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Monday, August 21, 2006

Next Season on NBC: Fear Factoring Drills

NBC Universal honcho Jeff Zucker on "Deal or No Deal": "Look, I think the best ideas are the simplest ones. And Deal or No Deal, which Howie hosts and is a huge hit, is not complicated. It’s not hard to figure out. And it’s impossible to stop watching."


Wikipedia on "Deal or No Deal": "To calculate the probability that the top prize will actually be reached, the following simplifying assumptions can be made:

  • Deals are most often accepted when there are two cases left. This is when the deal value is closest to the expected value of the remaining cases.
  • Since the variance of a $1,000,000-or-nothing deal is so high, virtually all contestants would accept a carefully constructed banker's deal in that situation. That means the top prize will be hit only when the two remaining boxes are of high value (say, $200,000 or more)

The likelihood, then, that we have a top prize winner is:

(the number of different two-case combinations with one $1,000,000 and the other $200,000 or more) /

(the total number of different two-case combinations) *

(the probability of picking the correct case of the two left)

= {5 \over {26 \choose 2}}*{1 \over 2}  = {5 \over 650}  = {1 \over 130}

Based on the assumption that the contestant will choose to take the banker's offer when there is one case with $1,000,000 and one case with an amount less than $200,000: At 1.5 contestants per episode, this would mean that $1,000,000 prize would be awarded about once every 87 episodes. However, since several contestants have taken deals earlier in the game with the $1,000,000 prize and another amount of $200,000 or more still on the board, these odds are likely too high.

  • The only time the $1,000,000 prize was ever chosen in the U.S. version was by LaKissa Bright, who ended up with a bank offer for $215,000, ironically after removing the third highest case, $500,000. Thorpe Shoenle holds the record for most money won on the American version, with $464,000.

This assumption amount set at $200,000 is only applicable to the U.S. version and is quite arbitrary. Similar arbitrary assumptions could be made based on the game boards of other versions. In addition, the assumption that humans exhibit fully rational thinking is rarely true, especially under stressful circumstances like in a game show. The contestant can also be a fame seeker wanting to be a $1 million dollar winner, possibly leading to his taking the additional risk."