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10.11.2008 at 08:51PM PDT, ID: 23807302
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7.4

snakes & ladders as markov chain

Asked by ArtemisF in Math & Science, Python Scripting Language, Algorithms

How may i find the expected number of throws to finish a snakes and ladders game depending on the value of the initial throw?

I have a board with 25 squares so I made a 26x26 matrix with probabilities of getting to the state.

For e.g. from a 0 the probability of me getting to 0 is _, 1 is _, 2 is _.......25 is _
from a 1 the probability of me getting to 0 is _, 1 is _, 2 is _.......25 is _
and so on.

I don't know how to proceed from here.

Of course I am doing this using python, you can have a look at the code that i have currently. Its just I don't know the concept of how I can find the expected number of throws ...so if someone could shed some light that would be goodStart Free Trial 
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import os
 
from pylab import *
from numpy import *
 
# get the probabilities of going from one state to another.
data = loadtxt("mat.txt")
data = data.reshape(-1,26)
 
# chop off the last row and column
# transition probabilities among the transient states
Q = data[0:25,0:25]
 
# the transition probabilities from transient to absorbing
R = data[0:25,25:26]
#print R
     
# M = (I-Q)^-1       
Matrix = linalg.inv(eye(25)-Q)
 
# B = M*R
B = Matrix*R
#print B
 
count = []
 
for i in Matrix:
    sum =0
    for m in i:
        sum = sum + m
    count.append(sum)
 
Keywords: snakes & ladders as markov chain
Title
1 snakes n ladder
2 snakes n ladders
3 Snakes and ladders in java.
4 Snake
5 Snaking columns
6 snaking columns
 
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[+][-]10.12.2008 at 01:24AM PDT, ID: 22696706

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[+][-]10.12.2008 at 02:28AM PDT, ID: 22696805

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[+][-]10.12.2008 at 02:02PM PDT, ID: 22698852

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About this solution

Zones: Math & Science, Python Scripting Language, Algorithms
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Solution Provided By: PaulKeating
Participating Experts: 2
Solution Grade: A
 
 
[+][-]10.13.2008 at 07:42AM PDT, ID: 22702814

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