On Board-Filling Games with Random-Turn Order and Monte Carlo Perfectness
In a game, pure Monte Carlo search with parameter T means that for each feasible move T random games are generated. The move with the best average score is played. We call a game “Monte Carlo perfect” when this straightforward procedure converges to perfect play for each position, when T goes to infinity. Many popular games like Go, Hex, and Amazons are NOT Monte Carlo perfect.
In this paper, two-player zero-sum games are investigated where the turn-order is random: always a fair coin flip decides which player acts in the next move. A whole class of such random-turn games is proven to be Monte Carlo perfect. The result and generalisations are discussed, with example games ranging from very abstract to very concrete.
KeywordsFree Cell Game Tree Veto Player Optimal Move Fair Coin
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