Maarten P. D. Schadd

Single-Player Monte-Carlo Tree Search

Classical methods such as A* and IDA* are a popular and successful choice for one-player games. However, they fail without an accurate admissible evaluation function. In this paper we investigate whether Monte-Carlo Tree Search (MCTS) is an interesting alternative for one-player games where A* and IDA* methods do not perform well. Therefore, we propose a new MCTS variant, called Single-Player Monte-Carlo Tree Search (SP-MCTS). The selection and backpropagation strategy in SP-MCTS are different from standard MCTS. Moreover, SP-MCTS makes use of a straightforward Meta-Search extension. We tested the method on the puzzle SameGame. It turned out that our SP-MCTS program gained the highest score so far on the standardized test set.

Single-player Monte-Carlo tree search for SameGame

Classic methods such as A^* and IDA^* are a popular and successful choice for one-player games. However, without an accurate admissible evaluation function, they fail. In this article we investigate whether Monte-Carlo tree search (MCTS) is an interesting alternative for one-player games where A^* and IDA^* methods do not perform well. Therefore, we propose a new MCTS variant, called single-player Monte-Carlo tree search (SP-MCTS). The selection and backpropagation strategy in SP-MCTS are different from standard MCTS. Moreover, SP-MCTS makes use of randomized restarts. We tested IDA^* and SP-MCTS on the puzzle SameGame and used the cross-entropy method to tune the SP-MCTS parameters. It turned out that our SP-MCTS program is able to score a substantial number of points on the standardized test set.

Best Reply Search for Multiplayer Games

This paper proposes a new algorithm, called best reply search (BRS), for deterministic multiplayer games with perfect information. In BRS, only the opponent with the strongest counter move is allowed to make a move. More turns of the root player can be searched resulting in long-term planning. We test BRS in the games of Chinese Checkers, Focus, and Rolit™. In all games, BRS is superior to the maxn algorithm. We show that BRS also outperforms paranoid in Chinese Checkers and Focus. In Rolit, BRS is on equal footing with paranoid. We conclude that BRS is a promising search method for deterministic multiplayer games with perfect information.

Best Play in Fanorona Leads to Draw

Fanorona is the national board game of Madagascar. The games complexity is approximately the same as that of checkers. In this article, we present a search-based approach for weakly solving this game. It is a well-chosen combination of Proof-Number search and endgame databases. Retrograde analysis is used to generate the endgame databases in which every position with 7 or fewer pieces on the board has been solved. Then, a Proof-Number search variant, PN2, exploits the databases to prove that the game-theoretical value of the initial position is a draw. Future research should develop techniques for strongly solving the game.

CHANCEPROBCUT: Forward pruning in chance nodes

This article describes a new, game-independent forward-pruning technique for EXPECTIMAX, called CHANCEPROBCUT. It is the first technique to forward prune in chance nodes. Based on the strong correlation between evaluations obtained from searches at different depths, the technique prunes chance events if the result of the chance node is likely to fall outside the search window. In this article, CHANCEPROBCUT is tested in two games, i.e., Stratego and Dice. Experiments reveal that the technique is able to reduce the search tree significantly without a loss of move quality. Moreover, in both games there is also an increase of playing performance.

Evaluation-function based proof-number search

This article introduces Evaluation-Function based Proof-Number Search (EF-PN) and its second-level variant EF-PN2. It is a framework for initializing the proof and disproof number of a leaf node with the help of a heuristic evaluation function. Experiments in LOA and Surakarta show that compared to PN and PN2, which use mobility to initialize the proof and disproof numbers, EF-PN and EF-PN2 take between 45% to 85% less time for solving positions. Based on these results, we may conclude that EF-PN and EF-PN2 reduce the search space considerably.

Improving Best-Reply Search

Best-Reply Search (BRS) is a new search technique for game-tree search in multi-player games. In BRS, the exponentially many possibilities that can be considered by opponent players is flattened so that only a single move, the best one among all opponents, is chosen. BRS has been shown to outperform the classic search techniques in several domains. However, BRS may consider invalid game states. In this paper, we improve the BRS search technique such that it preserves the proper turn order during the search and does not lead to invalid states. The new technique, BRS\(^+\), uses the move ordering to select moves at opponent nodes that are not searched. Empirically, we show that BRS\(^+\) significantly improves the performance of BRS in Four-Player Chess, leading to winning 8.3 %–11.1 % more games against the classic techniques max\(^n\) and Paranoid, respectively. When BRS\(^+\) plays against max\(^n\), Paranoid, and BRS at once, it wins the most games as well.