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

Posted By: Rich Munitz
Date: Sunday, 17 June 2018, at 8:26 p.m.

Effective immediately for all American Backgammon Tour (ABT) tournaments, the USBGF has established the following standard method for resolving all 3-way ties. There is no change to the way in which ABT points are calculated. That calculation continues to depend only upon the final place of finish for each player.

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HANDLING 3-WAY TIES

Some tournament formats may play down to a 3-way tie. That tie must be broken to determine a tournament winner, as well as second and third places. A round-robin playoff is undesirable because it requires 4 matches on average. A standard elimination playoff is undesirable because the late bye awards a very large equity bump to one player at the expense of the others.

The following “contingent bye” playoff format requires only two matches, but drastically reduces the equity swing produced by the late random draw to a level of only 1.3% for the ~5:3:2 payouts typical of Swiss, or 2.4% for the 4:2:1 payouts typical of Elimination.

All 3-way ties that occur at ABT tournaments must be resolved using the following playoff format:

• Label the three tied players A, B, C.

• A contingent bye is awarded to one player randomly chosen from among those who received the fewest byes previously in the event. Suppose A is chosen.

• B plays C. Suppose B wins.

• B plays A.

• If A wins, then A has earned the bye. Player A places first; B places second and C places third.

• However, if A loses, then the bye is given to player C instead of player A. The A vs. B match is recorded as the semi-final, and the B vs. C match is recorded as the final. B places first; C places second and A places third.

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The full ABT Policy and Formula document can be viewed here: http://usbgf.org/docs/ABT-policy-formula.pdf

Effectively, with the contingent bye method, one player receives 1/2 bye and the other two receive 1/4 bye, which is not too far off from the 1/3 bye that is perfectly equitable. This greatly reduces the absolute equity bump given to one player down to an acceptable level - roughly the same order of magnitude as a first-round bye.

The expected place of finish of all 3 players after the random draw remains exactly 2. The player receiving the contingent bye can only finish first or third, and does so with equal probability, so the average is 2.

Tournament directors remain free to distribute the prize money any way that they wish. With this contingent bye format, simply by paying 1/3 of the prize pool to second place, each player has exactly 1/3 equity before and after the random draw. Unlike equitable bye settlements in a standard-bye 3-way playoff format, in the contingent bye format the exact amount paid to each position can be set in advance and is not dependent on the outcome of future matches. While any division between first and third places of the remaining 2/3 of the prize pool maintains equal equity, a prize pool partition of 3:2:1 seems logical because it makes each match played worth the same 1/6 of the pot to the winner; we don't know before playing both matches which match is the semifinal and which match is the final, and both outcomes occur with equal likelihood.

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