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XG 4 ply RO of 61P 43

Posted By: eXtreme Gammon
Date: Tuesday, 12 January 2010, at 3:32 a.m.

In Response To: XG 4 ply RO of 61P 43 (Ian Shaw)

XG reports the 95% confidence interval, i.e 1.96 x standard error

In case of only two moves the chance that one is better than the other can be calculated easily assuming normal distribution, which my tests show as a good hypothesis and independence which i don't realy now how to proove, but seems reasonable ( I actualy did some Pearson test on it and it seems the hypothesis is valid but i must say that i did that on a very small sample of RO data [3 positions])

In the case of 2 moves, the join distribution of A-B has a mean of avg(A)-avg(B) and standard deviation of sqrt(stdev(A)^2+stdev(B)^2) and is a normal distribution. Then using the cummulative normal distribution function you can find the chance that one move is better.

using the rounded number give a standard deviation of 0.00255 for an difference of 0.004. ending up with 94.2%

I asked Neil to send me the file so i could get the number unrounded (in debug mode). The actual values are avg=0.224862188 std=0.003467619 avg=0.229081839 std=0.003795701

which come up as 94.62% chances 24/21 24/20 is better than 24/21 13/9.

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