The Statistics of Chutes and Ladders

A Tech article with View Comments posted 7 July 2009.
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Seeing this node on Chutes and Ladders over at PerlMonks, I thought it would be interesting to throw my hat into the ring. Chutes and Ladders can be represented as a time-homogenous Markov chain with 100 possible states. Each state transition can be represented in a matrix (size 100×100) of transition probabilities T, where T_ij is the probability of transitioning from state i to state j. Then you represent the probability of being in a certain state after a transition as the 1×100 matrix P, where for the beginning of the game (P_0) the first entry is 1 and the other ninety-nine are 0.

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