Kelly Criterion Explained: Optimal Bet Sizing
Kelly criterion explained with 4 worked examples. Learn the Kelly formula, why half Kelly beats full Kelly in practice, and how to size every +EV bet.
The bet sizing problem every bettor faces
You have found a +EV bet. The expected value calculation confirms there is edge. Now the question that separates profitable bettors from bankrupt ones: how much do you wager?
Bet too little and you leave profit on the table. Bet too much and a losing streak wipes out your bankroll before the math converges in your favor. This is not a theoretical risk. Professional bettors with real, verified edges go broke because of oversizing. The math of finding edge is simple. The math of sizing it correctly is what keeps you in the game.
The Kelly Criterion solves this problem. Developed by John Kelly at Bell Labs in 1956 for information theory (not gambling), it gives the mathematically optimal fraction of your bankroll to wager on any bet where you have an edge. It maximizes long-term growth rate. No other fixed-fraction strategy grows your bankroll faster over time.
The Kelly formula
For a two-outcome bet at decimal odds d with an estimated win probability p:
Kelly % = (p x d - 1) / (d - 1)
This is equivalent to:
Kelly % = p - (1 - p) / (d - 1)
The output is a fraction. Multiply it by your bankroll to get the dollar amount.
If the formula returns zero or a negative number, the bet is -EV. Kelly will never tell you to wager on a losing proposition. This makes it a useful sanity check independent of its sizing function.
Worked example 1: NFL underdog at +150
You estimate a 45% win probability on a +150 line. In decimal odds, +150 = 2.50.
Kelly % = (0.45 x 2.50 - 1) / (2.50 - 1) = (1.125 - 1) / 1.50 = 0.125 / 1.50 = 8.33%
On a $10,000 bankroll, full Kelly says bet $833. The edge is 12.5% (from the EV calculation), and Kelly translates that into a specific dollar amount.
Worked example 2: heavy favorite at -200
You estimate a 60% win probability on a -200 line. In decimal odds, -200 = 1.50.
Kelly % = (0.60 x 1.50 - 1) / (1.50 - 1) = (0.90 - 1) / 0.50 = -0.10 / 0.50 = -20%
Negative. Kelly says do not bet. Even though the favorite wins 60% of the time, at -200 odds you need to win 66.7% to break even. This bet is -EV. The Kelly formula caught it immediately.
Worked example 3: slight edge on a coin-flip market
You estimate 54% on a -110 line. In decimal odds, -110 = 1.909.
Kelly % = (0.54 x 1.909 - 1) / (1.909 - 1) = (1.031 - 1) / 0.909 = 0.031 / 0.909 = 3.41%
On a $10,000 bankroll, full Kelly says bet $341. This is a thin edge. The bet size reflects that. Kelly naturally scales your wager to your edge: bigger edge, bigger bet. Smaller edge, smaller bet.
Worked example 4: prediction market contract
You find a Kalshi contract at $0.40 (Yes) and believe the true probability is 52%. Decimal odds equivalent for buying Yes at $0.40 is 1 / 0.40 = 2.50.
Kelly % = (0.52 x 2.50 - 1) / (2.50 - 1) = (1.30 - 1) / 1.50 = 0.30 / 1.50 = 20%
Full Kelly says 20% of bankroll. That is aggressive. Before sizing, remember to account for platform fees. Kalshi's fee on profits reduces your effective decimal odds. After a 7% profit fee, your net payout on a win is $0.60 x 0.93 = $0.558 per contract instead of $0.60, making effective decimal odds approximately 2.395. Recalculating:
Adjusted Kelly % = (0.52 x 2.395 - 1) / (2.395 - 1) = (1.245 - 1) / 1.395 = 0.245 / 1.395 = 17.6%
The fee reduces your optimal position size from 20% to 17.6%. Fees always matter. The prediction market fee calculator computes the net impact automatically.
Why full Kelly is dangerous in practice
Full Kelly maximizes the long-term geometric growth rate. That is the theory. In practice, full Kelly has three serious problems that make it unsuitable for almost every bettor.
Problem 1: probability estimation error. The Kelly formula is extremely sensitive to the probability input. If you think you have 55% but the true probability is 52%, full Kelly oversizes substantially. A 3-percentage-point error in your estimate can double or triple the recommended bet size relative to what the correct input would produce. Nobody estimates probabilities perfectly. This estimation error alone is enough to make full Kelly reckless.
