative odds of 25 in 26 to have the 1,000,000 case within that group.....
> 
> the selected case on the table has the remaining 1 in 26 chance........


Problem here is, only 2 out of every 26 times you play the game will the 1 million case be one of the final 2.

Therefore, 24 out of 26 times no possible odds calculations are possible for what to do when there are 2 cases left.

-smak-


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> They do that for dramatic effect......
> 
> The money doesn't mean anything to NBC....
> 
> ...


Silly me for expecting you to understand the question.


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## shelly40 (Nov 20, 2000)

I'm only discussing the odds of collecting the $1,000,000 prize....



The odds of collecting one of the 2 biggest prizes....
say 750,000 or 1,000,000 

I would think would be 2 in 26... or 1 in 13......

Odds are , you still don't have one of the top 2 prizes, and in watching the show , I haven't seen anybody pick the 1st or 2nd prize value.....


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> The random unopened case on the stage is part of a group, with cumulative odds of 25 in 26 to have the 1,000,000 case within that group.....
> 
> the selected case on the table has the remaining 1 in 26 chance........


Yes and when that random unopened case is the last one remaining it's just like the random unopened case you picked in the beginning of the game. Only it sat on stage instead of your table. Making it equally as likely to have the million as the case you choose.


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> I'm only discussing the odds of collecting the $1,000,000 prize....
> 
> The odds of collecting one of the 2 biggest prizes....
> say 750,000 or 1,000,000
> ...


no you were arguing that swapping the cases would always be better.


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## shelly40 (Nov 20, 2000)

if it came down to the final 2 cases, and the biggest prize had not been revealed, 
it would be better to swap cases,.....

You would win the big prize MUCH more often....


Shelly


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## SnakeEyes (Dec 26, 2000)

No it wouldn't. The case on stage sitting unopened came from the same 26 unopened cases that you picked yours from. Each were one of 26 cases that could have the million. They have both been sitting idle doing nothing, the values in the case dont change during the game. The only difference is one is in a different location.

And with that I think this thread is done. Regardless of what anyone says you simply cannot comprehend the math or logic that shows you are wrong or you simply refuse to admit you are wrong, despite the fact nobody agrees with you, and you resorted to creating an alter to make it seem as though one person agreed with you. As if one person being wrong would make a difference among the many more people here that know what is correct. Therefore there isn't much left to say.


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## Neenahboy (Apr 8, 2004)

Any torrents for these? We watched Monday's, which I had recorded, and now we're hooked.


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## shelly40 (Nov 20, 2000)

---------------the values in the case don't change during the game-----------------


That is exactly the point..... When your choice was made it was, and still is 

1 in 26.............


Well... nice discussing this with ya.


I'm off to work.......

see yas 

Shelly


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> ---------------the values in the case don't change during the game-----------------
> 
> That is exactly the point..... When your choice was made it was, and still is
> 
> ...


No, the value INSIDE the case. You can't have 1/26 when there are only 2 cases left. There are 24 cases that have been eliminated from possibly having 1 million.


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## Amnesia (Jan 30, 2005)

shelly40 said:


> The random unopened case on the stage is part of a group, with cumulative odds of 25 in 26 to have the 1,000,000 case within that group.....
> 
> the selected case on the table has the remaining 1 in 26 chance........


True, but only at the beginning.

There's a 1/26 chance you pick the right case to start. Agree?

Let's say that you've already decided what order you plan to open the cases.
You pick 1 to keep and you plan to open 2, 3, 4, 5, etc.

So what are the odds that case 1 (your case) will have the $1M? 1/26.
What are the odds that case 26 will have the $1M? 1/26. Agree?
What are the odds that cases 2-25 collectively will have the $1M? 24/26. Agree?

OK, so you play the game. We already agreed that odds are overwhelming that the case is somewhere from 2 to 25. However, if you don't find it and then are just left with your case in hand (1) and one case on stage (26), then the odds are 50-50 that case 1 has the money.

As we just saw, originally the odds of case 1 having the money were originally 1/26 and the odds of case 26 (that exact case) were 1/26. It's certainly unlikely that we'll get all the way down to 2 remaining cases, but 1/13 times, that will happen (2/26 = 1/13). And as we saw, the odds of the money being in case 1 are the same as the odds of the money being in case 26. Right?

The relative likelihood of the money being in case 1 vs. case 26 doesn't change just because one case is on a stage and the other is on a table.


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## jschuman (Feb 20, 2001)

Shelly,
WATCH THE SHOW!!

As cases are opened, NBC repeatedly updates the odds that the case 'on the table' contains the largest cash prize left. If what you say is true then they would NEVER do this (because the odds would just stay at 1/26).

Unless, of course, you believe that this vast mathematical conspiracy extends to NBC, and they are flat out lying to us.


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## laststarfighter (Feb 27, 2006)

Wow, I come back to this thread thinking everyone would be at each other's throats and calling each other names. I know some of you are on the verge but GOOD JOB! on making it this far without completely losing your cool. 

