Can Python’s Minimax Reveal the Winning Strategy in Doudizhu?

Minimax

The core idea is the minimax algorithm, which splits decision making into a minimizing player and a maximizing player, similar to two opponents playing chess where each tries to maximize their own score while minimizing the opponent's.

Core Logic

A function hand_out simulates a player's move. It receives the player's hand ( me_pokers), the opponent's hand ( enemy_pokers), and the last played hand ( last_hand). The function returns true if the current player can force a win from this position, otherwise false .

Construction

Cards are represented by numbers (e.g., 3 for three, 11 for J, 12 for Q, etc.). All possible hand combinations are generated with a get_all_hands function. A comparator can_comb2_beat_comb1 checks whether one combination can beat another, respecting Doudizhu rules where only identical types are comparable except for bombs.

Efficiency

The search space grows factorially, leading to O(N!) time complexity. To mitigate repeated calculations, a cache dictionary stores results keyed by the string representation of the current hands and the last hand, reducing the effective complexity to exponential O(C^N).

Result

Running the solver shows that the farmer (the side that plays first) does not have a forced winning strategy; the landlord can always win if they play optimally. The code is released on GitHub under the MIT license for anyone to experiment with.