Kelly Criterion Calculator
The mathematically optimal bet sizing formula - but only for positive expected value situations.
Why Kelly Criterion Is Different
Kelly Criterion is NOT a betting system like Martingale or Fibonacci. Those systems attempt (and fail) to overcome negative expected value through bet sizing. Kelly is the opposite: it's a formula for optimizing growth when you already have an edge.
- Progression systems: Try to turn -EV into profit (impossible)
- Kelly Criterion: Optimizes +EV situations you've already found
- For casino games: Kelly says bet $0 (the house always wins)
Positive Expected Value Detected
Quick Examples (Positive EV Scenarios)
Betting Parameters
Total bankroll available
Need >50.0% for positive EV
e.g., 1 for even money
Max bet for simulation
How It Works
Understanding the Kelly Formula
The Kelly Criterion was developed by John Kelly at Bell Labs in 1956, originally for optimizing signal transmission. Gamblers quickly recognized its application to betting: given a known edge, how much should you bet to maximize long-term wealth growth?
The Formula
f* = (bp - q) / b
- f* = fraction of bankroll to bet
- b = payout odds (e.g., 1 for even money, 2 for 2:1)
- p = probability of winning
- q = probability of losing (1 - p)
When Kelly Works
Kelly Criterion applies in situations where you have demonstrated positive expected value:
- Sports betting with superior information or models
- Poker against weaker competition
- Blackjack with card counting
- Arbitrage opportunities
- Stock market positions with strong conviction
When Kelly Does NOT Work
Kelly Criterion cannot be applied to negative expected value situations:
- Roulette, craps, slots, or any casino game with house edge
- Sports bets where you don't have an edge over the line
- Any situation where EV is negative or unknown
Why Fractional Kelly?
Full Kelly maximizes growth but comes with brutal drawdowns. The variance can be psychologically devastating even when you're winning long-term. Fractional Kelly reduces bet sizes to smooth the ride:
- Half Kelly: 75% of optimal growth rate with significantly lower variance. Most commonly recommended for practitioners.
- Quarter Kelly: 50% of optimal growth rate with very smooth equity curve. Good for those who prioritize consistency.
Important: Kelly Criterion requires accurate edge estimation. If you overestimate your edge, Kelly will recommend overbetting, which can lead to ruin. When in doubt, use fractional Kelly as a safety margin. And remember - for casino games, the Kelly bet is always zero because the house edge makes your EV negative.
Frequently Asked Questions
Learn More: Guides
Why Betting Systems Always Fail
Mathematical proof of why the Martingale, Fibonacci, Labouchere, and Oscar's Grind cannot overcome the house edge.
Kelly Criterion & Flat Betting Guide
The only approaches with a mathematical foundation — flat betting as the honest baseline and Kelly for genuine positive EV.
Related Calculators
Expected Value Calculator
Calculate expected value to determine if Kelly Criterion applies (requires positive EV).
Risk of Ruin Calculator
Understand bankroll risk for both positive and negative EV scenarios.
Flat Betting Calculator
Compare Kelly-optimized betting to fixed flat betting strategies.
Bankroll Survival Simulator
Monte Carlo simulation to visualize bankroll trajectories over time.
Educational Disclaimer
This calculator is provided for educational purposes only. It demonstrates mathematical principles and does not constitute betting advice or encouragement to gamble. All casino games have negative expected value—the house always wins in the long run. See our full disclaimer.