Abstract—Expectimax, or expectiminimax, is a decision algorithm for artificial intelligence which utilizes game trees to determine the best possible moves for games which involves the element of chance. These are games that use a randomizing device such as a dice, playing cards, or roulettes. The existing algorithm for Expectimax only evaluates the game tree in a linear manner which makes the process slower and wastes time. The study intends to open new possibilities in game theory and game development. The study also seeks to make parallelism an option for enhancing algorithms not only limited to Artificial Intelligence. The objective of this study is to find a way to speed up the process of Expectimax which can eventually make it more efficient. The proponents used the game backgammon, written in Java, to apply Expectimax. The concept of parallel computing using thread pool is used to make the process of Expectimax faster. A game simulation between the existing Expectimax and the enhanced Expectimax is used as the test case for this study. After multiple test runs, the results showed that the enhanced Expectimax has chosen a move faster than the existing Expectimax 90% of the time. This shows that parallel computing speeds up the process of Expectimax. Index Terms—Expectimax, parallel search, non-deterministic games, enhancement I. INTRODUCTION Artificial Intelligence is the combination of computer science, physiology and philosophy which is concerned with making computers behave like humans. Old algorithms like Expectimax were not explored much. Some are not aware that these old programs have a lot more potential if enhanced. When these algorithms (e.g. minimax, Expectimax) were created, powerful hardware were not available at the time. Nowadays, there is a lot of technology that could be used to maximize an algorithm’s potential. This study combines the power of Expectimax and the hardware itself, particularly its processor. In order to combine the two, the principle of parallelism was used. The study will investigate an enhancement of the Expectimax search algorithm for two-player non-deterministic games. The focus is on zero-sum games with perfect information where the whole state of the game is visible. In this case, backgammon is the perfect game to be Manuscript received January 15, 2013; revised March 12, 2013. This work was supported in part by the University of Santo Tomas. Incongruity Theory Applied in Dynamic Adaptive Game Artificial Intelligence. R. A. Sagum is with the faculty of Engineering University of Santo Tomas Philippines. (e-mail:riasagum31@yahoo.com). R. G. Lamanosa, K. C. Lim, I. D. T. Manarang, and M. G. Vitug are with undergraduates of the University of Santo Tomas (e-mail: gielamanosa@gmail.com, kheiffer12@yahoo.com, ivan.manarang@gmail.com; yelvitug@gmail.com. used. The study will not divide the search on the min and max nodes since it will always contain a better choice. By parallelizing on the min and max nodes, lesser values will also be searched. Doing so would be impractical since the proponents are only interested in the best value of a move. The study will not cover previous enhancements of the Expectimax Search. The proponents only plan to demonstrate the concept of parallelizing the Expectimax Search and how it can generally enhanced the performance of artificial intelligence. Only the form of Expectimax will be subjected to parallelism. II. RELATED WORKS A. Expectimax Enhancements for Stochastic Game Players According to Veness’ study [1], some people argue that the Minimax assumption is perfect and suboptimal, because it assumes that the opponent does not take advantage of the opponent’s propensity. This statement is reasonable, but the application of Minimax performs well in domains such as chess and checkers. Veness [1] mentioned in his study that one of the many improvements in Expectimax is parallel search. This can be applied in any algorithm used in Expectimax. But he specifically stated that the parallel search should be implemented in the negamax algorithm. The succeeding statements discuss studies conducted on parallel search. B. Implementing a Computer Player for Carcassonne One of Heyden’s [2] computer players in her computer implementation for the game Carcassonne uses an Expectimax search. The computational complexity in this game proved to be relatively high thus, she uses a realistic value of about two or three for the search depth because of the high branching factor. The Expectimax player loses by a great margin to another computer player, which uses a Monte Carlo Tree Search (MCTS). Since Expectimax is a full-width search, the quality of an Expectimax algorithm is dependent on the evaluation function. C. *-Minimax Performance in Backgammon The star algorithms were introduced by Ballard [3] early in 1983 but surprisingly did not get much attention from the artificial intelligence community. The surprise comes from the significance of being able to search deeper in two-player perfect information games. Hauk, Buro, and Schaeffer [4], being curious about these reasons, set out to investigate the star algorithms on a game called Backgammon. The study Expectimax Enhancement through Parallel Search for Non-Deterministic Games International Journal of Future Computer and Communication, Vol. 2, No. 5, October 2013 466 Rigie G. Lamanosa, Kheiffer C. Lim, Ivan Dominic T. Manarang, Ria A. Sagum, and Maria-Eriela G. Vitug DOI: 10.7763/IJFCC.2013.V2.207