I gave some more thought to the issues I raised in yesterday's article about "Deal or No Deal" and expected value calculations. I said that I think that the game should be played entirely on the basis of the expected value of an unopened suitcase at any given time in the game. I'm sure some people will disagree with me on this, but here's why I think it's particularly worthwhile in the case of the play-at-home games like the Deal or No Deal Handheld or Deal or No Deal Tabletop games.
In the game played on the TV show, the contestant has only one opportunity to play the game. The entire game is geared around putting pressure on the contestant to go with his or her gut, rather than the odds. The home versions, however, are infinitely playable. This means that there should be much more of an incentive to play the odds properly.
NBC currently has an Internet-based version of Deal or No Deal on its website. I played that game several times in preparing this series of articles. In every case, The Banker offered me less than the expected value of an unopened case until after the $1,000,000 case had been opened. In a couple of games, he offered me more than the expected value of an unopened case after that. When I took that deal, I ended up with more money than I would have if I kept the case I chose until the absolute end of the game.
In one game, The Banker offered me slightly less than the expected value of an unopened case after the $1,000,000 case was opened. I took the deal in that case, and ended up losing money because I was holding the highest value unopened case remaining in the game.
This discussion gave me another idea: With a play-at-home version of the game, you could try any strategy you choose and document the results. With enough trials, you would know if the expected value approach to this game was the right one or not.