[orlp]

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.

[pvillano]

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

[orlp]

If it were just solely :) / :( then it is a freshman's exercise in expectiminimax.

[pvillano]

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

[orlp]

I think this fails to take into account that your opponent can also roll 'meh', making it your turn again.