Minimax

The following pseudo-code illustrates the Minimax algorithm for returning the optimal move in a 2-player zero sum game.

//This top-level function computes the best action for MAX to take
MINIMAX(state)
    (best_value, best_action) ← MAX-VALUE(state)
    return best_action
end

MAX-VALUE(state)
    if TERMINAL-TEST(state)
        return UTILITY(state)
    end

    value ← NEGATIVE-INFINITY
    action ← null
    for each a in ACTIONS(state)
        // Compute the highest possible utility (for MAX) if MAX were to take this action
        u ← MIN-VALUE(RESULT(state, a)) 

        if u > value
            value ← u
            action ← a        
    end

    return (value, action)
end

MIN-VALUE(state)
    if TERMINAL-TEST(state)
        return UTILITY(state)
    end

    value ← POSITIVE-INFINITY
    action ← null
    for each a in ACTIONS(state)
        // Compute the lowest possible utility (for MAX) if MIN were to take this action
        u ← MAX-VALUE(RESULT(state, a))

        if u < value
            value ← u
            action ← a
    end

    return (value, action)
end