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Compute ruin probability with bold betting

SIG (Susquehanna)Data Scientist · Online Assessment

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This question evaluates understanding of probability theory and stochastic processes, focusing on ruin probabilities under a bold betting strategy with state-dependent wagers.

You start with 3 tokens and aim to reach 5 tokens before running out. Each turn you bet as many tokens as possible but not more than needed to reach 5, and you win each bet independently with probability 3/5. What is the probability you reach 5 tokens before ruin?