Kelly Criterion Calculator

The Kelly criterion is the bet fraction that maximises the long-run growth rate of capital for a known edge. It answers one question: given a probability of winning and a payoff ratio, what fraction of the account should you stake to make the account grow as fast as mathematically possible over many repeated, independent bets. The fraction is f* equals p minus q divided by b, where p is the win probability, q is 1 minus p, and b is the reward-to-risk or payoff ratio. It was published by John Kelly in 1956 as a result in information theory and later applied to markets by Edward Thorp. The key word is known: Kelly is optimal only when the edge is measured exactly, which in trading it never is, and that gap is the entire reason professionals bet a fraction of the Kelly number rather than the number itself.

For a bet that wins with probability p and pays b times the amount risked on a win, and loses the amount risked on a loss, the growth-optimal fraction is f* equals (b times p minus q) divided by b, where q equals 1 minus p. This is algebraically identical to f* equals p minus q divided by b. The payoff ratio b is your average win divided by your average loss, so a system with an average winner twice the size of the average loser has b equal to 2. Worked at a 55 percent win rate and a payoff ratio of 2, f* equals (2 times 0.55 minus 0.45) divided by 2, which is 0.65 divided by 2, which is 0.325, so full Kelly is 32.5 percent of capital. If the formula returns zero or a negative number, the edge is not positive and no fraction should be staked.

Half-Kelly is simply half of the full Kelly fraction, and it is the number most professional risk managers actually use. The reason is the shape of the growth curve. Expected growth as a function of bet fraction is a concave hump that peaks at f* and falls away on both sides. Because the peak is flat, cutting the bet to half of f* keeps roughly three quarters of the maximum growth rate while cutting the variance of the bet, and the depth of the drawdowns, by about half. You give up a little growth and buy a large reduction in the size of the swings you have to sit through. Full Kelly is the mathematical ceiling that maximises growth on paper; half-Kelly is the version a human can actually execute without abandoning it in the first deep drawdown.

Growth-optimal means the fraction that maximises the expected logarithm of wealth, which is the same as maximising the compound growth rate over many repeated bets. Kelly does not maximise your expected rupees on the next bet; a larger bet always has a higher expected rupee value. It maximises the rate at which the account compounds when you bet the same fraction again and again, because compounding is multiplicative and the log turns a product of many bets into a sum you can optimise. This is why a bet larger than f* is self-defeating: it raises the arithmetic expectation of a single bet but lowers the geometric growth of the sequence, since the extra losses compound against you faster than the extra wins compound for you.

Because growth is a hump-shaped function of bet fraction, not a straight line. Below f* the growth rate rises with size; at f* it is at its maximum; above f* it falls, because the larger losses drag the compound rate down faster than the larger wins lift it. At exactly twice f* the expected growth rate falls back to about zero: you are taking risk and volatility for no compounding at all. Beyond twice f* the expected growth rate turns negative, so the account trends toward ruin even though every individual bet still has a positive expected rupee value. Overbetting is the most common way a genuinely positive edge is turned into a losing account, and it is why the calculator flags any fraction above roughly 25 percent as overbetting territory.

Three reasons, and they compound. First, estimation error: you estimate the win rate and the payoff from a small, noisy sample, and Kelly is highly sensitive to both, so a win rate that is a few points too high sizes you as if you had an edge you do not have, which is overbetting in disguise. Second, non-stationarity: a real market edge decays as conditions change, so the Kelly fraction computed on last year's numbers can be too large this year. Third, the drawdowns: full Kelly produces deep, prolonged drawdowns that are mathematically normal but psychologically unbearable, and a sizing rule you abandon in a drawdown is worse than a smaller rule you can keep. The practical resolution is to bet a fraction of Kelly, commonly a half or a quarter, and to treat the Kelly number as a ceiling rather than a target.

A zero or negative Kelly fraction means the system has no positive edge at the inputs you entered, and the correct bet size is zero. It happens whenever b times p is less than or equal to q, that is, when the win rate is too low for the payoff ratio on offer. For example a 45 percent win rate at a payoff ratio of 1 gives f* equals (1 times 0.45 minus 0.55) divided by 1, which is minus 0.10, a negative number. No position size rescues a negative-edge system; sizing math can only allocate an edge that already exists, it cannot manufacture one. The tool refuses to recommend a bet in this case and tells you the edge, not the size, is the thing to fix, by raising the win rate through selectivity or improving the reward-to-risk of the setups you take.

Not directly. The Kelly formula assumes one bet at a time, or many bets that are independent of one another. Real portfolios hold several positions at once, and those positions are often correlated: several long positions in the same sector behave like one larger position that all move and stop together. Sizing each of them at its own single-bet Kelly fraction stacks correlated exposure and overbets the combined position badly, because the true joint bet is far larger than any single leg. The multi-asset generalisation of Kelly accounts for the correlation matrix and shrinks the per-position fractions accordingly, but it needs a covariance estimate that is even noisier than the single-bet inputs. In practice desks handle this with a total portfolio heat cap on top of per-trade sizing, so that correlated bets cannot combine into one oversized Kelly position.

The SEBI study found that over 91 percent of individual traders in the equity derivatives segment were net loss-making in FY25, with aggregate net losses of about 1,05,603 crore rupees, up roughly 41 percent from the previous year. Not all of that is an edge problem; a large part is a sizing problem, and Kelly names it precisely. A trader who bets far above the Kelly fraction, which on leveraged F&O positions is easy to do without noticing, is in the region where expected growth is zero or negative even when the underlying method has a small positive edge. Overbetting converts a survivable edge into a losing account, and it does so through exactly the deep, compounding drawdowns that the Kelly curve predicts once the fraction goes past its peak.