Free Kelly Criterion Calculator
Find the mathematically optimal bet size based on your edge and odds. Supports full, half, and quarter Kelly with all major odds formats.
The odds do not compensate for the risk. Do not wager.
| Strategy | Fraction | Stake | Payout if Win |
|---|---|---|---|
| Full Kelly | - | - | - |
| Half Kelly | - | - | - |
| Quarter Kelly | - | - | - |
TL;DR
The Kelly Criterion tells you exactly what percentage of your bankroll to stake on a bet to maximize long-term growth. Enter your odds, your estimated true win probability, and your bankroll. If you have a positive edge, the calculator shows the optimal stake for full, half, and quarter Kelly. Half Kelly is the sweet spot for most bettors. It captures most of the growth while cutting variance dramatically.
What Is the Kelly Criterion?
The Kelly Criterion is a formula for optimal bet sizing developed by John L. Kelly Jr. at Bell Labs in 1956. Originally designed for information theory and long-distance telephone signal optimization, it was quickly adopted by gamblers and investors who recognized its power: it tells you the exact fraction of your bankroll to wager on each bet to maximize the long-term compound growth rate of your wealth.
The core insight is simple. Bet too little and you leave growth on the table. Bet too much and a losing streak will devastate your bankroll. The Kelly fraction is the mathematically precise sweet spot between the two extremes. It is the staking strategy that, over a large number of bets, produces the highest terminal wealth with probability approaching certainty.
For sports bettors and prediction market traders on platforms like Kalshi and Polymarket, the Kelly Criterion is the gold standard for bankroll management. Use it alongside our expected value calculator to validate your edge before sizing your positions.
The Kelly Formula Explained
The standard Kelly formula for a simple win/lose bet is:
f* = (b × p - q) / b
Where:
- f* = the fraction of your bankroll to bet
- b = net odds received (decimal odds minus 1). At decimal odds of 2.50, b = 1.50
- p = the probability of winning (your true estimate, not the implied probability from the odds)
- q = the probability of losing (1 - p)
If the result is positive, you have an edge and should bet that fraction. If the result is zero or negative, you have no edge at those odds and should not bet. A negative Kelly value is a clear signal to walk away, or consider betting the other side.
Worked Example
Suppose you find a line at decimal odds of 2.50 (American +150) and you estimate the true win probability at 45%. Here is the calculation:
- Net odds: b = 2.50 - 1 = 1.50
- Kelly fraction: f* = (1.50 × 0.45 - 0.55) / 1.50 = (0.675 - 0.55) / 1.50 = 0.0833
- On a $1,000 bankroll: Full Kelly stake = $83.33, Half Kelly = $41.67, Quarter Kelly = $20.83
- If the bet wins at 2.50, your full Kelly payout is $208.33 (profit of $125.00)
The edge in this case is (0.45 × 2.50) - 1 = 12.5%. That is a strong edge. But notice that full Kelly says to risk over 8% of your bankroll on a single bet. For most bettors, half Kelly ($41.67) is the smarter play.
Full Kelly vs Half Kelly vs Quarter Kelly
Full Kelly maximizes long-term growth, but it comes with gut-wrenching variance. Research shows that full Kelly can produce drawdowns of 50% or more even with a genuine edge. In practice, almost no professional bettor or trader uses full Kelly. Here is how the three strategies compare:
| Strategy | Growth Rate | Variance | Best For |
|---|---|---|---|
| Full Kelly | Maximum | Very high | Theoretical optimum, rarely used in practice |
| Half Kelly | ~75% of full | ~25% of full | Most professional bettors and traders |
| Quarter Kelly | ~50% of full | ~6% of full | Low confidence, new markets, longshots |
Half Kelly is the industry standard. You sacrifice roughly 25% of your expected growth rate but reduce variance by about 75%. That tradeoff is almost always worth it because your probability estimates are never perfectly accurate. If your true edge is smaller than you think, full Kelly will overbet and hurt you. Half Kelly builds in a natural buffer against estimation error.
Quarter Kelly is appropriate when you are exploring a new market, when your probability model is unproven, or when you are trading volatile prediction market contracts where prices swing fast.
Kelly Criterion for Arbitrage Betting
In pure arbitrage betting, where you cover all outcomes for a guaranteed profit, Kelly is not strictly necessary. Arbitrage has no risk in theory, so you stake the maximum your bankroll allows and collect the guaranteed spread. Our arbitrage betting calculator handles the optimal stake split between legs.
But real-world arbitrage is not risk-free. Legs can fail to fill, prices move between execution of leg 1 and leg 2, and prediction market contracts on Kalshi or Polymarket can have thin liquidity. In these quasi-arbitrage scenarios, Kelly helps you size exposure relative to the probability that the arb actually completes. If you estimate a 90% chance of completing both legs of an arb with a 3% guaranteed return, Kelly will tell you to stake less than if you had 99% confidence.
This is exactly the kind of situation Claw Arbs handles automatically. The execution engine accounts for fill probability, slippage, and naked leg risk when sizing positions across venues.