Problem 2: brutal variance. Full Kelly has an expected peak-to-trough drawdown of approximately 50% of your bankroll at some point during any extended betting sequence. Read that again. Even with a real, verified edge, you should expect to lose half your bankroll at some point before recovering. Most humans cannot psychologically handle that. And the emotional response to a 50% drawdown is almost always to abandon the strategy, which locks in the loss permanently.
Problem 3: risk of ruin is non-trivial. While theoretical Kelly has zero risk of ruin (because you are always betting a fraction), real-world constraints change the math. Minimum bet sizes, discrete bet amounts, and correlated bets mean actual risk of ruin is higher than the frictionless model suggests.
Fractional Kelly: what professionals actually use
Almost every serious bettor and professional trading operation uses a fraction of Kelly. This is not a compromise. It is the rational response to uncertain probability estimates.
| Strategy | Bet Size | Growth Rate | Variance | Best For |
|---|---|---|---|---|
| Full Kelly | 100% of Kelly | Maximum | Very high | Theoretical only |
| 3/4 Kelly | 75% of Kelly | ~94% of max | Moderate-high | Confident models |
| Half Kelly | 50% of Kelly | ~75% of max | Moderate | Most bettors |
| Quarter Kelly | 25% of Kelly | ~50% of max | Low | Uncertain edge |
Half Kelly is the standard among professionals. It captures approximately 75% of the maximum growth rate while cutting variance dramatically. For the NFL underdog example (full Kelly = $833), half Kelly means betting $417.
The math behind why half Kelly is so efficient: growth rate scales roughly linearly with Kelly fraction up to the full amount, but variance scales with the square of the fraction. Cutting the fraction in half reduces variance by 75% while only reducing growth by 25%. That tradeoff is almost always worth taking.
Quarter Kelly is appropriate when you are uncertain about your edge, working with a smaller bankroll, or dealing with correlated positions where multiple bets share the same underlying risk factor.
Sizing multiple simultaneous bets
Most bettors place more than one bet at a time. Kelly gets more complex here because simultaneous bets share the same bankroll.
The simple approach: if you have three simultaneous Kelly bets at 5%, 3%, and 4%, the total allocation is 12% of your bankroll at risk. If all three lose (unlikely but possible), that is a 12% drawdown in one round.
The conservative approach most professionals use: calculate Kelly for each bet independently, then apply your fractional Kelly multiplier (typically 0.5), and verify that total exposure across all active bets does not exceed a cap (commonly 20-25% of bankroll). If it does, scale every bet proportionally downward.
This is particularly relevant for cross-platform arbitrage where you might have positions open simultaneously on a sportsbook and a prediction market. The Kelly Criterion calculator handles individual bet sizing. For portfolio-level position management across multiple correlated bets, read the correlated positions guide.
When Kelly breaks down
Kelly is optimal under specific assumptions. When those assumptions are violated, the output is unreliable.
Simultaneous correlated bets. Standard Kelly assumes each bet is independent. If you bet the over on total points AND the over on a player prop in the same game, those bets are correlated. Kelly does not account for this without modification.
Unknown true probability. Kelly requires accurate probability input. If you are guessing, the output is worse than useless because it gives you false confidence in a specific bet size. Only use Kelly when you have a genuine basis for your probability estimate, whether from de-vigged sharp lines, a backtested model, or high-liquidity market prices.
Very small bankrolls. If your bankroll is $200, half Kelly on a 3% edge bet might recommend $3. Minimum bet sizes on most platforms exceed that. In this case, you are forced to overbet relative to Kelly, which increases your risk of ruin.
Ignoring bet frequency. Kelly tells you how much to bet. It does not tell you how often to bet. Both matter for long-term growth. A 3% edge at half Kelly over 500 bets per year produces far more growth than an 8% edge at half Kelly over 50 bets per year. This is the bankroll turnover concept. Kelly sizing and bet frequency are both inputs to the growth equation. The turnover calculator shows exactly how frequency affects compounding. If you can find consistent 2-3% edges on high-volume markets, the compounding from higher turnover can easily outperform occasional large edges on niche props.
Kelly for prediction market portfolios
Prediction markets introduce wrinkles that sportsbook Kelly does not address. The most important: you can sell positions before resolution.
On Kalshi or Polymarket, buying a Yes contract at $0.40 and selling at $0.55 before the event resolves is a valid strategy. Kelly was designed for bets that resolve to win or lose. When you can exit early, the optimal sizing depends on your holding period and exit assumptions.
