Hello Jason I think what you are trying to do can be done more easily.
A. You have a Bernoulli random variable whose result is 0 or 1 following an unknown probability p. (Excuse me for explaining obvious things, this is for anyone who reads it.) You want to estimate p from a random sample. The estimator of p computed from the sample is usually called p-hat (a "^" char on a "p") Of course, the same board position produces 0 or 1 with the same probability p. B. You cont the number of wins. Therefore, you have a random variable which follows a BINOMIAL (n, p) being n the sample size. C. To compare if a move is better than another, you have to compare _confidence intervals_. I.e. the interval in which p (the unknown probability) lies computed from your observed p-hat, n and a desired confidence level, say 95%. These intervals can be computed with methods you can find searching for "Confidence Interval for a Binomial Proportion". The most used are Wilson and Agresti-Coull intervals. These intervals include continuity correction as you mention in your post. Other ways of comparing proportions are: The difference between proportions, the relative risk and the odds ratio to name a few. My "Bible" for this is a book called "Categorical Data Analysis" from Alan Agresti published by Wiley & Sons. > To use these results, you must make some assumption > about the underlying distribution of a move's probability > of winning. That's the good news. You don't. There is no need to understand what complex mechanism produces p. Only that: same position == same p. *Do not* expect a sound statistical analysis to tell you the best move, unless it is very obvious, n is immense or your confidence level is extremely low. But, if you are lucky, it will tell you what moves are clearly bad and can be safely (= with a given confidence) pruned out. Computing distributions is not as hard as it may seem because you can interpolate from a LUT with reasonable precision. Anyway, even if I have the statistical skills to do that, I personally am not doing things "that well" because I believe computing time is more productive doing more simulations than "quality control". I may be wrong. Jacques. _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
