Grinstead-Snell-Probability · Problem 11.2.14

Markov Chains

Mathematics · absorbing-markov-chains

Problem

With the situation in Exercise 13, consider the strategy such that for i<4i < 4, Smith bets min⁡(i,4−i)\min(i, 4 - i), and for i≥4i \geq 4, he bets according to the bold strategy, where ii is his current fortune. Find the probability that he gets out of jail using this strategy. How does this probability compare with that obtained for the bold strategy?

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