diff --git a/simulation.py b/simulation.py
deleted file mode 100644
index 1741debc2017d58f09f24ade194745e2326c59f4..0000000000000000000000000000000000000000
--- a/simulation.py
+++ /dev/null
@@ -1,75 +0,0 @@
-import numpy as np
-import random as rd
-import matplotlib.pyplot as plt
-from tmc import TransitionMatrixCalculator as tmc
-from markovDecision import MarkovDecisionSolver as mD
-
-class Validation:
-    def __init__(self):
-        self.tmc_instance = tmc()
-
-    def simulate_games(self, layout, circle, num_games):
-        results = []
-
-        for _ in range(num_games):
-            result = mD(layout, circle)
-            # Assuming result is a tuple (costs, path) and you want the last element of 'costs'
-            results.append(result[0][-1])  # Append the number of turns to reach the goal
-
-        return results
-
-    def compare_strategies(self, layout, circle, num_games):
-        optimal_results = self.simulate_games(layout, circle, num_games)
-
-        suboptimal_strategies = {
-            "Dice 1 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 1 simulation
-            "Dice 2 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 2 simulation
-            "Dice 3 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 3 simulation
-            "Mixed Random Strategy": self.simulate_games(layout, circle, num_games),  # Replace with mixed random strategy simulation
-            "Purely Random Choice": self.simulate_games(layout, circle, num_games)  # Replace with purely random choice simulation
-        }
-
-        self.plot_results(optimal_results, suboptimal_strategies)
-
-    def plot_results(self, optimal_results, suboptimal_results):
-        strategies = ["Optimal Strategy"] + list(suboptimal_results.keys())
-        avg_costs = [np.mean(optimal_results)] + [np.mean(suboptimal_results[strategy]) for strategy in suboptimal_results]
-
-        plt.figure(figsize=(10, 6))
-        plt.bar(strategies, avg_costs, color=['blue'] + ['orange'] * len(suboptimal_results))
-        plt.xlabel("Strategies")
-        plt.ylabel("Average Cost")
-        plt.title("Comparison of Strategy Performance")
-        plt.show()
-
-    def run_validation(self, layout, circle, num_games):
-        solver = mD(layout, circle)
-        theoretical_cost, optimal_dice_strategy = solver.solve()
-
-        optimal_results = self.simulate_games(layout, circle, num_games)
-        optimal_average_cost = np.mean(optimal_results)
-
-        suboptimal_strategies = {
-            "Dice 1 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 1 simulation
-            "Dice 2 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 2 simulation
-            "Dice 3 Only": self.simulate_games(layout, circle, num_games),  # Replace with Dice 3 simulation
-            "Mixed Random Strategy": self.simulate_games(layout, circle, num_games),  # Replace with mixed random strategy simulation
-            "Purely Random Choice": self.simulate_games(layout, circle, num_games)  # Replace with purely random choice simulation
-        }
-
-        self.plot_results(optimal_results, suboptimal_strategies)
-
-        print("Theoretical Expected Cost (Value Iteration):", theoretical_cost)
-        print("Empirical Average Cost (Optimal Strategy):", optimal_average_cost)
-
-        for strategy, results in suboptimal_strategies.items():
-            avg_cost = np.mean(results)
-            print(f"Empirical Average Cost ({strategy}):", avg_cost)
-
-# Exemple d'utilisation de la classe Validation
-layout = [0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 1, 0]
-circle = True
-num_games = 1000
-
-validation = Validation()
-validation.run_validation(layout, circle, num_games)
diff --git a/tmc.py b/tmc.py
index 5941ed4fb1f1b0277693114af3bf1df1079a5c81..085fe462113a869528fec8eada34114390d0bb13 100644
--- a/tmc.py
+++ b/tmc.py
@@ -25,7 +25,7 @@ class TransitionMatrixCalculator:
 
 
     def _compute_safe_matrix(self):
-        for k in range(0,15):
+        for k in range(15):
             for s, p in enumerate(self.safe_dice):
                 if k == 9 and s == 1:
                     k_prime = 14
@@ -44,7 +44,7 @@ class TransitionMatrixCalculator:
         return self.matrix_safe
 
     def _compute_normal_matrix(self, layout, circle):
-        for k in range(0, 15):
+        for k in range(15):
             for s, p in enumerate(self.normal_dice):
                 if k == 8 and s == 2:
                     k_prime = 14
@@ -116,7 +116,7 @@ class TransitionMatrixCalculator:
         return self.matrix_normal
 
     def _compute_risky_matrix(self, layout, circle):
-        for k in range(0, 15):
+        for k in range(15):
             for s, p in enumerate(self.risky_dice):
                 if k == 7 and s == 3:
                     k_prime = 14