Compare n' Bet™
Compare n' Bet™
Calculate the mathematically optimal stake size based on your bankroll, the probability you assign to the outcome, and the price the sportsbook is offering. Also shows half-Kelly and quarter-Kelly recommendations for lower-variance bankroll management.
The Kelly Criterion is a mathematical formula for optimal bet sizing. It tells you what fraction of your bankroll to wager on a given bet, given the price offered and your estimated probability of winning. Over the long run, sizing bets by Kelly maximizes the growth rate of your bankroll.
The formula is simple: f* = (bp - q) / b, where f* is the fraction to bet, b is the decimal odds minus 1 (your profit multiplier), p is your estimated win probability, and q is 1 minus p. If the result is zero or negative, the bet is not positive expected value and the Kelly recommendation is to bet nothing.
You believe a team has a 55% chance to cover the spread. The sportsbook is offering +105 (decimal 2.05). Using Kelly: b = 1.05, p = 0.55, q = 0.45. f* = (1.05 × 0.55 - 0.45) / 1.05 = 0.128, or 12.8% of your bankroll. On a $1,000 bankroll, full Kelly says to bet $128. Half Kelly says $64. Quarter Kelly says $32.
Full Kelly is mathematically optimal only if your win probability estimate is exactly right. In the real world, your estimates have uncertainty, and overestimating your edge by even a little leads to wildly oversized bets and much higher bankroll drawdowns. Full Kelly also produces uncomfortable swings, sometimes recommending 10%, 20%, or even higher stakes on single bets.
Most serious bettors use fractional Kelly (half or quarter) to reduce variance and protect against estimate errors. Half Kelly gives up about 25% of the long-run growth rate in exchange for dramatically lower drawdowns. Quarter Kelly gives up about 44% of growth for even lower variance. For most practical purposes, half or quarter Kelly is the right place to be.
Kelly is a sizing framework, not a betting strategy. It tells you how much to bet if you already have an edge. It doesn't find edges for you. If your win probability estimates are inaccurate (which they often are), Kelly will size bets incorrectly in proportion. Garbage in, garbage out.
Kelly also assumes you have a bankroll that can realistically absorb the swings it produces, and that you're comfortable betting a percentage of it on each wager. If you're betting money you can't afford to lose, or if losing a Kelly-sized stake would change your life in any meaningful way, the math isn't the problem. The bankroll is too small for the bet size, and you should either bet less or stop.
If your estimated probability is equal to or less than the fair implied probability from the offered odds, the Kelly fraction is zero or negative. In that case, the recommended stake is $0. This is the correct answer. A negative edge bet should not be placed at any size. The calculator will display zero stakes and a negative edge to make this clear.
The bankroll management guide covers Kelly, unit sizing, and flat staking in depth. The expected value guide explains how to estimate your win probability. The no-vig calculator helps you establish the fair baseline probability to compare against.
This calculator is for informational purposes only. Kelly sizing depends on accurate probability estimates, which are hard to produce. Compare n' Bet does not provide betting advice, guarantees, or predictions. If you or someone you know has a gambling problem, call 1-800-522-4700 or visit ncpgambling.org.