## Deal or No Deal

**Category :**

*January 1st, 2006*

So much of decision science has been developed around game shows (remember the Monty Halls problem you studied in statistic?). There is one recently being aired on CNBC called “deal or no deal”. Here’s an excerpt from wikipedia

The game start with 26 cases, each containing a differennt amount of money from a known list. Initially, the contestant get to pick one case to keep. After picking his/her case, the contestant then selects six of the remaining 25 cases to reveal, one at a time. Once revealed, the specific amount in that case is “out of play” (since it must not have been in the chosen case). This is followed by a “phone call” by The Banker, who makes an offer to buy the contestant’s case for a certain amount, based on the cash amounts still in play. If the contestant accepts the buyout, he/she must lift a cover and press a button to confirm the decision. The game then ends, and the contents of his/her case are revealed (along with the whereabouts of the top remaining prizes).

Should the contestant refuse the offer (“No deal!”), he/she then must choose five of the remaining cases to eliminate from consideration. Another deal with The Banker is made, and play continues as before. Subsequent rounds have the contestant withdrawing four, three, and two cases from play; should the contestant continue to decline The Banker’s offer after this point, he/she then eliminates one case each time until there are two cases remaining. If the player does not accept the final offer, the host offers the contestant one opportunity to switch his/her case with the one remaining in the gallery. After the decision is made, the contestant wins the cash amount contained inside the case he/she last kept.

It’s a simple probability problem, where the expected value, E(x), of the chosen case is the average of all the cases still in play. But what’s interesting is in the episodes that I watch, the offer is almost always lower than the expected value of the chosen case. What the game is also demonstrating is the risk premium a player is willing to pay (difference between offer and E(x)), and how recent event such as eliminating a big prize will affect such premium.

Another interesting behavior is “satisficing”. Supposed the contestant is left with $0.01 and $1M, and the outstanding offer is $200K? The expected value of the chosen case is slightly more than $500K. If the constestant play the game over and over again, it is to his advantage to play “no deal”. But in 1957, Herbert A. Simon’s nobel prize winning economic theory suggested that instead of finding the optimal choice, people often settle for an option that will satisfy their minimum requirement. This minimum requirement varied with time and events. Even tho the expected value of the case is slightly over $500K, most people will still walk home with $300K less than the expected value because of fear of missing out on the $200K being offered.

A very interesting game. Definitely worth watching at least once.

Entry Filed under: random thoughts

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