September Low-Content Thread

[tessarji]

Lets consider the result of each 100 hands to be a measurement of your winrate, with a mean x=winrate and sigmax^2=variance. Each measurement is independent.

We want to know the mean and variance of a combination of several samples (X1, X2, X3...)

The mean of all samples is X = sum(x) = x1 + x2 + x3 ... + xn

The variance of all samples is sigmaX^2 = sum(sigmax)) = sigx1^2 + sigx2^2 + sigx3^2 ... + sigxn^2

In the special case where all xn and sigxn are the same, the formulas reduce to:

X = x*n
sigmaX^2 = sigx^2*n

Total mean is X and total standard deviation is sigmaX. For a normal distribution it is now simple to determine the chance that a random measurement from this distribution will be at a certain distance from the mean. Refer to any source on the normal distribution such as:

http://en.wikipedia.org/wiki/Normal_distribution

or the much simpler adhoc rule which I applied here:

http://en.wikipedia.org/wiki/Empirical_rule