[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

game_theory/fictitious_play.py

@@ -25,6 +25,7 @@ def fictitious_play(payoff_matrix_A, payoff_matrix_B, iterations=100):
 
     return strategy_A, strategy_B
 
+
 # Example usage
 payoff_A = np.array([[3, 0], [5, 1]])
 payoff_B = np.array([[2, 4], [0, 2]])

game_theory/minimax_algorithm.py

@@ -3,7 +3,7 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
         return values[node_index]
 
     if is_maximizing_player:
-        best_value = float('-inf')
+        best_value = float("-inf")
         for i in range(2):  # Two children (0 and 1)
             value = minimax(depth - 1, node_index * 2 + i, False, values, alpha, beta)
             best_value = max(best_value, value)
@@ -12,7 +12,7 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
                 break  # Beta cut-off
         return best_value
     else:
-        best_value = float('inf')
+        best_value = float("inf")
         for i in range(2):  # Two children (0 and 1)
             value = minimax(depth - 1, node_index * 2 + i, True, values, alpha, beta)
             best_value = min(best_value, value)
@@ -21,8 +21,9 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
                 break  # Alpha cut-off
         return best_value
 
+
 # Example usage
 values = [3, 5, 2, 9, 0, 1, 8, 6]  # Leaf node values
 depth = 3  # Depth of the game tree
-result = minimax(depth, 0, True, values, float('-inf'), float('inf'))
+result = minimax(depth, 0, True, values, float("-inf"), float("inf"))
 print("The optimal value is:", result)