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win probability for a PR difference and match length

Posted By: Rick Janowski
Date: Thursday, 20 September 2012, at 10:02 p.m.

In Response To: win probability for a PR difference and match length (Bob Koca)

But two players with large prs wont normally choose to play suboptimally for any tactical/insurances reasons. They will just play at their normal sub-optima standard.

The Backgammon Elo formula utilises something the Inside Backgammon article calls the "logistic" curve or equation, which I ever never heard of before.

The theory runs like this: If there are three players A, B and C.

If we know the odds A beating B are "x" to 1 and we know the odds of B beating C are "y" to 1 then the odds of A beating C will be the product "xy" to 1.

Use of normal distribution gives a very similar answer generally but is more complicated.

In reality there might be other factors that effect results (eg, C has more knowledge of B's specific cube and/or checker play weaknesses but has no info about A), but overall the relationship probably holds fairly well I would imagine.

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