The determination of odds is not a theoretical science. It is mathematics. Those arguing to switch are thinking this is debatable and a theory. Those arguing the 50/50 are saying it is non-debatable and a mathematical law. Talk to any math professor and every one of them will tell you that when it gets down to two cases your odds are now 50/50. Every one of them will say this.

I know that this "because I told you so" type of argument isn't going to convince you so I will try one more attempt to bring you over to "the dark side" of our way of thinking. 



aarb00 said:


> You have to look at it as on the stage vs. on the table because that is what is happening. We are discussing the odds of your case having the million vs. the million being on the stage. We are eliminating what is on the stage, and every time we eliminate a case on stage we are increasing the odds of any one of the remaining cases on stage going up, but not the odds of your cases going up.
> 
> Your cases odds dont go up, because when you picked it, there was a 1:5, or 1:26 chance of it being picked. On stage there was also a 1:26 chance of any one item on stage having the million, but as you eliminate each case it eventual goes down to a 25:26 shot.
> 
> ...


I think I see the disconnect. The fact is that yes you can in fact recalculate your odds and in fact you should.

Odds are 1/26 that you chose the right case when you choose it. If you were given the choice of keeping the ONE case or switch to the 25 cases then of course choose the 25.

Here is the disconnect: You think that your odds do not change once you get to two cases. We say that they do change.

Yes, the choice was 1/26 at the *moment* you made your choice. But any time you change the variables in the scenario and eliminate the known factors from the equation then you *must* recalculate.

Here is another way to look at it:



shelly40 said:


> 1/5 vs ( 1/5 + 1/5 + 1/5 + 1/5 )
> 
> or
> 
> ...


You calculated the mathematical odds of you choosing the right case perfectly. But using the same formula, calculate the odds of EACH case if you take one case away. By the way, we know this one case is shown to be not the winner so we can disregard it. This is important because this case changes to a *known variable* while the other 4 remain random and still a mystery.

So what is the formula for the odds with four left? Well, we have to recalculate.

1/4 vs (1/4 + 1/4 + 1/4)

or

1/4 vs 3/4
and of course the eliminated case which is 0/4 chance of being the winner. Add them up and we get:

1/4 + 3/4 + 0/4 = 4/4

in percentages this is:
25% + 75% + 0% = 100%

Now let's try the math without recalculating:

1/5 vs ( 1/5 + 1/5 + 1/5) + 0/5 _(this is still zero because we opened the case and we know for sure this one is NOT the winning case.)_

So let's add them up:

1/5 + 3/5 + 0/5 = 4/5

in percentages this is:
20% + 60% + 0% = 80%

Whoops, as you can see, we do not come up with 100%. This is why we need to recalculate whenever we get a new piece of information (i.e. every time a case is opened.)


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## shelly40 (Nov 20, 2000)

jschuman said:


> Shelly,
> WATCH THE SHOW!!
> 
> As cases are opened, NBC repeatedly updates the odds that the case 'on the table' contains the largest cash prize left. If what you say is true then they would NEVER do this (because the odds would just stay at 1/26).
> ...


 I'm not talking about the odds of the largest cash prize left.........

I'm talking about the odds of picking the case with the 1,000,000 in it....


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## astrohip (Jan 7, 2003)

jschuman said:


> Shelly,
> WATCH THE SHOW!!
> 
> As cases are opened, NBC repeatedly updates the odds that the case 'on the table' contains the largest cash prize left. If what you say is true then they would NEVER do this (because the odds would just stay at 1/26).
> ...


I decided to watch the show tonight, partially because of this thread.

(Wait, is it possible shelly40 is an NBC shill, simply making spurious arguments to get us to watch the show?!?!?!  )

Sorry, I digress. As jschuman noted, and as I saw on tonight's show, when it was down to a handful of cases, Howie goes, "You now have a 1/3 chance of having 500,000 or more". Wow, the odds *do* change as the game progresses.

(Aside #2: Have you noticed you can watch this show in ten minutes or less at 3X-FF?)

I still don't like this show. It's just random luck, and making a lucky guess (or not) as to when to stop. No skill. So it's not only on my _not To-Do List_ , so is this thread!


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> I'm not talking about the odds of the largest cash prize left.........
> 
> I'm talking about the odds of picking the case with the 1,000,000 in it....


no, again the arguement is about swapping cases. You keep falsely saying that you have better odds by swapping the cases at the end.


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## shelly40 (Nov 20, 2000)

you don't get to recalculate, because you don't make another choice....

You have to stay with your first choice....

One more scenario....


A million cases.... one case has $1,000,000

you pick a case.... 

1 in a million shot.... right ?

We go through 999,998 doors and amazingly , do not reveal the $1,000,000 case....

Do you think it is 50-50 that you picked the $1,000.000 ?


