Fractional Kelly bet calculator
What fraction of capital does half Kelly stake on a 60 percent even-money bet?
Full Kelly for a win probability of 0.6 at net odds of 1 is (1 x 0.6 - 0.4) / 1 = 0.2, a fifth of capital. Half Kelly multiplies that by 0.5, so the stake is 10 percent of current capital.
Kelly assumes the win probability is known; with an estimated probability, a full Kelly stake is usually too large.
Calculate the log-growth-optimal stake for a binary payoff, then apply an explicit fraction. Apply a selected fraction to the full stake.
A half-size wager
At p = 0.6 and net odds b = 1, full Kelly is 0.2. A half-Kelly setting c = 0.5 gives a stake of 0.1, or 10% of capital.
The calculation separates three claims that are often collapsed into a single stake recommendation. The probability is an estimate, the payoff is a contractual or modeled net amount, and the fraction is a deliberately chosen scaling factor. The displayed amount is a fraction of current capital, so a result of 0.1 corresponds to staking one tenth of current capital. Break-even probability is 1/(b+1). Below that point the unconstrained Kelly optimum is negative; the calculator prints zero because stakes are constrained to be nonnegative. At probability one it prints the algebraic upper value after applying the chosen fraction. That boundary case is mathematically well defined but practically fragile because observed win frequencies cannot establish certainty. If gains or losses vary by trade, a two-outcome model discards material information. Estimation error is especially consequential near the break-even point, where small probability changes reverse the decision.
Binary log-growth problem
Each trial has two outcomes: gain b times the amount staked or loss of the entire stake. The probability and payoff are fixed and trials are repeatable.
f* = max(0, (b p − (1−p)) / b); applied fraction = c f*The zero floor declines a bet whose stated probability does not exceed break-even probability. Fractional Kelly scales the mathematical optimum; it is not a confidence adjustment.
Probability is estimated
A probability estimate is uncertain. The calculator does not estimate that uncertainty, account for changing odds, or certify that any stake is tolerable. At p = 0 or 1 the formula remains algebraic, but the assumption of certainty deserves scrutiny.
Kelly's original paper
Kelly, J. L. Jr. (1956), A New Interpretation of Information Rate, Bell System Technical Journal 35, 917–926. The binary stake equation follows the log-growth objective. Original or institutional source.
Fractional Kelly · All tools
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</script>Cite this calculator
To cite the fractional Kelly bet calculator in a paper, a report or a post, copy the reference below. Its address is https://stochastly.com/tools/fractional-kelly-bet-calculator.
Stochastly (2026). Fractional Kelly bet calculator [web calculator]. https://stochastly.com/tools/fractional-kelly-bet-calculatorThe method behind the fractional Kelly bet calculator comes from the paper below: cite that paper for the method, and the reference above for the fractional Kelly bet calculator itself.
Kelly, J. L. Jr. (1956). A New Interpretation of Information Rate. Bell System Technical Journal 35(4), 917-926.