Kelly Criterion Poker Bankroll — The Optimal Bet Sizing Formula
Published on: July 2, 2026
The Kelly Criterion: The Mathematician's Betting Strategy
In 1956, a physicist named John Kelly published a paper that would revolutionize gambling and investing. His formula answers a simple question: "What percentage of my bankroll should I bet to grow it as fast as possible without going broke?"
The answer — the Kelly Criterion — is used today by professional poker players, sports bettors, hedge fund managers, and even Warren Buffett.
The Kelly Criterion Formula
$$f^* = \frac{bp - q}{b}$$
Where:
- f* = fraction of bankroll to bet
- b = decimal odds - 1 (the net odds received)
- p = probability of winning
- q = probability of losing (1 - p)
Example: You have a 60% chance of winning a bet at 2.00 decimal odds (even money):
$$f^* = \frac{1 \times 0.60 - 0.40}{1} = \frac{0.20}{1} = 0.20$$
Bet 20% of your bankroll.
Why Kelly Works: The Growth Rate
The Kelly Criterion maximizes the expected logarithm of wealth:
$$G = p \cdot \ln(1 + f \cdot b) + q \cdot \ln(1 - f)$$
This might look complex, but the intuition is simple: Kelly balances growth and survival. Betting too little leaves money on the table. Betting too much risks ruin.
| Strategy | Growth Rate | Risk of Ruin |
|---|---|---|
| Full Kelly | Maximum | ~15% |
| Half Kelly | 75% of max | ~2% |
| Quarter Kelly | 50% of max | <1% |
| Double Kelly | Negative | >50% |
Key insight: Betting more than Kelly reduces long-term growth. This is counterintuitive but mathematically proven.
Practical Example: Poker Tournament
You're in a poker tournament with a $1,000 bankroll. You identify a spot where you have 55% equity at 2.00 odds:
$$f^* = \frac{1 \times 0.55 - 0.45}{1} = 0.10$$
Full Kelly says bet 10% ($100). But in practice, most pros use Half Kelly — bet 5% ($50). This cuts variance in half while sacrificing only 25% of growth.
Kelly in Sports Betting
For sports betting, Kelly is particularly powerful because it accounts for both your edge AND the odds offered:
Example: You estimate a team has a 45% chance of winning at 2.50 odds:
$$f^* = \frac{1.50 \times 0.55 - 0.45}{1.50} = \frac{0.375}{1.50} = 0.25$$
Bet 25% of your bankroll. But if you're not confident in your edge estimate, use Half Kelly (12.5%).
Common Mistakes
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Overestimating your edge. If you think you have 60% equity but actually have 50%, full Kelly will destroy your bankroll. Always be conservative.
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Using full Kelly. The variance is brutal. Even with a genuine edge, you'll face long losing streaks. Use Half Kelly or Quarter Kelly.
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Ignoring bankroll changes. Recalculate after every session. If your bankroll drops 20%, your Kelly bet should drop 20% too.
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Applying Kelly to correlated bets. Kelly assumes independent bets. Don't apply it to multiple bets on the same game.
Try It Now
Use our Kelly Criterion Calculator to calculate optimal bet sizes for any scenario.
Use the Expected Value Calculator to determine your edge before applying Kelly.
Related Tools & Resources
- Kelly Criterion Calculator — Optimal bet sizing tool
- Expected Value Calculator — Calculate your edge
- Is This Bet +EV? — Quick EV checker
- Bankroll Management Guide — Bankroll strategy
- What is Expected Value (EV)? — EV fundamentals