Kelly Criterion Calculator: Optimal Bet Sizing for Any Edge
A free Kelly criterion calculator that computes the mathematically optimal bet size for any edge. Supports American, decimal, and fractional odds with full, half, and quarter Kelly options.
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Kelly Criterion Formula
f* = (bp − q) / b
- f* — fraction of bankroll to wager
- b — net decimal odds (decimal odds − 1)
- p — probability of winning
- q — probability of losing (1 − p)
Fractional Kelly (half, quarter) reduces variance at the cost of slower bankroll growth. If f* ≤ 0, the bet has no edge and should be skipped.
The Kelly Criterion assumes you know the true win probability — in practice, edge estimation is the hard part. Most professional bettors use fractional Kelly (typically half or quarter) to reduce drawdown risk.
The short answer
The calculator above takes three inputs — your bankroll, the odds on offer, and your honest estimate of the true win probability — and returns the mathematically optimal bet size. If you have an edge, it tells you how much to stake. If you don't, it tells you not to bet at all.
Key takeaway: The Kelly criterion maximises long-run bankroll growth by betting proportionally to your edge. Bet too much and a losing streak wipes you out; bet too little and your bankroll grows slower than it should. Kelly finds the exact balance — but only if your probability estimate is accurate.
How to use the calculator
- Enter your bankroll — how much you have available to bet.
- Set the odds — pick American, decimal, or fractional and type the number from the sportsbook.
- Estimate the true win probability — this is the hard part. Use the slider or type a number. Be honest: if you're not sure, round down.
- Choose your Kelly fraction — Full Kelly is mathematically optimal but volatile. Half Kelly cuts the bet in half for a smoother ride. Quarter Kelly is the conservative choice.
- Read the results — optimal bet size, percentage of bankroll, Kelly edge, and expected value per bet.
The Kelly criterion formula
The formula is simple. The hard part is knowing the right probability to feed it.
f* = (bp − q) / b
Where:
- f* = fraction of bankroll to bet
- b = net odds (decimal odds − 1)
- p = true probability of winning
- q = probability of losing (1 − p)
If f* is positive, you have an edge and should bet. If f* is zero or negative, the odds don't justify a bet at any size. The calculator shows this clearly — a negative Kelly edge appears in red with a "No bet" warning.
Why fractional Kelly?
Full Kelly maximises long-run growth, but it's famously volatile. A string of losses can cut your bankroll by 50% or more before it recovers. In practice, most professional bettors and traders use fractional Kelly:
- Half Kelly (0.5×): Captures ~75% of the growth rate with half the variance. The most popular choice among sharps.
- Quarter Kelly (0.25×): Very conservative. Slower growth, much smoother ride.
- Custom: Set any fraction between 0.01 and 1.0.
The reason fractional Kelly works: the growth curve is relatively flat near the peak. Half Kelly barely sacrifices long-term growth but dramatically reduces the chance of a painful drawdown. For a deeper dive, see our bankroll management guide.
When does the Kelly criterion apply?
Kelly works when you have a known, quantifiable edge. That happens in:
- Sports betting: Your model gives a team 60% but the line implies 52% — you have an 8% edge.
- Poker: You know your pot equity and can size bets accordingly. Our poker bankroll management guide covers the buy-in side of this.
- Provably fair games: When the house edge is published and verifiable, you know the exact probability.
Kelly does not work when you can't estimate the true probability. If you're guessing, the formula will happily output a number — but garbage in, garbage out.
How is this different from bankroll management?
The Kelly criterion is one specific mathematical rule for sizing individual bets. Bankroll management is the broader discipline — units, session budgets, stop-loss rules, and the mental game. Think of Kelly as the bet-sizing engine inside a larger bankroll management system.
Our Responsible Gambling & Bankroll course covers the full picture: units and staking, session budgets, tilt control, and when to stop.
What should I learn next?
- Bankroll Management 101: The complete guide to units, limits, and stop rules
- Poker Bankroll Management: How many buy-ins you need
- Value Betting: How to find edges the Kelly criterion can exploit
- Odds Payout Calculator: Calculate what any single bet pays
- Responsible Gambling & Bankroll Course: The full structured course
About the author
Trust & Responsible Play Writer
Marcus focuses on judging casinos before you deposit — licensing checks, red flags, scam patterns — and the bankroll habits and limit tools that keep play under control.