Poker Bankruptcy Probability Calculation and Risk Management Model
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This article introduces the calculation formula for poker bankruptcy probability and risk management models, helping players scientifically set bankroll management and game levels to reduce bankruptcy risk. Includes specific numerical examples and practical application steps.
Tool Purpose
Risk of Ruin (RoR) is a measure of the probability that a player will eventually lose all of their bankroll given a certain bankroll size, win rate, and variance. Bankroll management models are used to determine appropriate game levels and minimum bankroll thresholds to ensure long-term survival.
Calculation Formula Principle
The simplified formula for Risk of Ruin (assuming a fixed win rate and equal bet size) is:
RoR = ( (1 - w) / w )^B
Where:
- w = win rate (probability of winning each bet)
- B = bankroll units (total bankroll divided by single bet size)
In actual poker, due to variance and varying bet sizes, a more precise model is commonly used:
RoR = e^(-2 * WR * BR / Variance)
Where:
- WR = win rate (expected profit per hour or per 100 hands)
- BR = bankroll (in the same unit as WR)
- Variance = variance (a measure of fluctuation magnitude)
Usage Steps
- Estimate your win rate: Based on historical data or reasonable estimates (e.g., online NL10 about 5bb/100 hands).
- Estimate variance: Typical cash game variance is around 80-100 bb²/100 hands; tournaments are higher.
- Set an acceptable Risk of Ruin: Usually less than 5% (strict) or less than 1% (conservative).
- Calculate required bankroll: Rearrange the formula to find the minimum bankroll.
- Adjust dynamically: Move up in stakes as bankroll grows; move down as it shrinks.
Practical Example
Suppose you play $0.05/$0.10 cash games, with a win rate (WR) of 5bb/100 hands (i.e., winning $0.05 per 100 hands) and variance of 80 bb²/100 hands. Acceptable Risk of Ruin is 1%.
Calculate required bankroll (in bb): RoR = e^(-2 * WR * BR / Variance) = 0.01 Take natural log: ln(0.01) = -2 * 5 * BR / 80 -4.60517 = -10 BR / 80 => BR = (4.60517 * 80) / 10 = 36.84 bb
However, this is the simplest model. In practice, at least 20-40 buy-ins (about 200-400bb) are recommended. For example, at $0.05/$0.10 with a $10 buy-in (100bb), suggested bankroll is $200-$400.
Frequently Asked Questions
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Q: Why is the actual recommended bankroll much larger than the calculated value? A: The formula assumes a stable win rate, but in reality win rate fluctuates, and there are downswings and rake. Larger multiples are used conservatively.
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Q: When should I move up after winning money? A: When your bankroll reaches the minimum required for the new level (e.g., 20 buy-ins) and your win rate at the old level remains positive.
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Q: Is a 10% Risk of Ruin acceptable? A: It is possible but risky; 10% means a one-in-ten chance of going broke in the long run. Beginners are advised to stay below 5%.
Extended Learning
- Learn to use poker tracking software (e.g., Hold'em Manager, PokerTracker) to accurately estimate WR and variance.
- Study more advanced Kelly Criterion for bankroll growth.
- Understand the different bankroll management strategies for tournaments vs. cash games (due to variance differences).