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New GV article

Posted By: Timothy Chow
Date: Thursday, 17 December 2009, at 9:42 p.m.

In Response To: New GV article (Bob Koca)

I am not seeing the problem with the transposition, is it possible to give a simplified example to show how it is a problem?

It will take more time than I'm willing to put in right now to construct a fully worked-out example, but the idea is this. Suppose that from a given position of interest, the sequence of rolls 43-65-41 produces a position P1 that happens to be identical to the position P2 that arises from the sequence of rolls 41-65-43 (when the rolls are played using whatever ply-level you've chosen for the rollout). Then Var[equity(P1) + equity(P2)] will not be equal to Var[equity(P1)] + Var[equity(P2)]; it will be twice that, because equity(P1) and equity(P2) are really the same random variable.

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