Have any of you watched this game show on TV? The premise is that there are 30 suitcases containing sums of money ranging from a penny to a million dollars. The contestant chooses one, and without opening it, the sum inside is his to keep unless he sells it. The contestant then is asked to pick from the remaining cases in batches, and those "prizes" are removed from play. After each round, the show offers to buy the contestant's case, and he must decide whether to take the offer or continue removing cases.

Last night, there came a point where there were four cases left. The possible sums in each of those cases were $1, $400, $200,000, and $500,000 (meaning that the contestant's case contained one of those denominations).

The show offered to buy his case for $109,000, and he took the deal.

Here's my question: how many of you would approach the decision as if it were a pot odds question? In other words, it seemed to me that the contestant had a 25% of possessing any one of those denominations, so that the expected value of his case was approximately $175,000 (0.25 x (1 + 400 + 200,00 + 700,000)). If that's the right way to analyze the deal, he made a mistake by taking less than that figure.

Is this the correct analysis? Obviously, I have way too much time on my hands.

As someone who also has too much time on his hands, I actually started a similar thread a month ago. Anyway, the banker's offer is almost always going to be EV-. So, what is the sense of declining an EV- offer just to get another EV- offer? The game is a question of risk threshhold. In the situation you described, the player had a 50% chance of the banker increasing his next offer and a 50% chance of decreasing the next offer. Do you 'press your luck' if its 66% or 75% of increasing? What's your risk tolerence?
Or look at it this way:
If the current offer is 62% of EV and we assume that the next offer will be similar:
50% chance he picks a low case: offer is 145k
25% chance he picks 200k: offer is 103k
25% chance he picks 500k: offer is 40k
Next offer can be estimated at: 108k

Tough call. But I think he made the right decision.

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"There is a good chance I gave you a very bad description of something that doesn't work."

We have a similar show in Blighty - we only go up to £250,000 (as is usually the case). Now I'm quite new to this poker game, but let me see if I have learned anything! For the contestant, it's a one time shot - if someone offered me 109,000, shake on it now - or gamble it and maybe go away with a quid (or a "buck") I would have to take the money. If you are calculating pot odds - something I've not quite got yet, and probably why I'm losing so often - you are playing to the fact that so many times out of so many you will win, so in the long run you will be up - you're not playing to win every pot - just more pots than not. I guess on the other side, the banker (do you have a banker in your show? He is the one making the deals on the phone) is playing that game and while he may take a big hit once in a while, if he keeps offering ev-, in the long run he'll win.

Just my 2p/c worth

Andy

EDIT: Funnily enough, it's on now!

Yes, the one over here has a banker. And I take the money.

I'm sending in an application to be on this show.

thank you.

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part time poker player, full time money maker

im taking the money, if i get the case with $1 in it im gonna feel like a complete jackass for not taking the $106k

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If there wern't luck involed i guess id win everyone

interestingly enough this demonstrates perfect 'game theory' reason poker stats are dif to deal or no deal is poker is a repeat game but deal or no deal is a one off. Hence people act differently!

I only watch the show to watch greedy assholes make horrible decisions and end up with way less than what they expected.

At what risk do you bank your 100K? Lets say the cases left are 1mil and the rest are under 1k. If you pick the 1mil you go home with jack, but each time you avoid the 1 mil your offer increases. When do you walk:

6 cases (83% chance of avoiding the 1mil) offer: 108k
5 cases (80%) offer: 130k
4 cases (75%) offer: 160k
3 cases (66%) offer: 215k
2 cases (50%) offer: 350k

I think I'd risk it with 6 cases, but walk with 5 left.

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"There is a good chance I gave you a very bad description of something that doesn't work."

108k or 130k. I think the risk of not getting the 130k is worth taking the 108k.

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Chuck Norris put the "laughter" in manslaughter..