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Monday, August 20, 2007

An Appreciation of Chess Complexity


Even an experienced chess player can be amazed at the complexity of his or her favorite game. I somewhat randomly picked up a copy of New in Chess from 2006 and came across a review of David Shenk's The Immortal Game. The reviewer, GM Jonathan Rowson, provides this excerpt from the book:

It starts out so simply: In the first move, White is limited to twenty options. Black has the same twenty possible moves with his first response. But with chess, the number of legal moves is only a small part of the equation. Because while there are only forty possible first moves per pair of players, there are actually 400 possible board positions inherent in those moves. That's because for every one of White's twenty moves, Black's response can lead to twenty separate positions.

To the outsider, the distinction among all these early board positions may seem negligible, but the seasoned chess players knows from hard-won experience that every such variation is crucially distinct, that the dynamics of the game depend entirely on the exact position of the pieces. In the second move, the number of chess [positions] shoots up almost past belief; for every one of those 400 positions, there are as many as 27 options that each player has for a second move...the total number of distinct board positions after the second complete move is 71,852. After three moves each, the players have settled on one of approximately nine million possible board positions. Four moves and it raises it to more than 315 billion. The game has hardly started and already we are into hundreds of billions of game sets.


Now you can understand why you may feel just a bit overwhelmed at times!

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