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Winning probability doesn't depend on match length?!

Posted By: Art Grater
Date: Tuesday, 6 June 2023, at 7:18 a.m.

In Response To: Winning probability doesn't depend on match length?! (Timothy Chow)

I have the issue (Volume 1, Number 5, September-October 1991, page 21).

He starts with the rating difference "D" for the game of chess. Then goes on to modify it for BG:

"Now for the big question, the treatment of backgammon matches of unequal length. There are two issues: calculation of expectancy, and relative weighting. The first is tricky: if I am a 2-1 favorite in a 25-point match, how do we estimate my odds of winning a 5-point match or a 100-point match? Fortunately, an answer is provided b random walk theory, which says that the expected distance of a random walker from a starting point is proportional to the square root of the number of random steps he has taken. For backgammon matches, this means that if we quadruple the match length, we should halve the rating difference needed to attain any given expectancy. To allow for this in the rating formula, I replaced D/400 by (D times the square root of N)/2000, where N is the number of points in the match. This gives the same result for N=25 and adjusts properly (I believe) for matches of varying lengths."

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