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I am a new learner of AI. My assignment requires me to write a program in Python that plays the Game of Nim optimally (using the NegaMax algorithm).

If you're not familiar with the game, here is a brief description:

Nim is a simple two-player game. We start with a pile of n matches, where n ≥ 3.

Two players, Max and Min, take turns to remove k matches from the pile, where k = 1, k = 2, or k = 3. The player who takes the last match loses.

This is what I have already written:

def NegaMax(state, turn, bestmove): 
    max = -100000000000  
    if state == 1:
        if turn == 0:
            return (-1,bestmove)
        else:
            return (1,bestmove)       
    for move in range(1, 4):
        if state-move > 0:
            m = NegaMax(state-move, 1-turn, bestmove)
            m1 = -m[0]
            if m1 > max:
                max = m1
                bestmove = move
    return (max,bestmove)

def play_nim(state):
    turn = 0
    bestmove = 0
    while state != 1:
        [evaluation,move] = NegaMax(state, turn, bestmove)
        print(str(state) + ": " + ("MAX" if not turn else "MIN") + " takes " + str(move))
        state -= move
        turn = 1 - turn
    print("1: " + ("MAX" if not turn else "MIN") + " loses")

No matter what number of state I put in, both Min and Max always takes 1 match in every round.

I think the problem is that the evaluation is wrong, but I cannot see where I did wrong. Any help would be appreciated! Thanks!

Aref
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Li Voon Loke
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1 Answers1

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Check your stop condition.

You need :

if state == 1:
    return (-1,1)

And then everything runs smoothly.

I would also change the function signature for clarity because it only needs state :

def NegaMax(state):
    max = -100000000000
    if state == 1:
        return (-1,1)
    for move in range(1, 4):
        if state-move > 0:
            m = NegaMax(state-move)
            m1 = -m[0]
            if m1 > max:
                max = m1
                bestmove = move
    return (max,bestmove)

def play_nim(state):
    turn = 0
    while state != 1:
        [evaluation,move] = NegaMax(state)
        print(str(state) + ": " + ("MAX" if not turn else "MIN") + " takes " + str(move))
        state -= move
        turn = 1 - turn
    print("1: " + ("MAX" if not turn else "MIN") + " loses")

It plays optimally.

You can observe the results under optimal play, which is that MAX loses for states 1+4k (1, 5, 9, 13, 17, etc) and wins for every other states.

play_nim(5)
5: MAX takes 1
4: MIN takes 3
1: MAX loses

play_nim(11)
11: MAX takes 2
9: MIN takes 1
8: MAX takes 3
5: MIN takes 1
4: MAX takes 3
1: MIN loses
Ashargin
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