import numpy as np
import random
import matplotlib.pyplot as plt
n = 100
states_visited_Y = []
states_visited_X = []
gamblers_ruin = []
X_t = 30
Y_t = 70
while True:
print("gambler's ruin", (Y_t - X_t) % n)
gamblers_ruin.append( (Y_t - X_t) % n )
states_visited_Y.append(Y_t)
states_visited_X.append(X_t)
which_chain = random.choice(["X", "Y"])
move = np.random.choice([-1, 1])
if which_chain == "X":
X_t = (X_t + move) % n
else:
Y_t = (Y_t + move) % n
if X_t == Y_t:
break
gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 43 gambler's ruin 44 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 34 gambler's ruin 33 gambler's ruin 34 gambler's ruin 33 gambler's ruin 32 gambler's ruin 31 gambler's ruin 32 gambler's ruin 33 gambler's ruin 34 gambler's ruin 35 gambler's ruin 34 gambler's ruin 33 gambler's ruin 32 gambler's ruin 33 gambler's ruin 32 gambler's ruin 33 gambler's ruin 34 gambler's ruin 33 gambler's ruin 32 gambler's ruin 33 gambler's ruin 32 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 12 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 12 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 12 gambler's ruin 11 gambler's ruin 10 gambler's ruin 11 gambler's ruin 12 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 15 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 15 gambler's ruin 14 gambler's ruin 13 gambler's ruin 12 gambler's ruin 11 gambler's ruin 12 gambler's ruin 11 gambler's ruin 10 gambler's ruin 9 gambler's ruin 8 gambler's ruin 9 gambler's ruin 8 gambler's ruin 7 gambler's ruin 6 gambler's ruin 5 gambler's ruin 4 gambler's ruin 5 gambler's ruin 4 gambler's ruin 5 gambler's ruin 6 gambler's ruin 5 gambler's ruin 6 gambler's ruin 5 gambler's ruin 4 gambler's ruin 5 gambler's ruin 6 gambler's ruin 7 gambler's ruin 6 gambler's ruin 7 gambler's ruin 8 gambler's ruin 9 gambler's ruin 10 gambler's ruin 11 gambler's ruin 12 gambler's ruin 11 gambler's ruin 12 gambler's ruin 11 gambler's ruin 10 gambler's ruin 11 gambler's ruin 10 gambler's ruin 11 gambler's ruin 12 gambler's ruin 13 gambler's ruin 14 gambler's ruin 15 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 14 gambler's ruin 13 gambler's ruin 14 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 15 gambler's ruin 16 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 32 gambler's ruin 33 gambler's ruin 32 gambler's ruin 33 gambler's ruin 34 gambler's ruin 35 gambler's ruin 34 gambler's ruin 33 gambler's ruin 34 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 37 gambler's ruin 38 gambler's ruin 39 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 43 gambler's ruin 44 gambler's ruin 45 gambler's ruin 46 gambler's ruin 45 gambler's ruin 46 gambler's ruin 47 gambler's ruin 46 gambler's ruin 45 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 45 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 49 gambler's ruin 50 gambler's ruin 49 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 49 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 49 gambler's ruin 50 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 53 gambler's ruin 54 gambler's ruin 53 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 53 gambler's ruin 52 gambler's ruin 51 gambler's ruin 50 gambler's ruin 49 gambler's ruin 50 gambler's ruin 51 gambler's ruin 50 gambler's ruin 49 gambler's ruin 50 gambler's ruin 51 gambler's ruin 50 gambler's ruin 49 gambler's ruin 50 gambler's ruin 49 gambler's ruin 50 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 50 gambler's ruin 51 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 53 gambler's ruin 54 gambler's ruin 55 gambler's ruin 56 gambler's ruin 57 gambler's ruin 58 gambler's ruin 57 gambler's ruin 56 gambler's ruin 55 gambler's ruin 56 gambler's ruin 55 gambler's ruin 56 gambler's ruin 55 gambler's ruin 54 gambler's ruin 53 gambler's ruin 52 gambler's ruin 51 gambler's ruin 52 gambler's ruin 53 gambler's ruin 54 gambler's ruin 53 gambler's ruin 54 gambler's ruin 53 gambler's ruin 52 gambler's ruin 51 gambler's ruin 50 gambler's ruin 49 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 45 gambler's ruin 44 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 34 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 34 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 38 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 34 gambler's ruin 33 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 