python_scripts_rcsmit/leela scipython elegant.py at master · rcsmit/python_scripts_rcsmit · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
# -*- coding: utf-8 -*-
"""
Created on Tue Oct 27 15:25:34 2020

@author: rcxsm
"""
#https://scipython.com/book/chapter-6-numpy/additional-problems/analysing-snakes-and-ladders-as-a-markov-chain/
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns


#ladders = [(3,19), (15,37), (22,42), (25,64), (41,73),
#           (53,74), (63,86), (76,91), (84,98)]
#snakes = [(11,7), (18,13), (28,12), (36,34), (77,16),
#          (47,26), (83,39), (92,75), (99,70)]
#trans = ladders + snakes


laddersx = [(9,22),(16,68),(19,31),(

    21,59),(
    26,40),(
    27,49),(

    44,66),(
    36,65),(
    45,61),(
    53,67)]

snakesx = [(62,1),(
    54,2),(
    15,3),(

    28,5),(
    23,6),(
    11,7),(

    43,8),(
    51,34),(
    72,51)]

ladders = [
    (1,38),
    (4,14),
    (9,31),
    (21,42),
    (28,84),
    (36,44),
    (51,67),
    (71,91),
    (80,100)]
snakes = [(16,6),
    (47,26),
    (49,11),
    (56,53),
    (62,19),
    (64,60),
    (87,24),
    (93,73),
    (95,75),
    (98,78)]
trans = ladders + snakes
# Set up the transition matrix
T = np.zeros((101, 101))
for i in range(1,101):
    T[i-1,i:i+6] = 1/6

for (i1,i2) in trans:
    iw = np.where(T[:,i1] > 0)
    T[:,i1] = 0
    T[iw,i2] += 1/6

# House rules: you don't need to land on 100, just reach it.
T[95:100,100] += np.linspace(1/6, 5/6, 5)
for snake in snakes:
    T[snake,100] = 0

# The player starts at position 0.
v = np.zeros(101)
v[0] = 1

n, P = 0, []
cumulative_prob = 0
# Update the state vector v until the cumulative probability of winning
# is "effectively" 1
while cumulative_prob < 0.99999:
    n += 1
    v = v.dot(T)
    P.append(v[100])
    cumulative_prob += P[-1]
mode = np.argmax(P)+1
print('modal number of moves:', mode)

# Plot the probability of winning as a function of the number of moves
fig, ax = plt.subplots()
ax.plot(np.linspace(1,n,n), P, 'g-', lw=2, alpha=0.6, label='Markov')
ax.set_xlabel('Number of moves')
ax.set_ylabel('Probability of winning')

plt.show()