Kelly Criterion Bet Size Calculator for Betting
Calculate the optimal fraction of your bankroll to stake on a bet using the Kelly Criterion, based on your edge and the offered odds.
Kelly Criterion Bet Size Calculator for Betting
Calculator
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Formula: f* = (bp - q) / b
Worked example — Full Kelly: $55.50 (5.55%) | Half Kelly: $27.75 | EV: +5.05% per bet
Formula
f* = (bp - q) / b
Where f* is the optimal fraction of bankroll to wager, b is the net decimal odds (decimal odds minus 1), p is the probability of winning, and q is the probability of losing (1 - p). The result is multiplied by the chosen Kelly fraction (e.g., 50% for half Kelly) for risk management.
Worked Examples
Example 1: NFL Point Spread Bet
Problem:You have a $1,000 bankroll and estimate a 55% win probability on a point spread bet at decimal odds of 1.91 (-110). What is the optimal bet size?
Solution:Net odds (b) = 1.91 - 1 = 0.91 Win probability (p) = 0.55, Loss probability (q) = 0.45 Full Kelly: f* = (0.91 x 0.55 - 0.45) / 0.91 = (0.5005 - 0.45) / 0.91 = 0.0555 = 5.55% Optimal bet: $1,000 x 5.55% = $55.50 EV per bet: (0.55 x 0.91) - 0.45 = 0.0505 = 5.05% Half Kelly (recommended): 2.78% = $27.75
Result:Full Kelly: $55.50 (5.55%) | Half Kelly: $27.75 | EV: +5.05% per bet
Example 2: Underdog Value Bet
Problem:Bankroll of $5,000. You estimate a 35% chance on a bet paying decimal odds of 3.50 (+250). Using half Kelly.
Solution:Net odds (b) = 3.50 - 1 = 2.50 Full Kelly: f* = (2.50 x 0.35 - 0.65) / 2.50 = (0.875 - 0.65) / 2.50 = 0.09 = 9.0% Half Kelly: 4.5% = $5,000 x 4.5% = $225 EV per bet: (0.35 x 2.50) - 0.65 = 0.225 = 22.5% Implied probability: 1/3.50 = 28.6% (your edge: 6.4%)
Result:Full Kelly: $450 (9.0%) | Half Kelly: $225 | EV: +22.5% | Edge: 6.4%
Frequently Asked Questions
What is the Kelly Criterion and how does it apply to betting?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956 that determines the optimal percentage of your bankroll to wager on a bet with a positive expected value. The formula is f* = (bp - q) / b, where f* is the fraction of bankroll to bet, b is the net decimal odds (decimal odds minus 1), p is the probability of winning, and q is the probability of losing (1 - p). In sports betting, if you believe a team has a 55% chance of winning at decimal odds of 2.00 (even money), the Kelly formula suggests betting 10% of your bankroll. The beauty of Kelly staking is that it maximizes the long-term growth rate of your bankroll while mathematically preventing total ruin since bet sizes shrink proportionally as your bankroll decreases.
Why do most professional bettors use fractional Kelly?
Most professional sports bettors and advantage gamblers use fractional Kelly, typically between 25% and 50% of the full Kelly recommendation, for several important practical reasons. First, the Kelly Criterion assumes you know the exact probability of winning, but in reality probability estimates contain uncertainty and error. Overbetting due to overestimated edge is far more damaging than underbetting. Second, full Kelly produces extreme bankroll volatility with drawdowns of 50% or more being common, which is psychologically difficult to endure. Half Kelly produces approximately 75% of the long-term growth rate with significantly reduced variance and maximum drawdown. Third, fractional Kelly provides a margin of safety against estimation errors. Professional bettors consistently report that quarter to half Kelly provides the best real-world balance between growth and emotional sustainability.
How do I convert between different odds formats?
Sports betting uses three main odds formats that all represent the same information differently. Decimal odds show total return per unit wagered (2.50 means $2.50 back on a $1 bet, including the original stake). American odds use positive numbers for underdogs (+150 means $150 profit on $100 bet) and negative numbers for favorites (-200 means bet $200 to profit $100). Fractional odds show profit relative to stake (3/2 means $3 profit on $2 bet). To convert: American to Decimal, if positive: (American/100)+1, if negative: (100/|American|)+1. Fractional to Decimal: (numerator/denominator)+1. The Kelly Calculator requires decimal odds. For example, American +150 converts to decimal 2.50, and fractional 6/4 also converts to decimal 2.50. Always double-check your conversions before calculating optimal bet sizes.
