Yep, this is what I ended up doing as well! With how the game generate boards, the player that goes first always have a ~5% advantage. Since players switch hands each around they should have 50% win rate if both play optimally.
In practice, playing against author's AI I barely get ~60% win rate (small caveat, I count ties as 0.5 to both players). What about yours?
I think you have an error in the equation defining V(s).
You have component n_c * V(s) for the 'nothing happened' case, but I don't think that's correct. If you rolled that nothing happens the turn still passes to your opponent, so I think it should be n_c * V'(s).
