[T]here are many circumstances in which one should deviate from this "hold at 20" policy. [The analogue to "hold at 26" for the game evaluated here.] Why does this reasoning not dictate an optimal policy for all play? The reason is thatAlso see this paper, where the same authors analyze other similar games, including Pass the Pigs itself.risking points is not the same as risking the probability of winning.Put another way, playing to maximize expected score for a single turn is different from playing to win....
Overall, we see that the "hold at 20" policy only serves as a good approximation to optimal play when both players have low scores. When either player has a high score, it is advisable on each turn to try to win. In between those extremes, play is unintuitive, deviating significantly from the "hold at 20" policy, and being highly discontinuous from one score to the next.
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posted by Marisa Stole the Precious Thing at 11:02 AM on February 25, 2009 [2 favorites]