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Compute ruin probability with bold betting

Last updated: Mar 29, 2026

Quick Overview

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

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Compute ruin probability with bold betting

SIG (Susquehanna)

Aug 11, 2025, 12:00 AM

mediumData ScientistTake-home ProjectStatistics & Math

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?

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