Comment on Show HN: Probabilistic Tic-Tac-ToeparentComments−pvillano2yWRT to computing an exact solution, something something markov chains, transition matrices, eigenvalues. I think it is tractable−orlp2yUsually those are for additive/linear systems, the problem with game theoretic graphs like these is that you alternate between max and min nodes, so the system is highly nonlinear.−pvillano2yYou're right.I'll work on the simpler problem of :) / :( first. I think that can be done with just minimaxAnd then maybe win chance for each possible state of a purely random game−orlp2yIf it were just solely :) / :( then it is a freshman's exercise in expectiminimax.−pvillano2yit turns out you don't need anything more than minimax for the general case Here's my solution https://github.com/pvillano/probabalistic-tic-tac-toe−orlp2yI think this fails to take into account that your opponent can also roll 'meh', making it your turn again.−Labo3332yI just did: https://louisabraham.github.io/articles/probabilistic-tic-ta...
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WRT to computing an exact solution, something something markov chains, transition matrices, eigenvalues. I think it is tractable
Usually those are for additive/linear systems, the problem with game theoretic graphs like these is that you alternate between max and min nodes, so the system is highly nonlinear.
You're right.
I'll work on the simpler problem of :) / :( first. I think that can be done with just minimax
And then maybe win chance for each possible state of a purely random game
If it were just solely :) / :( then it is a freshman's exercise in expectiminimax.
it turns out you don't need anything more than minimax for the general case Here's my solution https://github.com/pvillano/probabalistic-tic-tac-toe
I think this fails to take into account that your opponent can also roll 'meh', making it your turn again.
I just did: https://louisabraham.github.io/articles/probabilistic-tic-ta...