Kelly Criterion for Poker Bankroll Management
The Kelly criterion is a mathematical formula that determines the optimal size of a bet to maximize long-term bankroll growth. Originally developed for gambling and investing, it is perfectly applicable to poker tournament selection and bankroll management.
The Kelly Formula
Kelly % = (bp - q) / b, where b = average win/buy-in ratio, p = win probability, q = loss probability (1 - p)
This gives the percentage of your bankroll you should risk on each tournament. For example, if you cash 35% of the time with an average cash of 3x buy-in, Kelly suggests risking about 11.7% of your bankroll per tournament.
Fractional Kelly
Full Kelly maximizes growth rate but produces high variance. Most professional players use fractional Kelly:
| Fraction | Growth Rate | Variance | Best For |
|---|---|---|---|
| Full Kelly (1.0) | Maximum | Very High | Theoretical optimal; rarely used |
| 3/4 Kelly (0.75) | ~94% of max | High | Aggressive players with confirmed edge |
| Half Kelly (0.5) | ~75% of max | Moderate | Most popular among professionals |
| Quarter Kelly (0.25) | ~44% of max | Low | Conservative; building bankroll safely |
Half Kelly is the sweet spot for most players: it sacrifices only 25% of the maximum growth rate while cutting variance in half.
Risk of Ruin
Risk of ruin is the probability of losing your entire bankroll. It depends on your edge, bankroll size, and bet sizing. With proper Kelly sizing, your risk of ruin approaches zero over time. But with over-betting (playing above your bankroll), even a winning player can go broke.
Practical Bankroll Rules
- 100 buy-ins — Minimum for aggressive players with a solid edge
- 200 buy-ins — Standard recommendation for full-time players
- 300+ buy-ins — Conservative, recommended for high-variance formats (MTTs)