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## SnakeEyes (Dec 26, 2000)

astrohip said:


> I decided to watch the show tonight, partially because of this thread.
> 
> (Wait, is it possible shelly40 is an NBC shill, simply making spurious arguments to get us to watch the show?!?!?!  )
> 
> ...


It can be played with some skill if you can calculate expected value.


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## shelly40 (Nov 20, 2000)

-----no, again the arguement is about swapping cases. You keep falsely saying that you have better odds by swapping the cases at the end. --------


Remember,, i'm only talking about collecting the $1,000,000

If we were down to 2 cases, and ther million had still not been revealed, yes....

it would be better to switch..... 

Still stand by that....


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> you don't get to recalculate, because you don't make another choice....
> 
> You have to stay with your first choice....
> 
> ...


You are failing to grasp basic match principles here. Do you know what odds calculation actually is?


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> -----no, again the arguement is about swapping cases. You keep falsely saying that you have better odds by swapping the cases at the end. --------
> 
> Remember,, i'm only talking about collecting the $1,000,000
> 
> ...


Stand by it all you want to but mathamatics proves otherwise.


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## SnakeEyes (Dec 26, 2000)

You can't have 1/26 when there is only 2 cases left. You can't have 26 because there are 26 other possibilities remaining. We know 24 of these 26 do not contain a million. Thus leaving only two possible outcomes.


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## Amnesia (Jan 30, 2005)

shelly40 said:


> I'm not talking about the odds of the largest cash prize left.........
> 
> I'm talking about the odds of picking the case with the 1,000,000 in it....


Right. As as I (and others have pointed out), if you do in fact make it down to two cases and the $1M is still up for grabs, it is a 50/50 chance as to whether the $1M is in your case or in the unopened case on stage.


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## AnotherWin95 (Dec 13, 2004)

newsposter said:


> didn't the guy yell like a girl? I'd be embarrassed. I guess they sort though and pick people like this for a reason though.


Yes one that is 369,000 dollars richer now!


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## mattack (Apr 9, 2001)

Chunky said:


> Reminds me a lot of Who Wants to Be a Millionaire - long drawn out fluff. This show could be condensed to 15 minutes tops.


That's why I'm watching it on my non-Tivo recorder where I can play it at the first FF speed with sound.

The show is interesting from a game-theory point of view. (The wikipedia entry on it is interesting too.)

Nowhere near as good as WWTBAM nor Weakest Link. (Of course, none of them holds a candle to Jeopardy!)


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## shelly40 (Nov 20, 2000)

SnakeEyes said:


> You can't have 1/26 when there is only 2 cases left. You can't have 26 because there are 26 other possibilities remaining. We know 24 of these 26 do not contain a million. Thus leaving only two possible outcomes.


 Yes you can, ...

one case is 1/26, the other is 25/26.....

which of course, combining the 2 makes a certainty..... I

We didn't find out the others contained nothing until AFTER we made our choice.....

When our choice was made, it was 1 in 26......

If I make my choice now, with 2 cases left, it is 50-50.....


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## vman41 (Jun 18, 2002)

shelly40 said:


> Yes you can, ...
> 
> one case is 1/26, the other is 25/26.....
> 
> ...


You're not choosing 1 case, you're choosing 2 cases. They just have a round-about way of having you reveal your second choice (identifying 1 by 1 the cases you are not picking). There is a 2/26 chance that 1 of the 2 cases you picked has $1,000,000. The 1 out of 13 times that happens, the million is equally likely to be in either case.

Think of this way: Pick 2 cases out of 26, what are the odds that first case picked has a higher value in it than the second case?


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## SnakeEyes (Dec 26, 2000)

shelly40 said:


> Yes you can, ...
> 
> one case is 1/26, the other is 25/26.....


25/26 is all the other cases combined. You are not choosing 25 cases at once. You are choosing 1 case at a time. Each case is part of the same group of 26 making the chance each case has of containing the million at 1/26, just the like the case you chose.

It's basic math. They should have taught you this in your government school (I assume it's government schooling otherwise someone didn't get a lot of money's worth)


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## Amnesia (Jan 30, 2005)

vman41 said:


> You're not choosing 1 case, you're choosing 2 cases. They just have a round-about way of having you reveal your second choice (identifying 1 by 1 the cases you are not picking). There is a 2/26 chance that 1 of the 2 cases you picked has $1,000,000. The 1 out of 13 times that happens, the million is equally likely to be in either case.


Yes, that's exactly right!

You pick "your" case and you (by default) pick the last case to sit on the stage. Why should the case you pick to sit on the stage have a higher probability of the money than "your" case?


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## Amnesia (Jan 30, 2005)

So for Monte it was down to $25K or $50K and the banker offered him $38K.

Is this the first time that the banker offered more than the expected value?


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## fredo (Jan 26, 2006)

shelly40 said:


> you don't get to recalculate, because you don't make another choice....
> 
> You have to stay with your first choice....


