"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.

guesswest · #6 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 · #7 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

luckyme · #8 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

Hopey · #9 04-07-2006, 03:21 PM

LOL...one of the guys who was arguing adamantly that you need to choose the suitcase on stage just came into my office to tell me that he has thought about the problem some more, and has decided that I was right all along.

Sigh. The sad thing is that we weren't even drinking at lunch, so it's not like he has much of an excuse. He seemed a little sheepish, though.

Brom · #10 04-07-2006, 09:23 PM

Going off on a bit of a tangent here.

Has anyone here ever figured out exactly how much -EV the deals are? For instance say the EV of all the cases left is $50k, and the banker offers the person $45k. This would mean that he is offering deals that are 90% of true value.

My question is if this 90% number is set for every deal, or if it changes based on the level? It seems to me through rudimentary calculations in my head that the deals turn steadily worse as the show goes on, i.e. the first deal is %90, the next 87%, ... , the last is only 75%. This would mean it is better to take the deals earlir in the show, even though the deals are much smaller, rather than waiting towards the end, when the deals are more -EV yet larger in absolute value.

Anyone else notice this, or care to comment?