Free Kelly Criterion Calculator | Sports Betting Stake Sizing | Mongoose Bets
Kelly Criterion Calculator
Optimal stake sizing for +EV bets. Quarter Kelly emphasized as the safe default.
What the Kelly criterion does
The Kelly criterion is a formula for calculating the optimal fraction of your bankroll to stake on a +EV bet, given your estimated win probability and the offered odds. It was derived by John Kelly at Bell Labs in 1956 and is the stake size that maximizes the expected long-run growth rate of your bankroll. Larger stakes risk too much; smaller stakes leave money on the table. Kelly is the sweet spot — in theory.
The formula
- Kelly fraction = (p × b − q) / b
- p = your estimated win probability (0-1)
- q = 1 − p (loss probability)
- b = net decimal odds (profit multiplier). For +150, b = 1.5. For -200, b = 0.5.
Worked example: 55% win probability at +100 (even money). b = 1.0, q = 0.45. Kelly = (0.55 × 1 − 0.45) / 1 = 0.10. Stake 10% of your bankroll. On a $1,000 bankroll, that's $100.
If the formula produces a negative number, the bet is -EV and Kelly recommends not betting at all. This calculator clamps to zero when that happens.
Why most pros use fractional Kelly (not full)
Full Kelly is theoretically optimal under three assumptions that often break in practice:
- You know p exactly. In sports betting, your probability estimate is always uncertain. Full Kelly is ruinous if you overestimate your edge.
- You can rebet the whole bankroll after each outcome. Real bet sizes are capped by book limits; you can't always deploy the full stake.
- You're optimizing only for long-run growth, not drawdown. Full Kelly has massive short-term variance. A 50% drawdown is normal even on +EV bets sized at full Kelly.
Common practice: quarter Kelly trades some long-run growth for dramatically reduced variance and protection against probability-estimate error. This calculator highlights quarter Kelly as the default recommendation; the other fractions are shown for comparison.
When to deviate from Kelly
Situations where Kelly sizing is wrong:
- Book limits. If your Kelly stake exceeds the book's per-bet cap, size to the cap and accept the suboptimal stake.
- Correlated bets. Kelly assumes independence. For correlated exposures (multiple bets on the same game), size each at a fraction of the Kelly calculation for the portfolio as a whole — the precise math gets thorny.
- Bankroll is for more than betting. If your "bankroll" includes money you can't afford to lose, use flat units instead.
- Short-term bankroll growth isn't the objective. Recreational bettors maximizing entertainment, not growth, should ignore Kelly entirely.
Frequently asked questions
- What is the Kelly criterion?
- The Kelly criterion is a formula that calculates the optimal fraction of your bankroll to stake on a bet, based on your estimated win probability and the offered odds. It maximizes long-run bankroll growth under the assumptions that your probability estimate is accurate and you can rebet your entire bankroll after each outcome.
- Why should I use fractional Kelly instead of full Kelly?
- Full Kelly assumes you know the true win probability exactly. In sports betting, you never do — your probability estimate always has error. Full Kelly is ruinous when you overestimate your edge. Quarter Kelly (25% of the full Kelly stake) trades some long-run growth for dramatically lower variance and protection against estimate error. Most professional bettors size at quarter or half Kelly.
- What happens if the Kelly calculation returns zero or negative?
- A zero or negative Kelly fraction means the bet is negative expected value — the book's odds don't compensate you enough for the risk. The correct action is not to bet. If you consistently get negative Kelly outputs across your bets, your probability estimates are likely too low or the market is efficient enough that retail edges are rare.
- Does Kelly work for parlays?
- In theory yes, but the math gets complex because parlay legs are often correlated and your probability estimates compound error. In practice, most bettors who use Kelly stick to single bets or straightforward two-leg same-game parlays. For multi-leg parlays, size the whole parlay as a single Kelly bet using the parlay's combined implied probability and your combined estimated probability — do not Kelly-size each leg independently.
For today's actual +EV MLB bets run through 2,500 Monte Carlo simulations, see Best Bets →