### Benjamin Soltoff

Father, husband, political scientist, data nerd

I’m currently teaching a math/stats course and we’ve recently covered a ton of different probability distributions. This problem can be defined by the multinomial distribution, which is a generalizable form of the binomial distribution. In the original setup of the problem, $n=12$, $k=3$, and probabilities $p_0 = 0.2, p_1 = 0.15, p_2 = 0.6$ for the better player winning, losing, and drawing respectively.
Based on the example here, I wrote a generalizable function to estimate the probability of win, lose, and draw for all possible outcomes for any number of $n$ matches and probabilities $p$, and applied it to matches with length between 1 and 300 using the probabilities identified in the problem.