A Monte Carlo simulation like your son did can be useful in problems like this, but to have faith in its accuracy you really need to run more than a few thousand simulations. Given that you are trying to check whether p= 0.0156, if you run 2,000 simulations you would expect to win 31 games and the standard deviation is sqrt(np(1-p)) = 5.5; thus his results of 0.0137= 27 out of 2000 is less than 1 sigma from the expected value, which means his simulation does not prove you wrong.