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Games with Perfect Information

Chess is by far the most well studied strategic game in the field of computer game playing. Many advances in computer science have resulted from this research, including developments in problem specification, exhaustive search techniques, parallel algorithms, and others. The body of literature on computer chess is quite extensive, including dedicated journals and magazines [1, 10] and collections of important papers [5, 11].

Until recently, the concentration of research on computer chess has overshadowed all other games. But with the dominating success of fast brute-force search techniques, other approaches to the problem have been unable to compete in terms of practical results. Consequently, interest in many other strategic games has grown dramatically over the past few years, with each new game offering new challenges and requiring novel approaches. The research on this broader scope of games has also been facilitated by collections of reprinted articles [6] and original material [7, 8, 9].

The best studied class of games are somewhat similar to chess in nature. These games are categorized as two-player deterministic zero-sum games with perfect information, and include Go, chess, checkers, Othello, Go-Moku, and tic-tac-toe. Search techniques have proven to be quite effective for many of these games, provided the search space is relatively small, or can be restricted with good heuristics. Programs based primarily on efficient search engines are approaching or have surpassed the level of the best human players for many games in this category.

Complementing the search progress is the technique of retrograde analysis, typically performing an exhaustive enumeration of all positions, working backwards from a final position. This has had a significant impact on the playing strength of chess [95, 92] and checkers programs [54], and was instrumental in solving several non-trivial games, including tex2html_wrap_inline1187 Tic-Tac-Toe [63, 16, 18], Connect-Four [13, 98, 14], Go-Moku [99, 17, 18, 19], and Nine Men's Morris [45, 46]. Other games in this category are either close to being solved or have programs which play stronger than the best human players, including Othello [66, 47], Awari [15, 18], and Renju [18, 19].

In recent years, the game of checkers has been the focus of intense investigation by researchers at the University of Alberta, headed by Jonathan Schaeffer [78]. The resulting program, Chinook, quickly achieved world-class strength and earned the right to challenge the human world champion, Marion Tinsley, but lost that 1992 match by a narrow margin [79, 80, 81, 82]. In the rematch of 1994, Chinook became the first computer program to win the official world championship for a game of skill, and decisively defended that title in 1995.

Chess appears to be more challenging than these other games. Despite being the flagship of computer game playing research, the best programs have achieved only a modest degree of success against the best human players. The strongest program, Deep Thought, plays at the level of a human grandmaster and is currently ranked among the top 200 players in the world [49]. While most researchers believe that a computer program will eventually overtake the human world chess champion, there is a disparity of opinion on how long it will take to achieve that milestone [18].

In contrast to the high skill level attained in the above games, the same techniques have failed, and appear to be hopeless, for the game of Go. The vast number of possible positions on the tex2html_wrap_inline1189 Go board and the high density of reasonable alternatives at each move make the effective search space prohibitively large. Achieving a respectable level of play by the standard techniques is computationally intractable. Considerable work has been done on Go by computer scientists who are also highly accomplished Go players. Despite this effort and expertise, the strongest programs have only reached the level of weak amateur [108, 67, 96, 21, 103, 85, 29, 30, 53, 64, 31, 65].

Fundamentally different problems arise with games having a non-deterministic element, such as the roll of dice or the drawing of cards. Backgammon is an example of a game which preserves all of the above characteristics but is non-deterministic. Conventional search techniques are not immediately applicable, since the breadth of all possible rolls makes it difficult to restrict the search space, and does not account for the stochastic nature of the game [25]. Recently, the game of backgammon has been the basis for a highly successful application of neural nets, resulting in a program of world-class strength [93, 94].


next up previous
Next: Games with Imperfect Up: Introduction: Why Study Previous: Introduction: Why Study

& Schaeffer
Thu Feb 12 14:00:05 MST 1998