What is the chance of winning a board game like Connect4 by chance? The player who makes the first turn could theoretically win in a perfect game all the time. How can I calculate the probability that this is achieved by playing random moves?
I assume a board game of 6x7. The opponent makes perfect moves, which should give the probability an upper bound. A tighter upper and lower bound would be great too. At the moment it looks like that in 300'000 games against a random player the winning probability for random is about 8-12%. Whilst writing this I just noticed that I didn't log how many of those 8-12% where ties... I'll add this in an update in another 300'000 games.
Which branch of mathematics deals with such kind of problems? Pure combinatorics or maybe game theory?