Bobby Fischer and Game Theory

by Stanley Goff
According to game theory, chess is a two-person, zero-sum, perfect information game.

According to game theory, chess is a two-person, zero-sum, perfect information game.

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Bobby Fischer was a towering 6-foot 3-inch savant with a borderline personality who revolutionized the game of chess. Before going into seclusion and dying in 2008, he had invented a new form of chess. Game theorists became interested in Fischer's abandonment of standard openings because it threw doubt on the idea that certain games could be "optimized."

The Idea of Optimization

Chess is a two-person game. It is, in the language of game theory, a zero-sum game in which all information is perfect. By game theory standards, these characteristics should make chess a simple game. Games that can result in cooperation as well as competition (non-zero-sum), games that involve more than two players and games that do not have a finite number of moves for a finite number of pieces on a finite and numbered playing field are all, by definition, more complex than chess. This led to the idea among some theorists that every game could be theoretically optimized, and many chess masters began to study standard if complex openings as the first stage in that optimization. Bobby Fischer disrupted all that.

Approaching Infinity

Bobby Fischer played against all conventional wisdom by opening games in what were apparently random and untested ways. That he could follow up on these unconventional openings was a sign of his genius at the game, but the intentional randomness of human decision only brought home the mathematical fact that chess has legally possible games that number 10 to the 44th power -- or more than the number of molecules in the universe.

Chess960

By 1996 Fischer had become frustrated with what he perceived to be "good memorizers" without a deep grasp of chess principles being able to "compute" winning games using clever openings. He then invented a game called Chess960, or Fischer random chess. In Chess960, the initial positions of the back row for both players are switched, with rules to compensate for differences on each side with regard to castling. A king may be all the way to one side and both bishops in the other corner, for example. Players then have to begin play without any memorized opening strategies.

Computation -- Necessary If Not Sufficient

Neither Fischer's genius nor his unconventional style of play set aside the fact that computation is critical in chess. Although good computation on the part of a player may not be sufficient to win a contest on the order of Fischer-Spassky, it is still absolutely necessary to play good chess. In every individual move, the player has a very finite number of options, and each of them results in an absolutely predictable board at the completion of that move, whereupon the opponent will have a finite number of options. The problem that Fischer learned to capitalize on with his deep knowledge of principles is that the opponent might have more than one move that does not lead to inevitable defeat, each of which opens more than one optimal possibility.

About the Author

Stanley Goff began writing in 1995. He has published four books: "Hideous Dream," "Full Spectrum Disorder," "Sex & War" and "Energy War," as well as articles, commentary and monographs online. Goff has a Bachelor of Arts in English from the University of the State of New York.

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