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Re: [Bug-gnubg] std and j.s.d

From: Jim Segrave
Subject: Re: [Bug-gnubg] std and j.s.d
Date: Mon, 28 Jul 2003 00:43:08 +0200
User-agent: Mutt/

On Sun 27 Jul 2003 (14:47 +0200), Achim Mueller wrote:
> For the documentation and translation:
> Can someone exactly point out for me what ist meant by ratio of
> std/value?

The ratio of the standard deviation (also referred to as standard
error) to the mean value of a normal distribution. In this case, if a
rollout shows in one of it's columns that the probability of a
win/gammon/backgammon ... etc is 0.250 with a (as labeled in the
window) standard error of 0.010, then the ratio being discussed is
0.010/0.250 = 0.040
> And what exactly does j.s.d mean?

This is the standard deviation of the difference in equities between a
given move or cube decision and the best move/cube decision being
rolled out. It is the square root of the sum of the squares of the
standard deviations of the two moves/decisions being compared.

Assume that move A has an equity of 0.100 and a standard
deviation of 0.010 and that move B has an equity of 0.075 and a
standard deviation of 0.005. The difference in equity is 0.100 - 0.075
= 0.025. The joint standard deviation is calculated as:
sqrt( 0.010 ^ 2 + 0.005 ^ 2 ) = 0.01095. 

The standard deviation gives us a way of saying that move A has an
equity that is 90% certain to be somewhere between 0.100 + 1.96 *
0.010 and 0.100 - 1.96 * 0.010

The joint standard deviation gives us a similar measure for the equity
differences. We can claim that the difference in equity between A and
B is 90% sure to be between 0.025 + 1.96 * 0.01095 and 0.25 - 1.96 *
0.01095. So in this case we are more than 90% sure that A is a better
move than B.

Jim Segrave           address@hidden

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