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GoldMember December 24th, 2009 11:20 PM

Deal or no Deal winning strategy
I was wondering about a winning strategy for the popular Television show Deal or no Deal.

The rules are


The central game of Deal or No Deal involves a contestant, a banker (unseen in some versions of the show), and a host/presenter who acts as Master of ceremonies for the game. The game revolves around the opening of a set of numbered briefcases, each of which contains a different prize (cash or otherwise). The contents of all of the cases are known at the start of the game, but the specific location of any prize is unknown. The value of each of the cases is indicated by a label or card sealed within it.

The contestant claims (or is assigned) a case to begin the game. The case's value is not revealed until the conclusion of the game.

The contestant then begins choosing cases to be removed from play. The amount inside each choice is immediately revealed; by process of elimination, the amount revealed cannot be inside the player's chosen case. Throughout the game, after a predetermined number of cases have been opened, the banker offers the contestant an amount of money and/or prizes to quit the game, the offer based roughly on the amounts remaining in play and the contestant's demeanor. The player then answers the titular question, choosing:

* "Deal", accepting the offer presented and ending the game, or
* "No Deal", rejecting the offer and continuing the game.

This process of removing cases and receiving offers continues, until either the player accepts an offer to 'deal', or all offers have been rejected and the values of all unselected cases are revealed. The player wins the value of the deal taken, or if no deal is taken, the contents of the player's case.

Should a player end the game by taking a deal, a pseudo-game is continued from that point to see how much the player could have won by remaining in the game. Depending on subsequent choices and offers, it is determined whether or not the contestant made a "good deal", i.e. won more than if the game were allowed to continue.

Since the range of possible values is known at the start of each game, how much the banker offers at any given point changes based on what values have been eliminated. To promote suspense and lengthen games, the banker's offer is usually less than the expected value dictated by probability theory, particularly early in the game[1]. Generally, the offers early in the game are very low relative to the values still in play, but near the end of the game approach (or even exceed) the average of the remaining values.
Taken from Wiki.

Case values

Case values
$ 0.01
$ 1
$ 5
$ 10
$ 25
$ 50
$ 75
$ 100
$ 200
$ 300
$ 400
$ 500
$ 750
$ 1,000
$ 5,000
$ 10,000
$ 25,000
$ 50,000
$ 75,000
$ 100,000
$ 200,000
$ 300,000
$ 400,000
$ 500,000
$ 750,000
$ 1,000,000

Now at any stage if the expected value of the money available on the board is less than the bankers offer we are told to choose the bankers offer. I was wondering if there are other strategies to win this game. If anyone has other thoughts regardin this game feel free to share -like decision making etc.

CRGreathouse December 25th, 2009 09:52 PM

Re: Deal or no Deal winning strategy
The core strategy is to add up the value of the remaining briefcases, divide by the number of briefcases, and compare this average to the total offered.

Add to this consideration the tax implications of winning. A contestant in the 15% tax bracket winning $10,000 will probably pay 15-20% of $10,000 in taxes, but above 35% in taxes on $1,000,000. So $1,000,000 is worth less than 100 times $10,000 to the contestant. So the modified strategy averages not the nominal amount but the post-tax amount.

Add to this consideration the contestant's risk-aversion. To many people, $50,000 is preferable to a 50% chance at $100,000 (and a 50% chance of $0).

There may be other considerations beside, but these are the only two that come to mind immediately.

GoldMember April 5th, 2010 02:42 PM

Re: Deal or no Deal winning strategy

If the host at the end gives you the option to exchange the briefcases, would you exchange them?

Say you know that one of the suitcases has $100000 and the other one $0. The probability of winning is 50% so is it optimal to exchange the briefcases?

CRGreathouse April 5th, 2010 05:59 PM

Re: Deal or no Deal winning strategy

Originally Posted by GoldMember
If the host at the end gives you the option to exchange the briefcases, would you exchange them?

If there are only two briefcases and neither you nor the host knows the contents, then it doesn't matter. If you know, pick the better one; if the host knows, I would be wary of a trade offer (maybe [s]he only offers to trade when you have the valuable one?).

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