Kelly Criterion Calculator

Put in the odds, your win probability and your bankroll. It shows the Kelly-sized stake at full, half and quarter, and the break-even price the bet has to clear before any of it is worth staking. No login, no email.

How the formula works

The Kelly Criterion answers one question: what fraction of a bankroll maximizes long-run growth, given a price and a win probability. It was published by John Kelly at Bell Labs in 1956 for signal transmission, and it applies to betting because the structure is the same. Repeated wagers, compounding capital, and a penalty for staking too much that is far harsher than the reward for staking a little more.

f*

The fraction of your bankroll to stake. A result of 0.05 means 5% of the bankroll, whatever the bankroll happens to be.

b

What one unit returns in profit if the bet wins. Decimal odds minus 1. At -110 you risk $110 to win $100, so b is 0.909. At +250 you risk $100 to win $250, so b is 2.5.

p

Your win probability. Your number, as a percentage. Not the book’s.

q

The probability the bet loses, which is simply 1 − p.

The numerator, bp − q, is the expected profit from staking one unit: what you win when you win, weighted by how often that happens, minus what you lose the rest of the time. When it is zero the bet is a coin flip in expectation. When it is negative the formula returns a negative number, which is the same as saying do not bet.

Dividing by b converts that expected profit into a fraction of bankroll. The numerator is measured in profit per unit staked, and b is how much profit a winning unit actually returns, so the division rescales the edge into the currency the answer is expressed in: how much to put at risk.

For a longer walk through the formula, with a worked slate, see the Kelly Criterion formula explained in plain English.

A worked example

These are the numbers the calculator above starts with, so you can follow along against it. A bet at -110, a win probability of 55%, and a bankroll of $1,000.

1. 1.Convert the price. -110 in decimal is 1 + 100/110 = 1.909. So b = 0.909.
2. 2.Find break-even. 1 / 1.909 = 52.4%. That is the win rate the price alone demands, before any edge.
3. 3.Measure the edge. 55% − 52.4% = 2.6 percentage points. That is the entire advantage, and it is smaller than it sounds.
4. 4.Run the formula. bp = 0.909 × 0.55 = 0.50. q = 0.45. So (0.50 − 0.45) / 0.909 = 0.055, or 5.5% of bankroll.
5. 5.Read it in money. 5.5% of $1,000 is $55 at full Kelly, $27.50 at half, and $13.75 at quarter.

The step worth sitting with is the third. A 55% read on a -110 line sounds substantial, but against a 52.4% break-even rate the actual edge is 2.6 percentage points. That is the number the formula sizes.

Full, half and quarter Kelly

Full Kelly assumes your probability estimate is accurate. In practice, even relatively small estimation errors can make full Kelly too aggressive. Our simulation of estimation error and bet sizing shows how quickly that can happen.

This is why fractional Kelly exists. Staking half or a quarter of the formula’s answer gives up some theoretical growth in exchange for a much smaller drawdown when the estimate is off, and in practice you do not know exactly how accurate your probability estimate is. The trade is not symmetric: overbetting compounds against you far faster than underbetting costs you.

There is no correct fraction. Half and quarter are common because they are blunt and easy to hold to, not because the math singles them out. The calculator shows all three at once so the size of the gap between them is visible before you pick one.

Break-even, and why the calculator sometimes says no bet

Every price carries a break-even win rate, and it is the first number the results panel shows. It is simply 1 divided by the decimal odds. At -110 that is 52.4%. At -150 it is 60%. At +200 it is 33.3%. Below that rate the bet loses money over time, no matter how good it feels.

So when the calculator returns no bet, it is not refusing to answer. Enter 52% at -110 and the formula returns a negative fraction, because the price demands 52.4% and you have supplied less. A negative stake is not something you can place, so the honest output is zero.

This is the most common sizing mistake in one line: treating a small lean as an edge. The gap between a confident 52% and a break-even 52.4% is invisible to intuition and decisive to the arithmetic.

What a single-bet calculator cannot capture

Everything above sizes one bet as though it were the only one. That is the assumption built into the formula, and it is why a calculator can be exactly right about a number and still be the wrong tool for a Sunday.

The bankroll is shared. Size six bets independently, each at a full-Kelly 5.5%, and the formula has quietly committed a third of the bankroll across the card. Each answer was correct in isolation; the total was never considered, because nothing in the formula can see the other five. Our post Kelly on one bet is not Kelly on a slate works through what happens to the first five positions when a sixth arrives.

Nor can it see anything you might want to hold to across the card as a whole, because those are properties of an allocation, and an allocation needs more than one bet to exist.

Common questions

What is the Kelly Criterion?

A formula for how much of a bankroll to stake on a bet, given the odds and your estimate of the win probability. It sizes the bet in proportion to your edge: a bigger edge takes a bigger fraction, and no edge takes nothing.

Why does the calculator sometimes say no bet?

Because the price already demands a higher win probability than you entered. When your number sits below break-even the formula returns a negative fraction, and a negative stake is not something you can place, so the honest output is zero. That is the formula working rather than failing.

Should I bet full Kelly?

Full Kelly maximizes long-run growth only if your probability is exactly right, and it never is. Betting a fraction of it keeps most of the growth while cutting the swings sharply, which is why half and quarter Kelly are common. The calculator shows all three so the trade is visible.

Where does the win probability come from?

You supply it. This calculator does not estimate probabilities and does not evaluate whether your number is any good. If the input is wrong, the stake is wrong with it.

What win rate do I need at -110?

52.4%. Break-even is 1 divided by the decimal odds, and -110 in decimal is 1.909, so the price demands 52.4% before a bet is worth anything. At -150 it is 60%, and at +200 it is 33.3%. Anything below the break-even rate loses money over time regardless of how the individual bet lands.