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?



You must log in to answer this question.

Browse other questions tagged .