import numpy as np
import matplotlib.pyplot as plt

bridges = ['TGGGG', 'TTGGG', 'GGGGG']
ps = [0.2, 0.2, 0.6]
trials = []

while len(trials) < 100000:
    bridge = np.random.choice(bridges, p=ps)
    creature = np.random.choice(list(bridge))
    if creature == 'T':
        if bridge.count('T') == 1:
            trials.append(1)
        else:
            trials.append(0)

cumulative_fractions = np.cumsum(trials) / (np.arange(len(trials)) + 1.)

plt.semilogx(cumulative_fractions)
plt.ylim(0, 1)
plt.axhline(1. / 3, color='red', linestyle='--')
plt.xlabel('Number of trials')
plt.ylabel('Cumulative fraction of safe passages');

%timeit np.random.choice(bridges, p=ps)