%matplotlib inline

import matplotlib.pyplot as plt
from random import random

a = 4     # player a's starting dollar amount
b = 6     # player b's starting dollar amount
p = 0.50  # probability that player a wins a round
          # p = 0.5 represents a fair coin

original_a = a
original_b = b

a_wins = 0
b_wins = 0

trials = 100000

prob_a_wins = []


for i in range(trials):
    while a != 0 and b != 0:
        if random() < p:
            a += 1
            b -= 1
        else:
            a -= 1
            b += 1
    if b == 0:
        a_wins += 1
    else:
        b_wins += 1

    prob_a_wins.append(1.0 * a_wins / (a_wins + b_wins))

    a = original_a
    b = original_b

plt.plot(prob_a_wins)
plt.ylabel("Estimated P(A wins)")
plt.xlabel("Trial Number")
plt.show()

print("P(A wins) = " + str(prob_a_wins[-1]))