Gambling Mathematics Academy
Risk of Ruin: The Question Sizing Has to Answer
Edge and variance together determine the probability that you ever go broke - here is how to think about it.
Direct Answer
Risk of ruin is the probability that a bettor's bankroll falls to zero (or any chosen threshold) given their edge, variance, and bet sizing. For a positive-edge bettor, risk of ruin can be made arbitrarily small with sufficiently conservative sizing.
Key Takeaways
- 01Risk of ruin is a function of edge, variance, and unit size.
- 02A bettor with positive EV can still go broke with excessive sizing.
- 03Conservative sizing approximates risk of ruin near zero.
- 04Monte Carlo simulation handles realistic distributions better than closed-form formulas.
The intuition
For a fixed-stake bettor with positive edge, risk of ruin falls roughly exponentially as unit size shrinks relative to bankroll. Doubling bankroll relative to unit size squares the survival probability.
Simulating it
Monte Carlo simulation - running thousands of randomized bet sequences - produces empirical risk of ruin under realistic assumptions about bet distribution and correlation. Closed-form formulas exist for simple cases but understate ruin probability when bets are correlated or when sizing is dynamic.
Frequently asked questions
What is a safe risk of ruin?+
Professionals typically size to keep risk of ruin below 1% over the relevant time horizon. Below that threshold, ruin becomes a tail event rather than a realistic outcome.
Does risk of ruin apply to fractional Kelly?+
Yes. Fractional Kelly reduces but does not eliminate ruin probability. Combined with conservative unit sizing, fractional Kelly produces both growth and survival.
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