Estimation of Rates Arriving at the Winning Hands in Multi-Player Games with Imperfect Information

In multi-player games with imperfect information, e.g., Poker and Mahjong, they have imperfect information differing from Shogi and Reversi. Therefore, it is difficult to decide optimal movements. In Mahjong, fold is very important, and it is necessary to check predominance between a player's hand and other players' hands. To this end, it is required to estimate the rate arriving at a winning hand. This paper proposes the estimation methods of rates arriving at the winning hands. The proposed methods use random simulation taking the discarded tiles in consideration, and tabu search without using the record of a game. In the experiment of evaluating the rate arriving at the winning hands, it can be estimated to some extent depending on the state by using tabu search. As the result, the possibility of the effective search of the estimation of the rate of tenpai by using tabu search is indicated. An application of the proposed method to other games with imperfect information is expected because these methods don't use the record of a game.