A little problem asked in TCEC chat

Laskos · Post by **Laskos** » Sat Apr 26, 2014 12:10 am

Someone in TCEC chat asked:
If one engine in matches of 8 games is expected to win in p=70% of matches against another engine, what is the probability it wins in matches of 64 games?

Assuming normal distribution approximation for the trinomial (valid for large number of games), the answer is in general case, after some manipulations:
N is the number of games in each match with a given probability p to win the match for one engine, then in N1 games each match, the engine has the probability p1

p1=(1 + Erf[(Sqrt[N1/N] * InverseErf[2*p - 1])])/2

to win the matches consisting of N1 games.

The answer to the original question is 93.1%.