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Chess Match: Math Problem

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Why is it that the 2012 world chess match will be between the #4 player and the #22 player, by Elo rating? I would tend to expect it to be between the #1 player and the #2 player. This question suggests a math problem.

Gelfand, the #22 player, qualified as challenger for Anand's world title by a series of 3 matches. They were 4 games, 4 games, 6 games. Short matches.

The Math Problem:

Each game is worth 1 point. If you win, you get the full point. If you lose, you get zero. If the game is a draw, each player gets half a point. If the match (series of games) is a draw, there is a tie break system.

Assume that the higher rated player on average scores 60%. Assume that the probability of a game being a draw is 50% (which is a little on the low side in real life).

Let N be the number of games in a match. What is the equation that expresses the relationship between N and the probability that the lower rated player wins the match?

Or, how the 773H did Gelfand qualify as challenger?


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