破产风险
Risk of Ruin
The probability that a poker player will lose their entire bankroll before recovering from downswings, given their win rate, variance, and bankroll size.
Overview
Risk of Ruin (RoR) is a crucial concept in bankroll management, quantifying the chance that a player will go broke due to natural variance. It depends on three key factors: win rate (expected value per hand or tournament), standard deviation (a measure of variance), and bankroll size. A lower RoR indicates a safer bankroll.
Mathematical Foundation
The classic formula for RoR in cash games is:
RoR = e^(-2 * WR * BR / SD²)
where WR is win rate per hand, BR is bankroll in the same unit, and SD is standard deviation per hand. For tournaments, the formula is more complex due to non-normal payout structures. The equation assumes a constant win rate and no withdrawals from the bankroll.
Factors Affecting Risk of Ruin
- Win Rate: A higher win rate reduces RoR exponentially. For example, a winning player with a 5 bb/100 win rate has a much lower RoR than a breakeven player.
- Standard Deviation: Higher variance increases RoR. Loose-aggressive styles and games with deeper stacks or high volatility (e.g., tournaments) have higher SD.
- Bankroll Size: Larger bankrolls reduce RoR. Common guidelines suggest 20–40 buy-ins for cash games and 100+ buy-ins for tournaments to achieve RoR below 5%.
Acceptable Levels
Most serious players aim for a RoR of 1–5%. A 5% RoR means that in 5% of hypothetical careers, the player would go broke before building wealth. For professionals, a 1% RoR or lower is often targeted, as bankruptcy is catastrophic.
Reducing Risk of Ruin
- Proper Bankroll Management: Keep sufficient buy-ins. For example, a 5% RoR with a 5 bb/100 win rate and 100 bb/100 SD requires about 30 buy-ins.
- Move Down in Stakes: If the bankroll drops significantly, drop to lower stakes to rebuild with lower variance.
- Improve Win Rate: Study, review hands, and work on leaks to increase edge.
- Reduce Variance: Tighten play, avoid high-variance spots, or choose games with softer competition.
Limitations
The RoR formula assumes a constant win rate and no tilt or external withdrawals. In reality, win rates can change due to skill improvement, game conditions, or emotional state. Additionally, players often replenish their bankrolls from deposits or other income, which complicates the pure mathematical model.
Conclusion
Understanding Risk of Ruin helps players make rational decisions about stake selection and bankroll growth. It is not a guarantee but a tool for risk assessment. By keeping RoR low, players can survive downswings and continue to profit long-term.