|
| 1 | +""" |
| 2 | +David vs. Goliath Gambler's Ruin Simulation |
| 3 | + |
| 4 | +This program simulates a gambling scenario between two players: David and Goliath. |
| 5 | +David has a skill advantage, represented by a 55% probability of winning each round, |
| 6 | +while Goliath has a size advantage with a larger initial amount of money. |
| 7 | + |
| 8 | +Assumptions: |
| 9 | +- David starts with 2,000,ドル and Goliath starts with 10,000ドル. |
| 10 | +- Each round of betting results in a transfer of 1,000ドル from the loser to the winner. |
| 11 | +- The game continues until one player runs out of money (i.e., their amount reaches zero). |
| 12 | +- The outcome of each round is determined by a random number generator, reflecting David's skill advantage. |
| 13 | + |
| 14 | +Mathematics: |
| 15 | +- The simulation models a stochastic process where each round can be viewed as an independent Bernoulli trial: |
| 16 | + - David wins with a probability of 0.55. |
| 17 | + - Goliath wins with a probability of 0.45. |
| 18 | +- The expected outcomes can be analyzed using concepts from probability theory and stochastic processes. |
| 19 | +- The simulation runs for a specified number of trials to gather statistical data on how often David wins compared to Goliath. |
| 20 | + |
| 21 | +Usage: |
| 22 | +1. Run the program in a Python environment. |
| 23 | +2. Input the desired number of simulations when prompted. |
| 24 | +3. The program will output the number of wins for both David and Goliath and display a bar chart of the results. |
| 25 | + |
| 26 | +This simulation provides insights into how skill can offset size advantages in competitive scenarios. |
| 27 | +""" |
| 28 | + |
| 29 | +import random |
| 30 | +import matplotlib.pyplot as plt |
| 31 | + |
| 32 | +def gambler_ruin(david_initial, goliath_initial, david_win_prob, simulations): |
| 33 | + results = [] |
| 34 | + |
| 35 | + for _ in range(simulations): |
| 36 | + david_amount = david_initial |
| 37 | + goliath_amount = goliath_initial |
| 38 | + |
| 39 | + while david_amount > 0 and goliath_amount > 0: |
| 40 | + # Simulate a single bet based on David's winning probability |
| 41 | + if random.random() < david_win_prob: # David wins |
| 42 | + david_amount += 1000 |
| 43 | + goliath_amount -= 1000 |
| 44 | + else: # Goliath wins |
| 45 | + david_amount -= 1000 |
| 46 | + goliath_amount += 1000 |
| 47 | + |
| 48 | + # Record the result: True if David wins, False if Goliath wins |
| 49 | + results.append(david_amount > 0) |
| 50 | + |
| 51 | + return results |
| 52 | + |
| 53 | +def plot_results(results): |
| 54 | + wins = sum(results) |
| 55 | + losses = len(results) - wins |
| 56 | + |
| 57 | + plt.bar(['David Wins', 'Goliath Wins'], [wins, losses], color=['blue', 'red']) |
| 58 | + plt.title('David vs. Goliath Simulation Results') |
| 59 | + plt.ylabel('Number of Simulations') |
| 60 | + plt.show() |
| 61 | + |
| 62 | +def main(): |
| 63 | + david_initial = 2000 # David's initial amount |
| 64 | + goliath_initial = 10000 # Goliath's initial amount |
| 65 | + david_win_prob = 0.51 # David's skill advantage (55%) |
| 66 | + simulations = int(input("Enter number of simulations: ")) |
| 67 | + |
| 68 | + results = gambler_ruin(david_initial, goliath_initial, david_win_prob, simulations) |
| 69 | + |
| 70 | + print(f"\nResults after {simulations} simulations:") |
| 71 | + print(f"David Wins: {sum(results)}") |
| 72 | + print(f"Goliath Wins: {len(results) - sum(results)}") |
| 73 | + |
| 74 | + plot_results(results) |
| 75 | + |
| 76 | +if __name__ == "__main__": |
| 77 | + main() |
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