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Re: [Bug-gnubg] Confidence intervals from rollouts

From: David Montgomery
Subject: Re: [Bug-gnubg] Confidence intervals from rollouts
Date: Thu, 5 Sep 2002 20:02:02 -0700

Douglas Zare wrote
> There was an interesting question on the Gammonline bulletin board about
> standard deviation in cubeless rollouts and the standard deviations of
> cube results. I've included an excerpt below, in which I attempt to
estimate a
> confidence interval for the difference between doubling and not doubling.
> not sure what the best way to do this is, but I suggest that an attempt
> be worth implementing in gnu.

Isn't the right way to do this a paired t-test?
This is what I thought, anyway, after talking with
Jeremy Bagai about it.  Each game forms a pair with
double and no-double result.  Since the two are so
highly correlated, you should get a much tighter
confidence interval than the joint standard deviation.

The same thing could be applied to checker plays, but
it's not as clean, especially for 3+ plays.  Then you
are probably supposed to do some multi-way analysis of
variance, of which I am unfortunately ignorant.


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