What this calculator answers
This calculator shows the share of a bankroll that the Kelly formula would stake, given your estimated win probability and the payoff. It works in three modes: trading, where you enter an average win divided by an average loss, betting, where you enter decimal odds, and prediction markets, where you enter a share price in cents.
You also choose a fraction of Kelly and a bankroll, and the page converts the result into a stake. The page shows the arithmetic only. It does not tell anyone what to do, and it cannot know whether your estimates are right. Every number below depends on them.
The formula
b = d − 1 (betting), b = (100 − c) / c (prediction market), K = p − (1 − p) / b, f = K × k, S = A × f, e = p × b − (1 − p)
Here p is your win probability as a fraction, and b is the net payoff for each 1 risked. K is the full Kelly fraction of the bankroll. k is the share of Kelly you choose, f is the fraction used, A is the bankroll and S is the stake. e is the edge per 1 risked.
In trading mode, b is the number you type. In betting mode, d is the decimal odds, which include your stake, so b is d minus 1. In prediction market mode, a share costs c cents and pays 100, so b is the profit divided by the cost. The form with p and b is the one Edward Thorp gives, and the criterion itself goes back to Kelly in 1956.
Worked example: trading
Say you estimate a 55% chance of winning, and your average win is 1.5 times your average loss. With half Kelly and a bankroll of 10,000, full Kelly is 25%. At your chosen half, the fraction used is 12.5%, and the stake is $1,250.00. The edge is 0.375 for each 1 risked.
These numbers show the arithmetic. They are not a suggestion to risk any amount.
Betting and prediction markets
A bet at decimal odds of 2.10 with a 50% chance of winning has a net payoff of 1.1, and full Kelly is 4.55%. A prediction market share priced at 40 cents, with the same 50% chance, has a net payoff of 1.5, and full Kelly is 16.67%.
When Kelly says do not bet
If you win 40% of the time and win only as much as you lose, the edge is -0.2. Full Kelly is shown as 0%, and the stake is $0.00. With no edge, the formula gives no stake. A negative stake would mean taking the other side of the trade, which this page does not model. If you later change your estimate of the win probability or the payoff, the edge can turn positive, and the page then shows a stake again.
Why many traders use a fraction
Kelly takes your win probability as exact. Suppose the 55% in the first example is really 50%, with the same payoff. Full Kelly is then 16.67% instead of 25%, so the first number would have over-staked by a wide margin. This is why many traders use a fraction of Kelly, which leaves room for estimates that are too high.
Thorp’s even-money example has a 53% win probability. Full Kelly is 6%, and half Kelly is 3%. The page also shows quarter Kelly. No fraction is the right one, and the choice is yours. Smaller fractions give a smaller stake and slower expected growth, and larger ones do the opposite.
What the result does not include
The result is a single number from a simple model, and real trading is messier. It leaves out fees, slippage, price gaps through a stop, correlated trades, changing odds and taxes. In trading mode, the percentage is the amount risked if the stop is hit, not the size of the position. To turn a risk percentage into shares or units, use the position size calculator. For a leveraged crypto trade, see the futures calculator.
FAQ
What is the Kelly criterion?
It is a formula John Kelly published in 1956. It picks the stake which maximises the long-run growth of a bankroll, given a known win probability and payoff. Gamblers and traders later adapted it to repeated bets and trades.
Is the Kelly percentage my position size?
No. In trading mode it is the share of your account you would lose if the stop is hit. The position size calculator turns a risk percentage into a number of shares or units.
What does "Kelly says don't bet" mean?
The edge, which is p times b minus (1 minus p), is zero or negative. That means the average result of each 1 risked is zero or a loss at your estimates. The formula then gives a stake of 0, and the page never shows a negative stake.
What is half Kelly, and why do people use it?
It is half of the full Kelly stake. It gives up some expected growth in return for smaller swings, and it is less sensitive to errors in your estimates. The page shows full, half and quarter Kelly side by side, and the stake uses the share you choose.
How do I get the win probability and the win/loss ratio?
You estimate them, for example from a record of past trades. Kelly is only as good as those two numbers, and small errors move the result a lot. A short history gives a noisy estimate. The overestimate example above shows 25% against 16.67%.
How do the three modes differ?
Only in how the net payoff b is found. In trading mode you enter the ratio. In betting mode b is the decimal odds minus 1. In prediction market mode b is (100 minus the price in cents) divided by the price.
Does Kelly guarantee a profit or avoid losing streaks?
No. It assumes repeated, independent bets with known odds. Losing streaks and drawdowns still happen, even at a positive edge, and the formula says nothing about any single outcome. A real series of trades is also rarely independent.