Odds, Probability & Bankroll
Risk of ruin
Risk of ruin is the probability that a bettor will lose their entire bankroll before the session ends or before recovery, given a fixed stake size and edge.
- Also called
- Probability of ruin; in insurance, ruin probability.
- Applies to
- Bankroll management, blackjack, video poker, finance, and actuarial solvency models.
- Key variables
- Stake size, volatility, edge, and number of trials all affect the probability 2.
- No fixed figure
- Risk of ruin is a probability, not a fixed number; it varies with each set of conditions.
Key points
- Risk of ruin is the chance of going bust before a session ends, not the chance of losing a single bet.
- A larger bankroll relative to bet size lowers the risk of ruin, but never eliminates it entirely.
- In blackjack, risk-of-ruin tables show the probability of losing a specific bankroll given a certain bet size and house edge 3.
- The concept also applies to insurance and finance, where ruin means liabilities exceed assets 1.
Example risk-of-ruin table (blackjack, 0.5% house edge)
| Bankroll (units) | Bet size (units) | Risk of ruin |
|---|---|---|
| 200 | 1 | ≈ 2% |
| 200 | 2 | ≈ 18% |
| 100 | 1 | ≈ 13% |
| 100 | 2 | ≈ 55% |
Where this term is used
Related terms
Odds & probability
Risk of ruin blackjack
Applies the general risk-of-ruin concept to blackjack bankrolls, with tables and calculators for session percentages.
Odds & probability
Risk vs odds
Explains the difference between risk (probability of an event) and odds (ratio of outcomes).
Odds & probability
Kelly betting
A staking method that aims to maximise bankroll growth while controlling risk of ruin.
Odds & probability
Roulette payouts
Lists the odds and payouts for common roulette bets, used to calculate session risk.
Odds & probability
Martingale strategy
A betting system that doubles after a loss, which can lead to rapid ruin if a losing streak exceeds the bankroll.
Odds & probability
Kelly criterion
A formula for optimal bet sizing that balances growth and risk of ruin.
Sources
- Ruin theory - Wikipedia en.wikipedia.org Explains ruin theory and the actuarial definition of ruin.
- Session Risk of Ruin Calculator - Wizard of Odds wizardofodds.com Describes the session risk-of-ruin calculator and the variables involved.
- Risk of Ruin in blackjack wizardofodds.com Covers blackjack-specific risk-of-ruin tables and calculations.
Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.