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

[Jacques Basaldúa]

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.

>>> 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.

> If you take a good look at your tests, they will make very specific null 
> hypothesis which in effect make at least some assumption about the 
> underlying distributions (or try to wash away all effects with the 
> central limit theorem).

Well, the "assumption" that p is estimated from the binomial because we 
are counting Bernoulli experiments of constant p is a mathematically
sound method used universally. It does not require go knowledge, that's
what i meant. When n is big enough, the binomial converges to the normal
and that's what we use for inference.


Jacques.