The game of the goose and markov chains.

markov.gameofthegoose.py

# Natalino Busa
 
# twitter.com/natalinobusa
# linkedin.com/in/natalinobusa
# www.natalinobusa.com

import numpy as np
from matplotlib import pyplot

def special(p, pos_start, pos_end):
  p[pos_start]= np.zeros(64)
  p[pos_start][pos_start]=1
  
  for i in range(64):
    pp = p[i][pos_start]
    p[i][pos_start] = 0
    p[i][pos_end]   = p[i][pos_end] + pp

def snake(p, pos_start, pos_end=0):
  if (pos_end<pos_start):
    special(p, pos_start, pos_end)

def ladder(p, pos_start, pos_end=63):
  if (pos_end>pos_start):
    special(p, pos_start, pos_end)

def fairgame():
  p=np.zeros((64,64))
  
  for i in range(64):
    for j in range(6):
      if (i+j+1<64):
        p[i][i+j+1]=1.0/6.0
  
  p[63][63]=1
  
  p[62][63]=6.0/6.0
  p[61][63]=5.0/6.0
  p[60][63]=4.0/6.0
  p[59][63]=3.0/6.0
  p[58][63]=2.0/6.0
  p[57][63]=1.0/6.0
  
  return p

a=np.zeros(64)
m=fairgame()
snake(m,15)
snake(m,10,8)

for k in range(63):
  pyplot.figure(1)
  pyplot.plot(m[0][0:62])
  
  pyplot.figure(2)
  pyplot.plot(k, m[0][63], 'b.', markersize=5)
  
  a=a+m[0]
  
  pyplot.figure(3)
  pyplot.plot(a[0:62])
  
  m=np.dot(m,p)

pyplot.show()