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Wastage in the one-checker model

Posted By: Fabrice Liardet
Date: Thursday, 6 May 2010, at 8:31 a.m.

In Response To: Wastage in the one-checker model (Maik Stiebler)

- No, V is second order variance (average of the squares of deviations)

Of course, silly me. With any other order there would be a little scaling problem.

- Have you read the Trice? It's a bit hard to explain, and my path to confirming Sam's 33/7 included some handwaving (as the article does, but in my case the handwaving is due to lack of understanding, in Trice's probably not). Here's a bit from the article that might help: In a very long, one sided N-Roll bearoff, what's the probability that your last checker is born off with a roll of doubles?

That is case {1,1,1,1,1,2} (in non-double rolls instead of pips) and yes I can compute that one quite easily, the wastage is 1/7 as your (A + V/A - 1) / 2 formula yields. What I am still unable to do is to derive the general formula.

I just got the crazy idea to apply that result in order to generalize to n checkers, but it would probably be of mere theoretical value since that is a non-calculatory result. I think that it could prove convergence in the n-checker case.

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