Optimal Stragetiges in "Deal or No Deal"
In this idealized version of Deal or No Deal, the bank always makes an offer equal to the expected value of your suitcase, which is the mean of the contents of all unopened suitcases. The objective is to develope a decision procedure whose expected value is greater than the mean of all 26 suit case values, which here we call the "initial mean". This simplest strategy it to make a deal if and only if the offer exceeds this initial mean.
Computer simulations show that this strategy has an expected value very close to the initial mean, suggesting that the expected value is equal to the initial mean. Four simulations of ten thousand games each yielded average net gains different from the initial mean by -$138.25, $30.89, -$222.68, and -$67.69. The average of these differences, -$99.43, represents only -.0756% of the initial mean, $131,477.53.
These results are not surprising because it has been shown mathematically that the optimal expected win is equal to the initial mean (see Nick May's proof). This means that a contestant would cannot do better on average than by opening the first suitcase each game.
Note: Previous results posted here indicated that the expected value of the above strategy was actually higher than the initial mean. However, thanks to Connor Sage, a bug in the simulation causing this result was identified. The above results are from the corrected simulation
Simulation Results
Simulation Code
Wikipedia Article on "Deal or No Deal"
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