Daphne Koller, Stanford University, and Alan Biermann, Duke University

The idea of getting a computer to play a complex game such as checkers or chess has been present in computer science research from its earliest days. The earliest effort even predated real computers. In 1769, Baron Wolfgang von Kempelen displayed a chess-playing automaton called “Turk.” It drew a lot of attention, until people realized that the cabinet of the “machine” concealed a human dwarf who was a chess expert.

The first real attempt to show how a computer could play a game was by Claude Shannon, one of the fathers of information science. The basic idea is to define a game tree that tells us all of the possible move sequences in the game. We can then ask, at each point in the tree, what a rational (selfish) player would do at that point. The answer comes from an analysis of the game tree beginning at the end of the tree (the termination of the game). For example, assume that one player has black pieces and the other white pieces. We can mark each game termination point as B—black wins, W—white wins, or D—draw. Then we can work our way from the termination points of the game backwards: If the white player, at her turn, has a move leading to a position marked W, then she can take that move and guarantee a win; in this case, this position is labeled with W. Otherwise, if she has a move leading to a position marked D, then she can force a draw, and the position is labeled with D. If all of her moves lead to positions marked B, then this position is a guaranteed win for black (assuming he plays optimally), and it is marked with B. Similar propagation rules apply to positions controlled by the black player. Thus, assuming perfect play by each player, we can completely understand the win potential of every board position.

This procedure is a great theoretical tool for thinking about a game. For example, it shows that, assuming both players play perfectly, we can determine without playing a single move which of the players will win, or if the game has a forced draw. We simply carry out the above procedure and check whether the initial position is marked with a B, a W, or a D. Unfortunately, for almost all realistic games, this procedure cannot be carried out because the size of the computation is too large. For example, the game tree for chess has approximately 10120 trajectories. As Shannon points out, a computer that evaluated a million positions per second would require over 1095 years just to decide on its first move!

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