Abstract
Summary TENZI, “the world’s fastest game,” sounds too simple: roll 10 dice until they all match, setting aside the dice you want to keep. How fast is it? That is, on average how many rolls does it take to get 10 matches? An intuitive strategy that keeps the largest group (LG) of matching dice after each roll turns out to be optimal. The average number of rolls, for both the optimal and a naive policy, are found recursively from basic combinatorics, with some ideas from order statistics and Markov chains. The LG strategy is shown to be optimal by formulating TENZI as a dynamic program, showing that it can be reduced to a much smaller problem, and numerically solving this problem to obtain the optimal policy.
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