What happens if the Kelly formula gives a negative number?
A negative Kelly value means the bet has a negative expected value, and you should not place the wager at all. This occurs when the implied probability from the odds is higher than your estimated true probability of winning. For example, if a bet offers decimal odds of 2.00 (implied 50% chance) but you estimate only a 45% probability of winning, the Kelly formula returns a negative value: (1 x 0.45 - 0.55) / 1 = -0.10. Negative Kelly essentially means the bookmaker has the edge, not you. In practice, most bets offered by sportsbooks have negative expected value, which is how bookmakers profit. Only bet when your analysis suggests the true probability exceeds the implied probability by a meaningful margin, ideally producing a Kelly fraction of at least 1-2% to justify the effort and emotional energy of placing the wager.
How does the Kelly Criterion relate to expected value in sports betting?
Expected value (EV) and the Kelly Criterion are complementary concepts in sports betting mathematics. EV tells you whether a bet is profitable on average: EV = (probability x net odds) - (1 - probability). A positive EV means the bet is worth making over many repetitions. However, EV alone does not tell you how much to bet. That is where Kelly comes in. The Kelly Criterion optimizes bet sizing to maximize the geometric growth rate of your bankroll given a known positive EV. Importantly, a higher EV does not always mean a larger Kelly bet. A bet with moderate EV but high probability might warrant a larger Kelly stake than a long-shot with higher EV but lower probability. Kelly accounts for both the edge and the odds, balancing potential profit against risk of loss to produce mathematically optimal bankroll growth over time.
What is the edge-over-odds form of the Kelly formula?
The Kelly fraction can be written as edge divided by odds. With decimal odds d and estimated win probability p, the edge is p times d minus 1 and the odds term is d minus 1, so f* equals (pd - 1) divided by (d - 1). This is algebraically identical to the (bp - q)/b form once you substitute b equal to d minus 1 and q equal to 1 minus p. The edge form is often easier at the betting window because p times d minus 1 is simply the expected return per unit staked, so a 5 percent edge at odds of 3.00 gives 0.05 divided by 2, a 2.5 percent stake.
How do you estimate the true probability that Kelly needs?
Kelly is only as good as p, and the odds themselves are the natural starting point. Convert each price to an implied probability by taking the inverse of the decimal odd, then remove the bookmaker's margin by dividing each implied probability by the sum across all outcomes. A two-way market priced 1.91 and 1.91 gives 0.5236 each, summing to 1.0471, so the no-vig probability is 0.50 for each side. Your own estimate must beat that fair line, not the raw price, before any positive Kelly stake is justified.
What happens if you bet more than the full Kelly fraction?
Growth rate as a function of stake size is an inverted curve that peaks at the Kelly fraction and falls away on both sides. Betting a little over Kelly gives you more volatility for less growth, which is a strictly bad trade. In the idealised repeated-bet model the growth rate falls back to zero at roughly twice the Kelly fraction, and beyond that point the bankroll trends downward over time even though every individual bet still has positive expected value. Since real probability estimates are uncertain, apparent overbetting is easier to fall into than it looks.
How does Kelly staking compare with flat staking?
Flat staking risks the same amount on every bet, which is simple, keeps variance predictable and does not require a probability estimate at all. Kelly scales the stake to the size of the edge and to the current bankroll, which maximises the long-run geometric growth rate and automatically shrinks bets after losses. The trade-off is sensitivity: flat staking degrades gracefully when your estimates are wrong, whereas Kelly amplifies estimation error directly into stake size. Many bettors compromise by using fractional Kelly with a cap on any single stake.
How should Kelly be applied to several bets at once?
The single-bet formula assumes each wager is settled before the next begins. When bets run simultaneously, the amounts at risk overlap and the sum of individual Kelly fractions can commit far more of the bankroll than intended. For genuinely independent events, one common practical approach is to compute each stake separately and then scale them all down so the total exposure stays within a chosen limit. For correlated bets, such as several selections from the same match, treat the combined position as one wager, since a single event can lose every leg at once.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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