[basic_stat]

Once you condition on the number of draws, you do get that binomial distribution.

Suppose you have a coin, which gives a random outcome X. But you can only observe the outcome of X when another independent binary random variable Y is true. How can you tell if X is biased? Since X and Y are independent, the observations where Y is false are irrelevant since they don't tell you anything about X. So you just keep the observations where Y is true, and from there you can apply a binomial statistical test to the observations of X.

[ In case you're wondering whether applying statistical tests to variable sample sizes is valid, the answer is yes: a p-value is a uniform random variable from the set of observables (augmented by a continuous random variable, since our set of observables is discrete) to [0,1]. Our p-value is a mixture of p-values on smaller sample sizes, so it is still uniform. ]

This is exactly what happens here: consider a random outcome {win,lose,draw}. If you don't have a draw, let Y be true and X be the outcome of the game. If you have a draw, let Y be false and X be a random coin with the same distribution as for non-drawn games. Then X and Y are independent random variables and the above applies.

Informally: draws are not useful information in determining whether there are more wins than losses.

[millstone]

I'm not sure that discounting draws is the right thing to do either. For example, Petrosian was not the strongest attacking player but was very, very tough to beat.

This also calls into the question the notion of "strongest chess player." Who is strongest, the flashy attacking player that wins half the time and loses the other half, or the stonewall that poses little threat but that you can never beat?