Log in

Market analysis

Kelly calculator

The Kelly criterion is a formula from 1956 that gives the fraction of capital which, at a given probability and odds, would in theory produce the fastest long-run growth of a bankroll. The calculator computes this fraction from your estimate; the output is an illustration of the formula, not a staking suggestion, and with a non-positive expected value Kelly returns zero.
Calculators
Analysis, not advice. The calculators' output is a mathematical illustration for the course chapters, not a betting recommendation, stake suggestion or financial advice. Every decision is your own responsibility.

Stake size

Kelly fraction

The Kelly criterion gives the theoretical fraction that maximises bankroll growth; the formula's output is a mathematical illustration, not a stake recommendation.

Enter the estimated probability and the odds; the divisor is the caution practice discussed in the variance chapter.

Chapter 25: Kelly criterionChapter 24: Bankroll basics

The formula

Kelly fraction = (probability × odds - 1) / (odds - 1), i.e. EV / (odds - 1). Fractional Kelly: the full fraction divided by the chosen divisor (2 = half Kelly, 4 = quarter Kelly).

Worked example

Estimated probability 55%, odds 2.00. EV = 0.55 × 2.00 - 1 = 0.10. Kelly = 0.10 / (2.00 - 1) = 10% of the bankroll; half Kelly is 5%, quarter Kelly 2.5%. If the true chance is only 50%, the EV is zero and the correct fraction is 0%: the 10% computed from the 55% estimate is pure overstaking.

Why fractional Kelly?

Full Kelly is extremely sensitive to errors in the probability estimate: an overestimated chance produces an oversized stake, which magnifies the error. That is why the literature typically studies fractional (half or quarter) Kelly. For scale: in the common unit-based practice one unit is typically 1-2% of the bankroll, while full Kelly often outputs a much larger fraction.

Common misunderstanding

The Kelly formula cannot know whether your estimate is any good: it optimises exactly the probability you type in. Overestimation leads to overstaking, and with Kelly overstaking erodes a bankroll faster than staking too small. In our own research the market's closing prices were more accurate than every one of our models, meaning the formula's most sensitive input, the probability, is inaccurate in most estimates.

01

What is the Kelly criterion?

John L. Kelly's 1956 formula, which gives the stake fraction that in theory maximises long-run capital growth at a given probability and odds. It assumes the probability is accurate, that there are very many repeated bets, and that the swings are bearable throughout.

02

Why does the calculator return 0%?

Because with the given numbers the expected value is not positive. The formula then allocates no capital: according to Kelly, the optimal stake is zero.

03

What is the difference between full and fractional Kelly?

Fractional Kelly is a divided version of the full fraction, for example a half or a quarter. It gives up part of the theoretical growth maximum in exchange for much smaller swings and less damage from errors in the probability estimate.

04

Is the Kelly fraction a staking recommendation?

No. The calculator shows the output of a formula with your inputs, as a mathematical illustration. Whether you bet, and whether you risk anything at all, is your decision and your responsibility.

05

What happens if I overestimate the probability?

The formula magnifies the estimation error into stake size: it outputs a larger fraction than warranted. Systematic overstaking can drain a bankroll quickly, even when the true expected value is positive.