[computer-go] MC - Estimating a moves true probability of winning

[Jason House]

Jacques Basaldúa wrote:
> Hello,
>
> Just an explanation on something I may have explained badly. I see we 
> agree in the fundamental.
>
>> Correcting bias in that estimate should lead to better sampling.
>
> This is usually called "continuity correction" 
> http://en.wikipedia.org/wiki/Continuity_correction. The estimator
> is not really biased, but because it is a quotient of integers it
> requires a continuity correction specially when the integers are small 
> or zero is involved. That is included in the intervals I suggested.

That's about how to fit a continuous curve to a discrete one.  It's 
really just an approximation that increases as the sample size gets 
better.  The article mentions that both np and n(1-p) must exceed 5 for 
most to consider the approximation to even be valid.  The analysis I 
gave has no restrictions on the sample size (it even works for a sample 
size of zero)