OK, you are saying you don't get to recalculate the odds that your case contains $1M, correct? At the beginning you pick a case and have a 1 in 26 chance of picking the million dollar case, we all agree on that. Then you pick a case to open of the 25 remaining cases. The case you open has the $1M in it. Are you still saying that the your case still has a 1 in 26 chance of containing the $1M in it? Obviously not right, at that point, your case has a 0 in 25 chance of containing the $1M.


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## Guindalf (Jun 13, 2001)

fredo said:


> OK, you are saying you don't get to recalculate the odds that your case contains $1M, correct? At the beginning you pick a case and have a 1 in 26 chance of picking the million dollar case, we all agree on that. Then you pick a case to open of the 25 remaining cases. The case you open has the $1M in it. Are you still saying that the your case still has a 1 in 26 chance of containing the $1M in it? Obviously not right, at that point, your case has a 0 in 25 chance of containing the $1M.


Actually, it's 0 in 26 (the total has to be the original number of cases), but you DO have a 1 in however many cases are left unopened of having any one of the amounts that are left. In other words, if there are 15 cases left after the million is revealed, you have a 1 in 14 chance that you have the highest remaining value OR the lowest. It's equal.

Last night, the player got down to two cases with $25k and $50k in them. He WAS offered the opportunity to swap, refused and got $25k (the offer was $38k, so it "cost" him $13k). This was, however, just the luck of the draw and not and example of why he should have swapped. Just thought I'd get that in before Shelly arrives!


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## Fl_Gulfer (May 27, 2005)

If you were paddleing your canoe across the desert and the wheels fell off, How many pancakes would it take to shingle a doghouse?

Thats about how much sence this arguement is.


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## Fl_Gulfer (May 27, 2005)

Oh the answer is: 13 because Ice Cream don't have bones.


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## danielhart (Apr 27, 2004)

To those of you who think that when it gets down to two cases it's anything more than an even money proposition, please report to my poker table immediately, and please bring lots of money


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## newsposter (Aug 18, 2002)

Hey this is my first look at the thread today. Did anyone think that guy Monday night would Kill Howie with the on stage antics? I know he doesn't like handshaking but i wonder if he likes the punching? It appeared he really wasn't liking the physical end of all that energy from mr....well...i forget his name but it's obvious they favor a certain type of person for this show.

When they got down to just a few cases left, I got to wondering, what if he did just have a big amount and the smaller one and what would he do? I mean, what are the odds he'd win big money if he traded at the last minute?


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## astrohip (Jan 7, 2003)

newsposter said:


> When they got down to just a few cases left, I got to wondering, what if he did just have a big amount and the smaller one and what would he do? I mean, what are the odds he'd win big money if he traded at the last minute?


I think it is pretty clear from this thread that you *always* want to trade at the end. The odds are 25/26 you will win a million dollars, even if the only two cases left are $1 and $5


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## shelly40 (Nov 20, 2000)

I make a pick....

I pick case 10.......

we all agree at this point my odds are 1 in 26....


I eliminate 16 cases, and the 1,000,000 is still not revealed....



so, all of you are saying that I now have a 1 in 10 chance of having the 1,000,000 ?

If my friend now makes a pick, with 10 cases left , we have the exact same 10% chance ?

Even though I picked with 26 cases, and he only had to choose from 10 ?


Shelly


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## MikeMar (Jan 7, 2005)

shelly40 said:


> I make a pick....
> 
> I pick case 10.......
> 
> ...


Yup, because you are essentially PICKING your case again and again to keep.

After you pick down to 10 left plus yours, and you go again, you are basically saying every time, I want my case again and repick.


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## shelly40 (Nov 20, 2000)

MikeMar said:


> Yup, because you are essentially PICKING your case again and again to keep.
> 
> After you pick down to 10 left plus yours, and you go again, you are basically saying every time, I want my case again and repick.


 What ? I already made my pick when the odds were 1 in 26

I can't change cases

Shelly


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## newsposter (Aug 18, 2002)

astrohip said:


> I think it is pretty clear from this thread that you *always* want to trade at the end. The odds are 25/26 you will win a million dollars, even if the only two cases left are $1 and $5


thanks for the great advice. I'm also going to change which case i pick for my 10K prize after every commercial to give myself an advantage!


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## MikeMar (Jan 7, 2005)

shelly40 said:


> What ? I already made my pick when the odds were 1 in 26
> 
> I can't change cases
> 
> Shelly


You aren't but you are ESSENTIALL picking your case over and over again.


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## MikeMar (Jan 7, 2005)

There are 5 cases left, including yours (so 4 out there)

They offer you $100,000 and if you don't take it you have to open another case (one of the 4) If you say no deal, you basically say, I want my case again and you pick another. You have a 1 out of 5 chance of picking the million out there. 

