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Winning probability doesn't depend on match length?!

Posted By: Timothy Chow
Date: Tuesday, 6 June 2023, at 4:01 a.m.

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

Your point number iv) is something Art mentioned as well. I agree that the PR derived from the match itself is a noisy estimate of the player's average PR, but I don't see why it would tend to make the winning probability be independent of match length.

Do you have access to Kaufmann's original Inside Backgammon article, or anywhere that tries to justify the √N factor? One simple approach to try to estimate the effect of match length is to play a bunch of bot-versus-bot games where random noise is added to simulate different playing strengths. I wonder if anyone has done that?

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