Actually I thought about it more. There are a few approaches
so you only need to decide 1 of 4 moves at the beginning
1. min max to a finite horizon using a heuristic utility function (as implemented)
2. Dynamic program/MCMC to a finite horizon and use the heuristic. Good at modelling the opponent behaviour, but could lead to bad results with a bad heuristic. (commented out approach)
3. Sample till the game ends (infinite horizon), pick the first move that lead to the game that went the longest (or won). This avoids developing an ad hoc heuristic.
so you only need to decide 1 of 4 moves at the beginning
1. min max to a finite horizon using a heuristic utility function (as implemented)
2. Dynamic program/MCMC to a finite horizon and use the heuristic. Good at modelling the opponent behaviour, but could lead to bad results with a bad heuristic. (commented out approach)
3. Sample till the game ends (infinite horizon), pick the first move that lead to the game that went the longest (or won). This avoids developing an ad hoc heuristic.
So now I vote for 3. :p