Now if there are 3 cases left (including yours) and you opt to say No Deal, you are saying, I pick my case again. Then you open one of the two out there and it's not the million. Now they offer $500,000 and you say No Deal. You still have your case. There are now 2 cases left, 1 with the million, and 1 without (we all agree on that) and now you get to pick your case or the other (swapping) and this is a 50/50 shot because you know the contents of the 2 cases and you get to pick.


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## ducker (Feb 21, 2006)

haha... I liked this show before my Tivo days... now with my Tivo days I usually rip through it to see what "I picked" was the prize, and usually slow down a little bit during the banker's offers.


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## laststarfighter (Feb 27, 2006)

OMG, we are still arguing this? Did you not see my post where *I showed you the math?* The numbers don't lie.

Now you guys are talking about "repicking." Come on, people. Picking a case is not the only factor in computing odds.

This is like saying that I was the first to enter into a sweepstakes so I am guaranteed to win because when I entered my odds were 1:1. Even though 1 million people entered after me, my odds are still 1:1. Nobody else has a chance because as shelly40 says, _you can't recalculate odds no matter what happens afterwards._


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## zsmooth (Nov 26, 2002)

shelly40 said:


> I make a pick....
> 
> I pick case 10.......
> 
> ...


That's exactly right.

Let me ask you this: When you finally get down to the last case, and open it to find $1,000,000 in it, are the chances of it having $1,000,000 in it still 1/26? That's essentially what you're arguing.


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## newsposter (Aug 18, 2002)

starting March 20th on mon/wed/fri


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## astrohip (Jan 7, 2003)

I noticed on one of the shows last week, when it was down to two cases, Howie mentioned that there is a 50-50 chance of winning the bigger prize.

I thought there would be a 25/26 chance the larger prize would be the case on the stage?  :up:


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## zyzzx (Jan 22, 2002)

In case this hasn't been said yet:

Shelly, YOU'RE WRONG!

Just drop it. It's simple math.


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## newsposter (Aug 18, 2002)

astrohip said:


> I noticed on one of the shows last week, when it was down to two cases, Howie mentioned that there is a 50-50 chance of winning the bigger prize.
> 
> I thought there would be a 25/26 chance the larger prize would be the case on the stage?  :up:


wouldn't it be a 2/26 chance that they will win something?


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## Guindalf (Jun 13, 2001)

newsposter said:


> wouldn't it be a 2/26 chance that they will win something?


No, actually it's a 26/26 (or 1/1) chance that they will win _something_!!


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## Dssturbo1 (Feb 23, 2005)

astrohip said:


> I noticed on one of the shows last week, when it was down to two cases, Howie mentioned that there is a 50-50 chance of winning the bigger prize.
> 
> I thought there would be a 25/26 chance the larger prize would be the case on the stage?  :up:


At the beginning YES, it is 25/26 of the bigger prize being one of the stage cases.

BUT at the end it is 50/50. Because it changes with every eliminated case. And you said "the bigger prize". Of course with every case holding a different amount one of the two cases (1/2= 50% chance) remaining will have "the bigger prize".
obviously even if it is a known fact that the $1M prize has not been eliminated and therfore is in one of the two remaining cases the odds are now exactly 1 in 2 as to which cases it is in.


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## astrohip (Jan 7, 2003)

Dssturbo1 . . . I should have been more clear, I was being sarcastic. We had this convoluted discussion last week, and we all know it is 50-50, but we couldn't get a couple to understand.


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## alansh (Jan 3, 2003)

The reason (as explained on the Wikipedia page) that this is different from the Monty Hall problem is that the cases are selected at random. If Howie picked the cases to open, deliberately avoiding the case with the $1 million, then yes, you should switch.


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## astrohip (Jan 7, 2003)

alansh said:


> The reason (as explained on the Wikipedia page) that this is different from the Monty Hall problem is that the cases are selected at random. If Howie picked the cases to open, deliberately avoiding the case with the $1 million, then yes, you should switch.


smeek


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## shelly40 (Nov 20, 2000)

So in regards to having the $1,000,000 case being the one initially chosen,

If all the women opened the cases at the same time, I think most would agree that the odds are 1 in 26 of having the $1,000,000 case.....

Why do the odds of having the $1,000,000 case change ?

The only difference is that the cases are opened one at a time.....instead of all at once.....


Shelly


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## verdugan (Sep 9, 2003)

shelly40 said:


> So in regards to having the $1,000,000 case being the one initially chosen,
> 
> If all the women opened the cases at the same time, I think most would agree that the odds are 1 in 26 of having the $1,000,000 case.....
> 
> ...


/me bangs head!!!


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## Guindalf (Jun 13, 2001)

Shelly, for the last time. YOUR ODDS INCREASE WITH EVERY CASE THAT'S OPENED!!!!

If you open one case that does NOT have the $1,000,000, then the odds go from 1 in 26 to 1 in 25, then after then next one is opened, 1 in 24, all the way to 1 in 2 - or 50/50.

