# Calculating the Z Score

### From ADS-AC

These calculations are based on z score calculator http://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html by John Walker, the author of AutoCad, the equations have also been taken from that page. Calculate the z score when percentage from 10,000 games was 52%. So percentage p=52 and n=10,000. Then, we can calculate z score for 10,000 games using the equation z=(n*p/100-n/2)/sqrt(n/4). We get z=4. Now, we use z score calculator to calculate probability. The probability is 1 in 31574, ie 1/q0=31574. But we run that structure file a lot of time before that, some 3 months so far, but maybe much more until we get that result. Of course it had to learn first, but we have to show that the result did not occur only as a result of random event after running a big number of games, but is a result of training. Consider that we have been running the program some 5 months, in a day it can run usually not more than 20,000 games, so we can safely say that in 5 months it doesn't run more than 5*30*20,000=3,000,000 games, which is 300 times more than our n, say m=300. Then the probability for such event to occur, that after 3,000,000 games the percentage in the last 10,000 games was 52%, 1/q=1/q0/m=31574/300=105.25. Then q=0.0095, and using the z score calculator, we find that z=2.35. z score more than 2 is considered significant, so what we need for getting a significant result, is 52% from 10,000 games. Unfortunately the highest percentage so far was 50.84% from 12322 games, the z score is probably not more than 1 (unfortunately the z score calculator goes out of range and cannot calculate z scores less than 1.2), and therefore very unsignificant.