Create gamblers_ruin.py

Author: devAmoghS

gamblers_ruin.py

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+"""
+David vs. Goliath Gambler's Ruin Simulation
+
+This program simulates a gambling scenario between two players: David and Goliath.
+David has a skill advantage, represented by a 55% probability of winning each round,
+while Goliath has a size advantage with a larger initial amount of money.
+
+Assumptions:
+- David starts with $2,000, and Goliath starts with $10,000.
+- Each round of betting results in a transfer of $1,000 from the loser to the winner.
+- The game continues until one player runs out of money (i.e., their amount reaches zero).
+- The outcome of each round is determined by a random number generator, reflecting David's skill advantage.
+
+Mathematics:
+- The simulation models a stochastic process where each round can be viewed as an independent Bernoulli trial:
+  - David wins with a probability of 0.55.
+  - Goliath wins with a probability of 0.45.
+- The expected outcomes can be analyzed using concepts from probability theory and stochastic processes.
+- The simulation runs for a specified number of trials to gather statistical data on how often David wins compared to Goliath.
+
+Usage:
+1. Run the program in a Python environment.
+2. Input the desired number of simulations when prompted.
+3. The program will output the number of wins for both David and Goliath and display a bar chart of the results.
+
+This simulation provides insights into how skill can offset size advantages in competitive scenarios.
+"""
+
+import random
+import matplotlib.pyplot as plt
+
+def gambler_ruin(david_initial, goliath_initial, david_win_prob, simulations):
+    results = []
+    
+    for _ in range(simulations):
+        david_amount = david_initial
+        goliath_amount = goliath_initial
+        
+        while david_amount > 0 and goliath_amount > 0:
+            # Simulate a single bet based on David's winning probability
+            if random.random() < david_win_prob:  # David wins
+                david_amount += 1000
+                goliath_amount -= 1000
+            else:  # Goliath wins
+                david_amount -= 1000
+                goliath_amount += 1000
+        
+        # Record the result: True if David wins, False if Goliath wins
+        results.append(david_amount > 0)
+    
+    return results
+
+def plot_results(results):
+    wins = sum(results)
+    losses = len(results) - wins
+    
+    plt.bar(['David Wins', 'Goliath Wins'], [wins, losses], color=['blue', 'red'])
+    plt.title('David vs. Goliath Simulation Results')
+    plt.ylabel('Number of Simulations')
+    plt.show()
+
+def main():
+    david_initial = 2000  # David's initial amount
+    goliath_initial = 10000  # Goliath's initial amount
+    david_win_prob = 0.51  # David's skill advantage (55%)
+    simulations = int(input("Enter number of simulations: "))
+
+    results = gambler_ruin(david_initial, goliath_initial, david_win_prob, simulations)
+    
+    print(f"\nResults after {simulations} simulations:")
+    print(f"David Wins: {sum(results)}")
+    print(f"Goliath Wins: {len(results) - sum(results)}")
+    
+    plot_results(results)
+
+if __name__ == "__main__":
+    main()