Man, I'm exhausted! Listen to EVERYONE. You are the ONLY one who thinks this way. 1001 math whizzes can't be wrong!


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## SnakeEyes (Dec 26, 2000)

This person is either mathematically challenged or a troll. Just let it go and remember who this person is in case of further trolling in future arguements where then you can just use ignore.


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## newsposter (Aug 18, 2002)

That dude last night sure got lucky. He really was pretty greedy. I would have taken it at the initial 198K or whatever that was.


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## Dssturbo1 (Feb 23, 2005)

everyone notice how the show producers have gotten softer. 

they are now giving more money considering the odds. a little extra incentive on the good side, when they started the show they were shorting the money compared to the odds a little.


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## newsposter (Aug 18, 2002)

wonder why they aren't doing anything other than 1 mil anymore? too many people winning? And geeez um, stretching this out to 1 person per show would be enough of a cost saving measure dont you think?

that guy last night wasn't as bad as some. I liked that he made his decisions quickly and didn't spend minutes agonizing. You could tell towards the end that howie was being given the streeeeeetch signal in his earpiece. 

wonder if his daughter got paid and why she wasn't in one of those dresses? (or at least something better than jeans)

I'm also wondering why the offer wouldn't have been just 300K and instead was 330K when all he had left was 200/300/400. My math isn't that poor. 300 is the average right?


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## MikeMar (Jan 7, 2005)

What was in last nights case (3/20) at the end, it got cut off after he accepted the deal.


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## newsposter (Aug 18, 2002)

the big amount..500K..or was it 400, i forget


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## Guindalf (Jun 13, 2001)

PLEASE PEOPLE!! This is NOT a spoiler thread!! I haven't seen last night's show yet - there's not a lot of point now.

If you want to discuss last night's show, please do it in a thread marked Spoilers or at least with the date of the show you're talking about.

Thanks.


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## MikeMar (Jan 7, 2005)

Spoiler



Wow, what a stupid girl on the show tonight. You have to take the deal if you only have 1 case left that is really high.


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## Guindalf (Jun 13, 2001)

MikeMar said:


> Spoiler
> 
> 
> 
> Wow, what a stupid girl on the show tonight. You have to take the deal if you only have 1 case left that is really high.


Gee thanks, Mike - another show ruined for me!

I repeat the comment in my post just before yours. THIS IS NOT A SPOILER THREAD!

PLEASE DON'T POST SPOILERS HERE OR ANYWHERE THAT IS NOT IDENTIFIED AS A SPOILER THREAD! YOU RUIN THE SHOW FOR OTHERS IF YOU DO!

Edit: Happy now NP?


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## newsposter (Aug 18, 2002)

---waiting to see if he edits his quote  ---------


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## bruinfan (Jan 17, 2006)

I think there is 25/26 chance they pick the lamest, most obnoxious people to play the game.

Haven't been in this thread since before the math debate, I have to tell you, it was entertaining. Shelly, taking on the world on her quest to change the face of mathematics...

But seriously though, 2 points to make at the risk of starting a whole new rant...
1. Without getting into the math, the minority opinion is stuck on one piece of faulty rule, if you will. While I can totally see the 25/26 logic, and it's tempting to think that, but it based on a false rule that messes up the whole problem. And they can't see that their rule is false.

2. Even if you know zip about math or stats, and you had to pick a side... do you really think that NBC would put themselves in a position where they are 96% underdogs??? Really? Regardless of the fact "$1mil is not alot of money", would they put themselves in that position? Based on that alone, I would put my faith in the 50/50 camp, if I knew nothing and I had to choose a side.

3. And a third, even though I only said 2, Can EVERYONE ELSE really be wrong?? Including the omniscient Howie Mandel?? And the Banker dude in the balcony??

So, despite how strongly one may feel about the 25/26 chance of winning, isn't there a point where you question if what you are saying is really correct? When do you start to question yourself, instead of insisting you are right? Interesting.


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## astrohip (Jan 7, 2003)

bruinfan said:


> I think there is 25/26 chance they pick the lamest, most obnoxious people to play the game.


 :up:


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## MikeMar (Jan 7, 2005)

God, when the girl last night had the choice of taking 500k or going for the million, god what a moron!!!! 











Joking, never happened


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## newsposter (Aug 18, 2002)

did you see that person pick that case that had money in it? I was shocked


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## mike3775 (Jan 3, 2003)

I'm waiting for someone to get greedy and have a high amount and a low amount left as the two choices, and then trade the cases and end up with the lowest amount.


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## bruinfan (Jan 17, 2006)

mike3775 said:


> I'm waiting for someone to get greedy and have a high amount and a low amount left as the two choices, and then trade the cases and end up with the lowest amount.


25 out of 26 times.... eehhhhh.


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## mcdougll (Jan 27, 2003)

SnakeEyes said:


> This person is either mathematically challenged or a troll. Just let it go and remember who this person is in case of further trolling in future arguements where then you can just use ignore.