Worked example 5: multi-contract prediction market portfolio
You have a $5,000 prediction market bankroll and find three simultaneous opportunities:
| Contract | Price | Your Prob | Decimal Odds | Kelly % | Half Kelly |
|---|---|---|---|---|---|
| Kalshi event A | $0.35 | 45% | 2.857 | 8.1% | 4.0% |
| Polymarket event B | $0.60 | 70% | 1.667 | 10.0% | 5.0% |
| Kalshi event C | $0.50 | 58% | 2.000 | 16.0% | 8.0% |
Total half Kelly allocation: 4.0% + 5.0% + 8.0% = 17.0% of bankroll ($850 across three positions).
That is within a reasonable 20-25% portfolio cap. But before committing, check whether events A and C on Kalshi are correlated. If both are political events that depend on the same underlying outcome, your true risk is higher than independent Kelly suggests. The correlation calculator quantifies how much to discount, and the correlated positions guide explains the framework.
After accounting for fees, your effective odds decrease. Kalshi's 7% x p x (1-p) taker fee and Polymarket's 2% profit fee both reduce the edge that drives your Kelly sizing. Always run fee-adjusted numbers through the prediction market fee calculator before finalizing position sizes.
When to use fractional Kelly on prediction markets
Quarter Kelly is more appropriate than half Kelly in several prediction market scenarios:
- Low-liquidity markets. If the order book is thin, your entry price will be worse than the displayed price. The liquidity calculator simulates this slippage.
- Long-duration contracts. A contract that resolves in 6 months ties up capital. The opportunity cost of locked capital reduces your effective edge.
- Correlated event clusters. Election markets, economic indicators, and weather events often have hidden correlations. Treat correlated positions as partially overlapping bets and reduce sizing accordingly.
- First-time probability models. If your probability estimate comes from a new or unvalidated model, size conservatively until you have a track record of calibration.
Putting it together: the sizing pipeline
Finding edge is the first step. Sizing that edge correctly is how you survive long enough to realize it.
- Strip the vig to find true probability. Use the de-vig calculator.
- Calculate expected value to confirm the bet is +EV. Use the EV calculator.
- Run the Kelly formula with your probability and the available odds. Use the Kelly Criterion calculator.
- Apply half Kelly (or quarter Kelly if your edge estimate is uncertain).
- Verify total portfolio exposure stays below your cap.
- Place the bet. Track closing line value to verify your edge over time.
Kelly does not make you profitable. Finding +EV bets makes you profitable. Kelly keeps you in the game long enough for the math to work. That distinction matters more than most bettors realize.
For prediction market traders managing multiple positions across platforms, the position sizing guide extends Kelly into a full portfolio framework. For the broader bankroll strategy, including how turnover rate affects compounding, read the bankroll management guide.
Frequently asked questions
- What is the Kelly Criterion in betting?
- The Kelly Criterion is a formula that determines the optimal fraction of your bankroll to bet based on your edge and the odds. The formula is: Kelly % = (p x d - 1) / (d - 1), where p is your estimated win probability and d is the decimal odds. It maximizes long-term bankroll growth.
- Why do most bettors use half Kelly instead of full Kelly?
- Full Kelly produces brutal variance, with expected drawdowns of 50% or more. It is also extremely sensitive to probability estimation errors. Half Kelly captures about 75% of the growth rate while cutting variance by roughly 75%. The tradeoff is almost always worth taking.
- What happens if the Kelly formula returns a negative number?
- A negative Kelly output means the bet is -EV. Do not take it. The formula will never recommend wagering on a losing proposition. A zero or negative result is a signal to pass on the bet entirely.
- Does the Kelly Criterion work for prediction markets?
- Yes. Convert the contract price to decimal odds (1 / price), estimate the true probability, and run the formula. Remember to adjust for platform fees on Kalshi or Polymarket, which reduce your effective odds and therefore your optimal position size.
- How much of my bankroll should I bet on a single wager?
- It depends on your edge and odds, but most professional bettors cap individual bets at 2-5% of bankroll using half Kelly. If your Kelly calculation suggests more than 5% even at half Kelly, verify your probability estimate carefully. Large recommended sizes often indicate overestimated edge.
- How do I use Kelly with correlated prediction market positions?
- Standard Kelly assumes independent bets. For correlated positions (e.g., two political contracts that depend on the same outcome), calculate Kelly independently for each, then apply a correlation discount. A 50% correlation between two positions means reducing combined sizing by roughly 25%. The correlated positions guide covers the full framework.
- Should I use full Kelly or half Kelly for prediction markets?
- Half Kelly at minimum. Prediction markets add fee drag, liquidity risk, and capital lockup that sportsbook bets do not have. Quarter Kelly is appropriate for low-liquidity markets, long-duration contracts, or when your probability model is unvalidated.