Compute ruin probability with bold betting

Q: Compute ruin probability with bold betting

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Question

Probability of Reaching 5 Tokens Before Ruin

Setup

You start with 3 tokens, target is 5 tokens, and ruin is 0.
On each turn, you bet as many tokens as possible but not more than needed to reach 5. That is, if you have x tokens you bet b(x) = min(x, 5 − x).
Each bet is an independent Bernoulli trial: win with probability 3/5, lose with probability 2/5.

Question: What is the probability that you reach 5 tokens before hitting 0?

Compute ruin probability with bold betting

Probability of Reaching 5 Tokens Before Ruin

Setup

Solution

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