Probability of winning a board game by chance
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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?
combinatorics game-theory
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
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add a comment |
$begingroup$
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?
combinatorics game-theory
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
$endgroup$
add a comment |
$begingroup$
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?
combinatorics game-theory
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
$endgroup$
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?
combinatorics game-theory
combinatorics game-theory
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
asked Dec 19 '18 at 6:42
Mr.Sh4nnonMr.Sh4nnon
286
286
add a comment |
add a comment |
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