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Re: [Bug-gnubg] Confidence intervals from rollouts

From: Nis Jorgensen
Subject: Re: [Bug-gnubg] Confidence intervals from rollouts
Date: Thu, 05 Sep 2002 11:00:56 +0200

--On 04  Sep 2002  08:22 -0700 David Montgomery <address@hidden> wrote:

Consider a single position, for which we have 3 rollout
samples A, B, and C.  The idea of rotating the first ply
or two is that the variance of the *difference* between
two plays should be reduced, since one aspect of the
luck has been eliminated.

Permission to disagree, sir. I lack the understanding of exactly what you mean above, but I do understand that I disagree on several levels.

The idea of rotating the first ply or two should be to reduce the difference between the "true" value of a position and the results of rollouts. The variance (or rather standard error) is just a _measure_ of how much we trust the result, and reducing the value is not a goal in itself.

This is very important to stress, especially in cases like this, where we should expect the standard error to go _up_ even though the actual trustworthyness of the rollout should improve

Also, I don't understand why you bring "different plays" into this. This is of course relevant for the "duplicate dice" evaluation, but not for the rotation (for which I would reserve the word "stratification").

So, for example, we would
expect that the standard error of abs(A - B) would be
less than sqrt(2)*[true standard error of rollout of
that size of that position].

I am not sure what you mean by the "standard error of abs(A-B)". I assume you just mean Abs(A-B)?

So I think what I did was to consider that from C
I could get an unbiased estimate of this true standard
error, and then I compared this (* sqrt(2)) with abs(A-B).
I repeated with C-A vs B and C-B vs A, and repeated the
whole thing for hundreds or thousands of positions.

Hmmm - I think I start to see what you are doing here. I am not convinced that this is a good way to estimate the value of stratification.

I think I will do some simple coin experiments, and see if this brings me any insights.

Nis Jorgensen

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