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How to adjust entry fee in 2^n brackets for first round byes?

Posted By: Daniel Murphy
Date: Thursday, 30 August 2012, at 8:31 p.m.

In Response To: How to adjust entry fee in 2^n brackets for first round byes? (Colin Owen)

This almost slipped by me: "there's no need to greatly increase the chance element in a tournament by randomly assigning some players double the tournament equity." To which the simplest response is first, the need for randomly assigning byes in a knock-out tournament is obvious, and second, randomly assigning byes does not increase the "chance element" in a tournament.

Regarding your follow-up, saying "just" instead of "fair" in this context isn't conveying any meaning to me other than "fair."

Seems to me that there are two options:

(1) First, all players pay the same entry fee. Then a random draw allots byes.

(2) First, a random draw allots byes, and players who do not receive byes pay a lower entry fee than players who receive byes (or, as in Tom's proposal, players who receive byes are ineligible for part of the prize pool, which amounts to meeting your concern about money equity in a different way).

I think the best you can say is that of these two options, the second seems better to you. Or perhaps, seems less offensive to your sense of fairness. Or perhaps, has less variance, therefore is better. In any case, I don't see a good argument for one option being any less "fair" or "just" or equitable. Casper may be on to something, though, with the notion that with the second option expected results might converge more quickly. But that, I think, has more to do with variance than "fairness." It's been argued, with regard to various proposals for improving tournament conditions, that "less variance" must mean "more fair." In past discussions of such proposals, that's not an argument I found convincing. There are many ways to reduce variance, many of which (ever longer matches, duplicate rolls, seed manipulation, etc.) have little support. So a certain amount of variance is at the least tolerated, and I daresay welcome.

With regard to Leo going with (1) or (2), I recommended (1) basically because I don't think whatever (2) gains in some aspect is worth the bother of changing entry fees depending on the number of participants in a small, regularly scheduled tournament, and convincing participants who are used to (1) that (2) is the better option. (2) certainly does seem fair to me, however. Perhaps your usual small tourney companions will come around!

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