Actually, anyone who has taken a college level Statistics & Probability course would agree with Shelly40.

Try this: 5 doors (Doors A, B, C, D & E), 1 has $100 behind it, the rest $0. 
You get to pick one door(Say, Door A). What is the chance your door has the $100? 
Answer: 1 out of 5 or 20%

After that, someone opens three of the remaining doors (the ones you didn't pick, Door B, C & D), and they each have $0 in them. 
What is the chance that the final door (Door E) you didn't choose has the $100? 
Answer: 80%

The fact that the three opened doors didn't have anything in them doesn't change the fact that the four doors you didn't pick (Doors B, C, D, & E) collectively had an 80% chance of having the $100.

Did that help? or am I beating an already (REALLY) dead horse? Or both?


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## MikeMar (Jan 7, 2005)

very very very very very very very very very very very very very very very very dead horse 

Noooo moooooore stats on this!


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## DancnDude (Feb 7, 2001)

mcdougll said:


> After that, someone opens three of the remaining doors (the ones you didn't pick, Door B, C & D), and they each have $0 in them.
> What is the chance that the final door (Door E) you didn't choose has the $100?
> Answer: 80%
> 
> Did that help? or am I beating an already (REALLY) dead horse? Or both?


You are talking about the situation where someone with prior knowledge opens up cases. This is NOT how Deal or No Deal works. No one knows which cases have what in them.


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## astrohip (Jan 7, 2003)

mcdougll said:


> Actually, anyone who has taken a college level Statistics & Probability course would agree with Shelly40.
> 
> Try this: 5 doors (Doors A, B, C, D & E), 1 has $100 behind it, the rest $0.
> You get to pick one door(Say, Door A). What is the chance your door has the $100?
> ...


As a math major (eons ago), I took more stat courses than any person should be subject to. And I assure you, *no college stat student* would agree with you or Shell40.

It is a dead horse. Back from the dead. 

In a nutshell, if Doors B/C/D were picked with knowledge they had $0 behind them, YES FLIP. If they were picked randomly, then it makes no difference. Switching does nada.


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## laststarfighter (Feb 27, 2006)

mcdougll said:


> Actually, anyone who has taken a college level Statistics & Probability course would agree with Shelly40.
> 
> Try this: 5 doors (Doors A, B, C, D & E), 1 has $100 behind it, the rest $0.
> You get to pick one door(Say, Door A). What is the chance your door has the $100?
> ...


LOL. Man, this horse has more lives than Jesus. 

mcdougll, the reason why all 5 doors have an equal chance is *because nobody knows what is in them.* The odds change each time you open a door and discover the truth. Here's the math again:

*Odds for each door prior to choice:*
A: 20% (1/5)
B: 20% (1/5)
C: 20% (1/5)
D: 20% (1/5)
E: 20% (1/5)

If you choose door A then your odds are 1/5 or 20%. The rest of the doors are a *combined * 4/5 or 80%. In math terms this would be:

B + C + D + E = 1/5 + 1/5 + 1/5 + 1/5 = *4/5*

*Odds after door B is opened:*
A: 25% (1/4)
*B: 0% (0/4)*
C: 25% (1/4)
D: 25% (1/4)
E: 25% (1/4)

Note that the odds of door B is now *zero* percent because we know know the door is empty. *We cannot ignore this fact.* The door is empty so we know that door B has zero percent chance of holding the money.

So now there are only four doors whose contents are still unknown. As you can see, the range for the odds of each door changed from five to four. Now each door has 1/4 chance of holding the money. In math terms this would be:

C + D + E = 1/4 + 1/4 + 1/4 = *3/4*

*Odds after door B, C and D are opened:*
A: 50% (1/2)
*B: 0% (0/2)
C: 0% (0/2)
D: 0% (0/2)*
E: 50% (1/2)

When we open up three doors, those three doors now become zero percent chance of holding the money. This leaves two unknown doors, the one you picked (door A) and the last door you didn't pick (door E).

As you can see, the odds *have* to change because you cannot ignore knowledge that you gain. Whenever you open a door you cannot pretend still that the opened door (or case) could possibly have money in it. It's the very definition of the "process of elimination."


----------



## newsposter (Aug 18, 2002)




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## maaaak (Apr 10, 2008)

It's a dead horse to those who've talked it out but I'd like to chime in anyway.

What some are you are forgetting is that once the case chosen for the table is selected it is out of the running, it is no longer a part of the stage group. At that point you can choose any case on the stage but you can't select the one on the table again so, while each case selection on stage reduces the odds of any one case holding the big prize, the odds of the one on the table containing the big prize can not change because it is no longer a part of the stage group. It remains 1 in 26.

If you get down to two cases, one on the stage and the one on the table, it can't be 50/50 unless the selection starts all over again. If a brand new person came on stage and made a fresh selection between the two the odds would be 50/50. BUT, and it's a big BUT, the person who selected the case originally must make a change in cases for the odds to be in his/her favor. For the person who did the original selection the odds of the one on the table holding the big prize remains 1 in 26. I'd take the one on stage without a second thought.

