Comments on: Deal or No Deal: A Statistical Deal

By: Tom Scott

Tom Scott — Fri, 20 Apr 2018 07:08:52 +0000

hilarious! and mathematically enlightening…..all at once.

By: bill soriano

bill soriano — Sun, 21 Jan 2018 13:29:08 +0000

I play this game at home with my grand daughter and the only advice I give is when I am down to just 2 suit cases and one has a lot of money and one has a little bit of money I never trade in my suitcase , I always keep my original suitcase and I always come out on top

By: DJ

DJ — Thu, 29 Jun 2017 17:05:51 +0000

Mostly right but slightly flawed. Does not take into account likelihood bankers offer will increase after next case opening and/or standard deviation. Sharpe ratio is better metric

By: Vivian

Vivian — Fri, 13 Mar 2015 14:26:48 +0000

I won the million! I had the 1 dollar case and the 1,000,000 case, and I stayed with my case and won a million :)

By: Betty

Betty — Thu, 12 Mar 2015 13:24:00 +0000

Impressive analytical skills. @David, from my assessment, the chances are more equal than they differ. Using your conviction, pick one and stick with it..

By: David

David — Thu, 11 Dec 2014 23:49:25 +0000

Great commentary! I am a math novice, but capable. What would be the best position to be in when competing in the final spin of the game show, The Price is Right”, 1st, 2nd, or 3rd? I would assume 3rd, is this correct, to take into consideration the predetermined amount you have to beat of the first 2 contestants? Am I missing something?

By: Joseph B

Joseph B — Tue, 27 May 2014 20:43:17 +0000

This is an amazing discussion and I stayed up way too late reading through it. Even though it’s long dead, I wanted to add a few thinking points for the next guy or girl who might come along thinking the Monty Hall Problem applies.

Point 1: Why does the million dollar case get special treatment? In any proposed scenario where the million dollar case seems more likely to be in a particular place than any other non-eliminated case, it’s prominence in that scenario has clearly been artificially inflated. To test this, pretend you’re hoping for a different case and run the same scenario. The new “target” case will now be especially prominent. How can that be? Just by hoping for it, it now appears? Very suspect…

Point 2 (which might explain point 1): The odds that the contestant picked the “target” case are a solid 1/26 because in that scenario, the “target” case is GUARANTEED to make it to the final 2 (assuming, as we are, that no deal is to be made). The odds that the “target” case is on the other side, though much higher to start with, aren’t nearly so solid. They start at 25/26 but in many scenarios, the “target” case is ELIMINATED before reaching the final 2. These instances cannot be discarded or ignored, they must be factored in to the odds. I believe all such instances would appear as 0/26 on the other side’s scorecard. After crunching the numbers, these unfavorable “elimination” scenarios drag the other side’s odds down to… 1/26.

After writing that out, It doesn’t actually seem to offer anything new. Perhaps it’s at least a slightly different perspective though. Getting this to ‘click’ seems to take different thinking for different folks.

***

Reading through, it seems like some possibly great and certainly interesting minds have come before me. I feel a strange sort of honored to be a part of it, however belated and irrelevant my part is.
*deep thoughts*

Anyway, 6AM greetings from Australia! (where the top prize is $200,000, FYI)

By: Deal or No Deal Lover

Deal or No Deal Lover — Fri, 14 Jun 2013 15:16:52 +0000

I have a winning strategy.
1) Calculate the odds of getting a better offer by counting the number of briefcases that, if eliminated, would increase the average value of the briefcases.
2) Calculate the odds that the briefcase you hold does not contain more money than the banker’s offering.

If either odds are too low, don’t accept the banker’s offer.

By: Kyle Mart

Kyle Mart — Thu, 14 Feb 2013 08:44:25 +0000

Due to the fact that the banker’s offer is likely to go up after rejecting the deal distorts all the probabilities of just looking at the mean. By saying no deal in the situation she rejects 80,000 which is 9,700 more than 70,300. But given that she succeeds in not picking the 300,000, her next offer might have been even higher. For example in the situation where there is $100, $400, $1000, $50,000, and $300,000 say she said no deal and happened to pick $1000. What would be left would be $100, $400, $50,000 and $300,000. now the average is $87,625. Now the banker might decide to offer $122,675. As you can see the new offer is higher than the previous offer and 40% greater than the now current mean. By saying no deal she has opened herself up to higher EV. This is of course if she assumes that the banker will increase the next offer by a larger amount than the next mean.

To make this make more sense say the banker would offer $120,000 next no matter what case is revealed unless she picks $300,000 then the banker offers $21,000. In EV terms she has the following given her two choices:

No Deal now and accept next immediate offer: (4/5)*120,000 + (1/5)*21,000 = $100,200

Accept Deal: $80,000

As you can see $100,200 > than $80,000 therefore there is reason in saying no deal.

Even after she says no deal there is still the option of saying no deal again on further rounds that might include more +EV situations.

P.S. Also note that I am not saying that picking “No Deal” is the correct decision, I am just saying there is a mathematical rational for rejecting the offer.

By: Rikki Morley

Rikki Morley — Sun, 20 Jan 2013 15:16:29 +0000

Ok, don’t know if anyone else has written it here yet but I’m from england, and over here where the show originated therefore me having many many years of knowledge of it, the banker quite simply does not play a game of mean averages, he has never once gone above the mean. For instance one person was left with the jackpot 250 grand, and a mere 5 grand. The mean here being about 130 grand, the banker offered her 40 grand. He is far more ‘notorious’ that the US one and is very ungenerous and unforgiving. The simple idea to him being people in general do not wish to risk 40grand for the hope 250 grand as 40 is so big, it happens on that occasion she risked it and became our second jackpot winner, but I don’t play it by mean, I play it by quit when the money is enough to do with what you wish, or what makes you happy, because then no matter what, you cannot have any regrets :)