"Deal or No Deal" math

Hopey · #1 04-07-2006, 01:32 PM

I was out for lunch today with some of my co-workers and they were having the following debate:

-You are playing "Deal or no Deal"
-All of the briefcases except for one (and the one you chose initially) have been chosen.
-The two dollar amounts left are $1 million and .01.
-You are given the choice to keep the briefcase that you chose initially, or to switch it with the briefcase that is left on stage.
-What do you do?

I argued that it doesn't matter what you do, you have a 50/50 shot at the $1 million, no matter which briefcase you decide to open. However, a couple of guys were arguing adamantly that you should always choose the briefcase that is left on stage. I argued that the fact that you moved one of the briefcases off the stage initially does not affect the contents of the briefcase, and does not affect the probability that it contains $1 million.

Can someone please put this issue to rest? I feel like an idiot for asking this question, but no matter how much I argued, they kept insisting that I was wrong.

DougShrapnel · #2 04-07-2006, 01:39 PM

You are correct. They are wrong.
it's a 50/50 shot no matter what you choose.
Ask them to figure out the exact chances of each breifcase.

felson · #3 04-07-2006, 01:44 PM

"you should always choose the briefcase that is left on stage."

It sounds like they have confused Deal or No Deal with the Monty Hall problem, which is different. Either that, or they are superstitious.

guesswest · #4 04-07-2006, 01:47 PM

Yes, makes no difference. If you had two briefcases with 1c and one with $1 million, and someone took away one of the 1c briefcases for you after you'd selected a briefcase (and were bound by the rules to do so 100% of the time) - then you should switch.

Hopey · #5 04-07-2006, 01:48 PM

[ QUOTE ]
"you should always choose the briefcase that is left on stage."

It sounds like they have confused Deal or No Deal with the Monty Hall problem, which is different. Either that, or they are superstitious.

[/ QUOTE ]

Yeah, one guy brought up Monty Hall, and I pointed out to him how that show was different.

I just had one of the guys come into my office with a pack of cards to illustrate his point to me. I took the cards from him and did a quick demonstration of how the show works by having him pick a card initially (and not look at it), and then pick each remaining card one at a time until there was only one left. I then asked him to tell me which of the two cards left (the one that he picked initially, or the one that was left) was of a higher denomination. I think he finally got it then.

luckyme · #6 04-07-2006, 01:54 PM

The simplest way to look at it is that initially you picked 2 cases. One you put on the table, the other you left on stage to be opened last.

There are no factors that make one a favorite over the other to hold any specific amount. You could just as well have left all on stage and made the choice of which of the final two to put on the table after there was just the two of them sitting there.

When I run into people like that I try to cajole them into a prop bet.

oh, and math won't help them see it.

gluck, luckyme

guesswest · #7 04-07-2006, 01:55 PM

And another (kinda unrelated thing) is, you should deal! People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

luckyme · #8 04-07-2006, 02:03 PM

[ QUOTE ]
And another (kinda unrelated thing) is, you should deal! People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

[/ QUOTE ]

Whenever I've seen the show I've never seen an offer that was worth taking. They always short you on the odds. The only reason to take a deal is because of bankroll considerations if you're out of your league in coin.

Taking the deal is like paying insurance on a big poker pot. It's not +EV, it's simply variance control.

I'd never take their 'deal', luckyme

guesswest · #9 04-07-2006, 02:09 PM

Right, the deal is always less than represents value. But, for instance in the 1c vs $1mil - they'd probably offer you $450,000 or something. So +$500k = +EV and -$500k = -EV, so technically it's a -EV offer. But you're never going to be in that situation again, so you probably should be controlling variance since you have no long term. In exactly the same way you wouldn't sit down with your whole bankroll in a game way bigger than you usually play. Am I missing something?

luckyme · #10 04-07-2006, 02:26 PM

[ QUOTE ]

Right, the deal is always less than represents value. But, for instance in the 1c vs $1mil - they'd probably offer you $450,000 or something. So +$500k = +EV and -$500k = -EV, so technically it's a -EV offer. But you're never going to be in that situation again, so you probably should be controlling variance since you have no long term. In exactly the same way you wouldn't sit down with your whole bankroll in a game way bigger than you usually play. Am I missing something?

[/ QUOTE ]

I can't tell from what you've stated.
I totally agree with the bankroll issue, and most people should take the deal only because they shouldn't be gambling with so much money on one shot.

Your original comment didn't mention bankroll considerations as the reason though --
[ QUOTE ]
People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

[/ QUOTE ]

Every situation has an expectation attached. Offers that are below that are bad deals, offers that are above that are good deals. It's irrelevant that you'll never be in the same situation again, that applies to virtually every situation we find ourselves faced with.

I used to play backgammon for some serious swag with a friend who made the same claim. He'd lay down to the cube too often with the comment, "sure I know the long-term odds are to take, but we'll never be in this situation again." And he was correct, it was exceedingly unlikely that we would be. That didn't make his folds correct though. Same applies to "Deal or No Deal".

Long-term, smlmong-term.. good deals are odds based.

hope that clarifies what I was commenting on, luckyme