32 gambler's ruin 33 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 33 gambler's ruin 32 gambler's ruin 33 gambler's ruin 34 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 34 gambler's ruin 35 gambler's ruin 34 gambler's ruin 35 gambler's ruin 34 gambler's ruin 33 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 24 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 19 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 17 gambler's ruin 18 gambler's ruin 19 gambler's ruin 20 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 22 gambler's ruin 21 gambler's ruin 22 gambler's ruin 21 gambler's ruin 20 gambler's ruin 21 gambler's ruin 22 gambler's ruin 23 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 24 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 26 gambler's ruin 25 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 29 gambler's ruin 28 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 27 gambler's ruin 26 gambler's ruin 27 gambler's ruin 28 gambler's ruin 29 gambler's ruin 28 gambler's ruin 29 gambler's ruin 30 gambler's ruin 31 gambler's ruin 32 gambler's ruin 31 gambler's ruin 32 gambler's ruin 33 gambler's ruin 34 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 36 gambler's ruin 35 gambler's ruin 36 gambler's ruin 37 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 44 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 44 gambler's ruin 43 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 41 gambler's ruin 40 gambler's ruin 39 gambler's ruin 38 gambler's ruin 39 gambler's ruin 40 gambler's ruin 41 gambler's ruin 42 gambler's ruin 43 gambler's ruin 44 gambler's ruin 43 gambler's ruin 44 gambler's ruin 43 gambler's ruin 44 gambler's ruin 45 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 45 gambler's ruin 46 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 48 gambler's ruin 47 gambler's ruin 46 gambler's ruin 47 gambler's ruin 46 gambler's ruin 45 gambler's ruin 46 gambler's ruin 45 gambler's ruin 44 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ruin 62 gambler's ruin 61 gambler's ruin 62 gambler's ruin 61 gambler's ruin 62 gambler's ruin 61 gambler's ruin 60 gambler's ruin 59 gambler's ruin 58 gambler's ruin 59 gambler's ruin 60 gambler's ruin 59 gambler's ruin 58 gambler's ruin 59 gambler's ruin 58 gambler's ruin 59 gambler's ruin 60 gambler's ruin 59 gambler's ruin 58 gambler's ruin 57 gambler's ruin 58 gambler's ruin 57 gambler's ruin 58 gambler's ruin 57 gambler's ruin 56 gambler's ruin 57 gambler's ruin 56 gambler's ruin 57 gambler's ruin 56 gambler's ruin 55 gambler's ruin 54 gambler's ruin 55 gambler's ruin 56 gambler's ruin 57 gambler's ruin 56 gambler's ruin 55 gambler's ruin 56 gambler's ruin 55 gambler's ruin 56 gambler's ruin 57 gambler's ruin 56 gambler's ruin 55 gambler's ruin 54 gambler's ruin 53 gambler's ruin 54 gambler's ruin 55 gambler's ruin 56 gambler's ruin 57 gambler's ruin 58 gambler's ruin 57 gambler's ruin 58 gambler's ruin 59 gambler's ruin 58 gambler's ruin 57 gambler's ruin 56 gambler's ruin 57 gambler's ruin 58 gambler's ruin 59 gambler's ruin 60 gambler's ruin 59 gambler's ruin 60 gambler's ruin 61 gambler's ruin 62 gambler's ruin 63 gambler's ruin 64 gambler's ruin 63 gambler's ruin 64 gambler's ruin 63 gambler's ruin 62 gambler's ruin 61 gambler's ruin 60 gambler's ruin 59 gambler's ruin 60 gambler's ruin 61 gambler's ruin 62 gambler's ruin 63 gambler's ruin 64 gambler's ruin 63 gambler's ruin 62 gambler's ruin 63 gambler's ruin 64 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 68 gambler's ruin 67 gambler's ruin 68 gambler's ruin 67 gambler's ruin 68 gambler's ruin 69 gambler's ruin 68 gambler's ruin 67 gambler's ruin 66 gambler's ruin 65 gambler's ruin 64 gambler's ruin 63 gambler's ruin 64 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 66 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 66 gambler's ruin 67 gambler's ruin 68 gambler's ruin 67 gambler's ruin 66 gambler's ruin 67 gambler's ruin 68 gambler's ruin 69 gambler's ruin 68 gambler's ruin 67 gambler's ruin 66 gambler's ruin 65 gambler's ruin 64 gambler's ruin 65 gambler's ruin 66 gambler's ruin 67 gambler's ruin 66 gambler's ruin 67 gambler's ruin 68 gambler's ruin 69 gambler's ruin 68 gambler's ruin 69 gambler's ruin 68 gambler's ruin 69 gambler's ruin 70 gambler's ruin 69 gambler's ruin 70 gambler's