Kelly for Prediction Markets
Prediction markets like Kalshi and Polymarket use probability-based pricing rather than traditional odds. A Kalshi contract at 62 cents implies a 62% probability; a Polymarket contract at 0.38 implies 38%. To use Kelly, convert the contract price to decimal odds using our odds converter:
- Kalshi 62 cents → decimal odds of 1 / 0.62 = 1.613
- Polymarket 0.38 → decimal odds of 1 / 0.38 = 2.632
Then plug those decimal odds into the Kelly formula along with your true probability estimate. If you believe the true probability is 55% but Kalshi is pricing it at 48 cents (decimal 2.083), your Kelly fraction tells you the correct position size for that edge.
The key challenge in prediction markets is estimating the true probability accurately. Unlike sports where you can build statistical models from historical data, many prediction market events are unique (elections, macro events, policy outcomes). This is why most prediction market traders default to half or quarter Kelly because the uncertainty in your probability estimate is the biggest risk, not the trade itself.
Common Kelly Criterion Mistakes
- Overestimating your edge. The single biggest mistake. If you think your win probability is 55% but it is really 50%, full Kelly will have you overbetting massively. Always be conservative with probability estimates and use fractional Kelly as insurance.
- Ignoring fees and slippage. Kalshi charges taker fees (default 7% tier), Polymarket has gas costs, and sportsbooks bake in vig. Your true odds after fees are worse than the displayed price. Always calculate Kelly on the after-fee odds.
- Using Kelly on correlated bets. The basic Kelly formula assumes bets are independent. If you have five open bets on the same NFL game (spread, total, player props), they are correlated and the total Kelly exposure should be reduced. Use our hedge calculator to manage correlated positions.
- Not recalculating as bankroll changes. Kelly is a fraction of your current bankroll, not your starting bankroll. After a winning streak, your stakes should increase. After losses, they should shrink. This automatic scaling is what makes Kelly so powerful at avoiding ruin.
- Applying Kelly to parlays or accumulators. Multi-leg bets require a generalized Kelly formula. The simple f* = (bp - q) / b only applies to single-outcome wagers.
When Not to Use Kelly
Kelly is not a universal solution. Skip it when you have a fixed bankroll with a hard stop-loss (Kelly assumes infinite time horizon), when betting purely for entertainment with no edge, or when your value betting strategy relies on high volume with tiny edges where transaction costs dominate.
For guaranteed arbitrage opportunities, focus on maximizing stake rather than optimizing the Kelly fraction. The arbitrage detection process matters more than sizing when the profit is locked in.
Frequently asked questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 that determines the optimal fraction of your bankroll to wager on a bet with positive expected value. It maximizes the long-term geometric growth rate of your wealth while minimizing the risk of ruin. The formula is f* = (bp - q) / b, where b is the net odds (decimal odds minus 1), p is the probability of winning, and q is the probability of losing (1 - p).
How do you calculate the Kelly Criterion?
To calculate the Kelly fraction, use the formula f* = (bp - q) / b. First, convert your odds to decimal format. Then subtract 1 to get b (net odds). Multiply b by your estimated win probability (p) and subtract the loss probability (q = 1 - p). Divide the result by b. For example, at decimal odds of 2.50 with a 45% win probability: b = 1.50, f* = (1.50 × 0.45 - 0.55) / 1.50 = 0.083, meaning you should stake 8.3% of your bankroll.
What is half Kelly and why is it recommended?
Half Kelly means staking exactly 50% of the amount suggested by the full Kelly Criterion. It is widely recommended because full Kelly assumes you know the true probability with perfect accuracy, which is rarely the case. Half Kelly reduces variance by approximately 75% while sacrificing only about 25% of the expected growth rate. Most professional bettors and traders use half Kelly or less to account for estimation errors in their edge calculations.
When should you use quarter Kelly?
Quarter Kelly (25% of the full Kelly stake) is appropriate when you have low confidence in your probability estimate, when you are betting on high-variance outcomes like longshots, when you are new to a market and still calibrating your edge, or when you want maximum protection against ruin. Quarter Kelly is also common in prediction market trading where contract prices can be volatile and true probabilities are difficult to estimate precisely.
Can the Kelly Criterion be used for arbitrage betting?
In pure arbitrage where you cover all outcomes for a guaranteed profit, Kelly is not strictly necessary because there is no risk, so you simply stake the maximum your bankroll allows. However, Kelly becomes valuable for quasi-arbitrage situations: when one leg might not fill, when there is execution risk, or when trading correlated positions across prediction markets like Kalshi and Polymarket. In these cases, Kelly helps size your exposure relative to the probability that the arb actually completes.
What happens if the Kelly Criterion gives a negative result?
A negative Kelly value means you have a negative expected value. The odds do not compensate you for the risk. The correct action is to not bet at all. A negative Kelly can also signal that you should bet the other side if possible. For example, if Kelly is negative on 'Yes' at certain odds, the 'No' side at those same odds has positive expected value. Never force a bet when Kelly is negative; it indicates the bookmaker's odds are worse than your estimated probability.