Lessons from Game Theory DP

Three patterns you've seen:

$1.$ Score difference: Track $dp[\text{state}] =$ my score $-$ opponent's score. Opponent's gain is my loss (subtraction).

$2.$ Extra parameters: Some games have changing rules (like $M$ in Stone Game II). Include them in the state.

$3.$ Bitmask + game theory: When tracking used elements from a small set, combine bitmask DP with minimax thinking. The core stays the same: I win if I have any move that puts opponent in a losing state. I lose if all my moves put opponent in a winning state.