For two words that are not subwords of each other in a Markovian letter stream, the probability of reaching A points before losing B points and the expected game duration can be computed by reducing the process to a correlated random walk.
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On a Variation of Gambler's Ruin Problem
For two words that are not subwords of each other in a Markovian letter stream, the probability of reaching A points before losing B points and the expected game duration can be computed by reducing the process to a correlated random walk.