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Playoff with 3 finalists - complicated

Posted By: Bill
Date: Saturday, 9 January 2010, at 4:35 a.m.

Thank you all for the input on the 3 finalists problem. It sounds like that problem is solved pretty nicely. Here is the twist that I am afraid of in the Swiss format:

Suppose one of the three players had an early round bye. The early-round bye player has one fewer win, so should have half as much equity as the other two. The solution must be pretty similar to the earlier problem. We can draw a two round playoff, only making the bye available to the two anti-bye players, but how to equalize the equities?

In one solution, the player that doesn't get the bye would immediately cash out 1/5 of the prize pool.
The player with the early round bye has equity: 25% of 4/5 = 1/5
The player that has to play an extra round has equity: 1/5 + 25% of 4/5 = 2/5
The player that gets the bye in the playoff has equity: 50% of 4/5 = 2/5

If you feel the need to complicate matters further, you could allow the two anti-bye players bid or negotiate for the playoff bye. I liked the earlier suggestion that part of the money be pulled out to make sure that everyone gets something. Are there other ways to do this?

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