I think NBC fully understand the odds and they believe that the person making the selection will, 9 times out of ten, think their original selection would hold the big prize so there's less chance of them having to make a big payout.


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## newsposter (Aug 18, 2002)

i'm convinced they could have 1/2 the cases 1 M and no one would ever win


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## verdugan (Sep 9, 2003)

You are wrong 

Is this going to replace the "Leah Remini is fat" as the thread that refuses to die?


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## alansh (Jan 3, 2003)

Nope, think about it this way. Suppose you get to the end with the penny and $1M left. You think that there's a 1/26 chance you picked the $1M case meaning there's a 25/26 chance it's on the stage, so you should swap. However, there's also a 1/26 chance you picked the penny, so there's a 25/26 chance it's on the stage, so you should not swap.

Clearly this doesn't work.

One of three things happens.
1. You picked the million.
2. You open the million case on the stage before getting to the last two.
3. The million is the last case on the stage.

#1's odds are 1/26. #2's odds are 24/26. #2's odds are 25/26*24/25*23/24* ... *2/1 = 1/26. So at the end the odds are even -- 1/26 of the time you'll have the $1M, 24/26 of the time you'll open it before getting to the last two, and 1/26 it will be the last case on the stage.

The difference between this and the Monty Hall problem is that #2 and #3's odds are 0/26 and 25/26 because he knows where the top prize is and never shows (assuming a 26-door game, like DoND). In this situation, #3, the swap option, is the best move.


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## ewolfr (Feb 12, 2001)

Congrats on the impressive first post maaaak. But next time can you not dig up a two year old thread just to rehash everything?


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## maaaak (Apr 10, 2008)

ewolfr said:


> Congrats on the impressive first post maaaak. But next time can you not dig up a two year old thread just to rehash everything?


I can read dates. I put in my two cents worth because after reading all the posts nobody else had looked at it just as I did. They all included the table case with the stage cases when considering the odds. After the original choice they are two separate sets of cases.


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## verdugan (Sep 9, 2003)

maaaak said:


> I can read dates. I put in my two cents worth because after reading all the posts nobody else had looked at it just as I did. They all included the table case with the stage cases when considering the odds. After the original choice they are two separate sets of cases.


I don't really know how to say this, but ... no. You're still wrong. 

Welcome to tivo community :up:


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## DrFace007 (Apr 12, 2008)

Here is what I gather.

There are 26 cases. You pick 1, hoping to pick the million. Howie says "i know where the million is, and of the remaining 25, I will get rid of 24 that DON'T have the million"

Now there is the case you picked and the other case. The chance that your original case has the million is 1/26 and the chance that the other case has the million is 25/26.

This is because he knows where the million is and will for sure not get rid of it from the 24 that he gets rid of. It is knowing this certainty that is the reason for the probability of the remaining case to be 25/26. 

Had the cases been picked off one by one randomly. The probability of each case to have the million (including yours) becomes 1/(total number of cases remaining). 1/26 for each, then 1/25 for each, and 1/24 for each, as the cases come off the board (assuming the million doesn't come off). Going about it this way, when there are two cases remaining. The one you originally picked and the other one. Then the chance that yours has a million is 1/2 and the other is also 1/2. This is because that certainty from the previous example does not exist. The cases were opened at random.

Can you see if you can find the answers to the 2 scenarios below.
1. He says that of the 25 remaining cases, he will get rid of 24 of them. He will get rid of them either randomly OR he will get rid of them knowing that he won't get rid of the million. Whether it is random or if he chooses to not get rid of the million is also random. So there is a 50/50 chance that he will go either way in deciding how to get rid of the cases.
a. He shows you what was in the 24 cases he got rid of and none of them have a million.
b. He doesn't show you what was in the 24 cases he got rid of and you don't know if one of the ones he got rid of has a million or not.

2. He says that of the 25 remaining cases, he will get rid of 20 of them. He will get rid of them either randomly OR he will get rid of them knowing that he won't get rid of the million. Whether it is random or if he chooses to not get rid of the million is also random. So here too, there is a 50/50 chance he will go either way in deciding how to get rid of the cases.
a. He shows you what was in the 20 cases he got rid of and none of them have a million. Of the remaining 5 cases on the board, you get to open 4 of them 1 by 1 at random until there is 1 case left. (the 4 random ones you open don't have the million)
b. He doesn't show you what was in the 20 cases he got rid of and you don't know if one of the ones he got rid of has a million or not. Of the remaining 5 cases on the board, you get to open 4 of them 1 by 1 at random until there is 1 case left. (the 4 random ones you open don't have the million)

What is the chance in scenarios 1a, 1b, 2a, 2b that if you switch your case to the one remaining that it will be a million?


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