ruin 69 gambler's ruin 70 gambler's ruin 71 gambler's ruin 70 gambler's ruin 71 gambler's ruin 72 gambler's ruin 71 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 75 gambler's ruin 74 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 73 gambler's ruin 72 gambler's ruin 71 gambler's ruin 70 gambler's ruin 71 gambler's ruin 72 gambler's ruin 71 gambler's ruin 70 gambler's ruin 69 gambler's ruin 70 gambler's ruin 71 gambler's ruin 70 gambler's ruin 71 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 71 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 76 gambler's ruin 75 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 73 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 75 gambler's ruin 74 gambler's ruin 75 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 75 gambler's ruin 76 gambler's ruin 75 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 71 gambler's ruin 70 gambler's ruin 71 gambler's ruin 72 gambler's ruin 73 gambler's ruin 72 gambler's ruin 71 gambler's ruin 70 gambler's ruin 69 gambler's ruin 70 gambler's ruin 71 gambler's ruin 70 gambler's ruin 71 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 73 gambler's ruin 72 gambler's ruin 73 gambler's ruin 74 gambler's ruin 75 gambler's ruin 76 gambler's ruin 77 gambler's ruin 76 gambler's ruin 77 gambler's ruin 78 gambler's ruin 79 gambler's ruin 80 gambler's ruin 81 gambler's ruin 80 gambler's ruin 81 gambler's ruin 82 gambler's ruin 83 gambler's ruin 82 gambler's ruin 81 gambler's ruin 82 gambler's ruin 81 gambler's ruin 82 gambler's ruin 83 gambler's ruin 84 gambler's ruin 83 gambler's ruin 84 gambler's ruin 85 gambler's ruin 86 gambler's ruin 87 gambler's ruin 86 gambler's ruin 85 gambler's ruin 84 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 84 gambler's ruin 83 gambler's ruin 82 gambler's ruin 83 gambler's ruin 82 gambler's ruin 83 gambler's ruin 84 gambler's ruin 83 gambler's ruin 84 gambler's ruin 83 gambler's ruin 82 gambler's ruin 81 gambler's ruin 82 gambler's ruin 83 gambler's ruin 84 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 84 gambler's ruin 85 gambler's ruin 84 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 86 gambler's ruin 85 gambler's ruin 84 gambler's ruin 85 gambler's ruin 86 gambler's ruin 87 gambler's ruin 88 gambler's ruin 87 gambler's ruin 86 gambler's ruin 87 gambler's ruin 88 gambler's ruin 89 gambler's ruin 90 gambler's ruin 89 gambler's ruin 90 gambler's ruin 91 gambler's ruin 92 gambler's ruin 93 gambler's ruin 92 gambler's ruin 91 gambler's ruin 90 gambler's ruin 89 gambler's ruin 88 gambler's ruin 89 gambler's ruin 88 gambler's ruin 89 gambler's ruin 90 gambler's ruin 89 gambler's ruin 90 gambler's ruin 89 gambler's ruin 88 gambler's ruin 87 gambler's ruin 88 gambler's ruin 89 gambler's ruin 88 gambler's ruin 87 gambler's ruin 88 gambler's ruin 87 gambler's ruin 88 gambler's ruin 87 gambler's ruin 88 gambler's ruin 89 gambler's ruin 90 gambler's ruin 89 gambler's ruin 90 gambler's ruin 89 gambler's ruin 90 gambler's ruin 91 gambler's ruin 90 gambler's ruin 91 gambler's ruin 92 gambler's ruin 91 gambler's ruin 92 gambler's ruin 93 gambler's ruin 94 gambler's ruin 95 gambler's ruin 94 gambler's ruin 93 gambler's ruin 94 gambler's ruin 93 gambler's ruin 94 gambler's ruin 95 gambler's ruin 94 gambler's ruin 95 gambler's ruin 96 gambler's ruin 97 gambler's ruin 98 gambler's ruin 97 gambler's ruin 96 gambler's ruin 97 gambler's ruin 98 gambler's ruin 99
# First 10 visited states
T = len(states_visited_X)
states_visited_X[:10], states_visited_Y[:10]
([30, 30, 29, 29, 28, 28, 27, 27, 28, 27], [70, 69, 69, 68, 68, 67, 67, 68, 68, 68])
%matplotlib inline
fig, (ax1, ax2) = plt.subplots(2)
ax2.plot(range(T), gamblers_ruin, c="green", label="distance $Y_t-X_t$")
ax1.plot(range(T), states_visited_X, label="$X_t$")
ax1.plot(range(T), states_visited_Y, label="$Y_t$")
ax1.legend()
ax2.legend()
<matplotlib.legend.Legend at 0x7f742c858210>
#%matplotlib qt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(range(T),
np.cos(2*np.pi*np.array(states_visited_X)/n),
np.sin(2*np.pi*np.array(states_visited_X)/n),
label="X_t")
ax.plot(range(T),
np.cos(2*np.pi*np.array(states_visited_Y)/n),
np.sin(2*np.pi*np.array(states_visited_Y)/n),
label="Y_t")
plt.legend()
ax.set_axis_off()
for a in range(n):
ax.plot(range(T),
np.cos(2*np.pi*a*np.ones(T)/n),
np.sin(2*np.pi*a*np.ones(T)/n),
c="grey", alpha=0.1)
