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Swiss vs random draw

Posted By: Timothy Chow
Date: Thursday, 14 March 2013, at 2:59 p.m.

In Response To: Swiss vs random draw (Robert Wachtel)

Before one can think about proving anything, one has to be more precise about the question.

For example, as I said before, it's not clear exactly how many rounds of a Swiss tournament constitutes a "fair" comparison between Swiss and triple elimination. One way around this would be to forget about triple elimination and just set up a Swiss with random pairings at each round. I suspect that that's what Tom Keith did in his simulation although I'm not sure. Would that address your question sufficiently?

There's another complication which is that the answer may depend on the exact distribution of player strengths.

Having said all that, I think that one fact ought to be fairly robust to variations in these details. Namely, in a Swiss, it will be harder for the very weak players to win the tournament. To win, you have to defeat a fair share of strong players, and this is hard for a weak player to do. In a random draw, you have some chance of winning without facing any strong players.

It doesn't quite follow, though, that the strongest player will have a better chance of winning a Swiss. I don't see a quick way to analyze this question.

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