Created
November 18, 2013 05:34
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Solve http://www.puzzlor.com/2013-10_ChutesLadders.html using http://en.wikipedia.org/wiki/Absorbing_Markov_chain
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# 1 2 3 5 8 10 11 | |
Q = [0, 1/3, 1/3, 1/3, 0, 0, 0; #1 | |
0, 0, 1/3, 2/3, 0, 0, 0; #2 | |
0, 0, 0, 2/3, 0, 0, 1/3; #3 | |
0, 1/3, 0, 0, 1/3, 0, 1/3; #5 | |
0, 0, 0, 0, 1/3, 1/3, 1/3; #8 | |
0, 0, 0, 0, 0, 0, 1/3; #10 | |
0, 0, 0, 0, 0, 0, 0] #11 | |
N = (eye(7) - Q) ^ - 1 | |
t = N * ones(7,1) | |
## Q = | |
## 0.00000 0.33333 0.33333 0.33333 0.00000 0.00000 0.00000 | |
## 0.00000 0.00000 0.33333 0.66667 0.00000 0.00000 0.00000 | |
## 0.00000 0.00000 0.00000 0.66667 0.00000 0.00000 0.33333 | |
## 0.00000 0.33333 0.00000 0.00000 0.33333 0.00000 0.33333 | |
## 0.00000 0.00000 0.00000 0.00000 0.33333 0.33333 0.33333 | |
## 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.33333 | |
## 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 | |
## N = | |
## 1.00000 0.73684 0.57895 1.21053 0.60526 0.20175 0.86550 | |
## 0.00000 1.42105 0.47368 1.26316 0.63158 0.21053 0.85965 | |
## 0.00000 0.31579 1.10526 0.94737 0.47368 0.15789 0.89474 | |
## 0.00000 0.47368 0.15789 1.42105 0.71053 0.23684 0.84211 | |
## 0.00000 0.00000 0.00000 0.00000 1.50000 0.50000 0.66667 | |
## 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.33333 | |
## 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 | |
## t = | |
## 5.1988 # Expected number of moves from space 1 | |
## 4.8596 # Expected number of moves from space 2 | |
## 3.8947 # Expected number of moves from space 3 | |
## 3.8421 # Expected number of moves from space 5 | |
## 2.6667 # Expected number of moves from space 8 | |
## 1.3333 # Expected number of moves from space 10 | |
## 1.0000 # Expected number of moves from space 11 |
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