Bayesian statistics allowed Deep Blue to defeat Gary Kasparov, the greatest chess player of all time. Previous attempts at chess computation, which is difficult because of the enormous size and scale of the game’s possible developments, all resulted in chess computers that were inherently alien and inferior to skilled humans. Consider the standpoint of early programmers. It’s enormously difficult to assign weights to pieces in a game that continually changes. The engine can’t know which pieces to prioritize when the game’s dynamic nature makes the importance of pieces relative to positions on the board, the strengths of either player or the strategies being played unless the engine can learn to reassess the value of its pieces based on a statistical database of similar games. This reassessment is possible thanks to finely tuned statistical models and algorithms applied to “the book,” which is a massive theoretical index of the best possible moves in a recognized openings and defenses and really only solves the problem of defensive maneuvering. The computer reasons “my opponent is attacking my bishop with his kings-side knight, my best response based on decision tree analysis is to move my bishop.” Chess computers mastered this kind of defense long before anything else because the statistical computation is relatively simple, consisting only of “how do I escape” thinking. It is much more difficult to ask a computer to take the initiative in a game. Imagine the size of the decision tree computers would have to generate to make the second move in a game. To solve the problem of perpetual calculation, programmers built in time-out clocks that force computers to weight the outcomes of their possible choices while the analysis is still young. This was the Achilles heel of chess computation; computers would select seemingly random, throwaway moves because they were considering trillions and trillions of alternative scenarios and couldn’t decide between them. Weak chess programs, such as the one on my phone, still have this problem. In order to beat the program, all the human has to do is play as passively as possible and the phone will give up piece after piece as it looks for something to respond to. A lot has changed since the early days of chess computing. The algorithms used by freely distributed engines like Rybka 4 and Houdini are far more complex, and now no human could hope to beat such a program unaided by another program.

# Chess Computers

Advertisements

The article is very interesting because it points out that a complex rational probability calculation like in a chess game cannot be solved through a computer system, but can be through the use of Bayes’ Rule. Since the chess game is quite complicated with a huge variety of responses to the other players moves, the Bayes’ Rule simplifies it, being based on the behavior in the past and not a probability calculation. I am quite sure that there exist many examples where the Bayes’ Rule is more useful than the probability calculation and it delivers a solution where probabilities fail.