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In a round-robin tournament (where a player versus every other in the tournament in turn), do players who drop out of the tournament after a few rounds affect the probability of winning for those who played against them throughout the course of the tournament so far (in the cases that some competitors lost to this player while others won)?

If they do affect such probabilities of winning, do we retroactively change the points awarded for wins/draws/losses/forfeits against this player? What is the fairest way to handle such a situation, or do we perhaps design the points system in preparation such that this is not a problem?

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Interesting question. Perhaps the United States Chess Federation has encountered it and come up with a policy to deal with it. It might be worth the effort to have a look at their website. –  Gerry Myerson May 15 '12 at 12:25
    
@RobertIsrael knows a something about this. Perhaps if I say his name, he will appear. –  MJD May 15 '12 at 14:21

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You basically have two choices – keep the points earned against the players dropping out and try to award points to the players who didn't play the players dropping out in some average way to make up for the fact that they didn't have a chance to earn points against them; or just forget about all games played against the players dropping out. The second option is fair because the results are just as they would have been if the players dropping out had never existed (except perhaps for the fact that playing them was a drain on concentration or other resources), but might be somewhat frustrating for the players who had already played them. The first option is bound to be somewhat unfair. For instance, if there are two very good players in the tournament who could easily beat all others and one had already played the player(s) dropping out and the other hadn't, awarding only some average number of points to the other player would be unfair and would lower his or her chances to win the tournament.

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