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New standard method for resolving 3-way ties on the ABT

Posted By: Bob Koca
Date: Monday, 2 July 2018, at 2:33 p.m.

In Response To: New standard method for resolving 3-way ties on the ABT (Sean Garber)

I agree entirely.

If one insists on looking at the value of the bye when it occurs then consider the following: Suppose there are 48 players in a winner takes all tournament and the following two isomorphic brackets are drawn. Bracket A uses 3 groups of 16 and then once those games are played there is a redraw and a bye is given. At the time it occurs the bye is worth 1/4 of the prize fund. Bracket B uses a 64 player bracket meaning 16 players get a bye into round 2. At the time they occur each is worth 1/64 of the prize fund. Multiplied by the 16 players who get them the total alue of the byes is 1/4 which is exactly the same as in Bracket A. But somehow 1/4 of the equity being given out in byes only matters for bracket A.

Here is yet one more way to look at it. In bracket A above it is probabilistically equivalent to do that drawing in advance. Then it becomes the same as bracket B.

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