The Kelly Criterion: How Much to Bet When You Actually Have an Edge

The question nobody asks until it is expensive

You can be right more often than you are wrong and still end the year down. Bet size, not accuracy, decides which.

In 1956 a physicist at Bell Labs called John Kelly published a paper about noisy telephone lines that turned out to contain the answer to a gambling problem: given a bet you expect to win, what fraction of your money should you put on it? Fortune's Formula is the story of what happened next — the people who used it to beat blackjack, and the fund managers who argued about it for the following fifty years.

The reason it matters to someone with a brokerage account is that it makes a hidden decision visible. Most beginners decide what to buy carefully and decide how much by feel — how confident they happen to be that morning. Kelly's contribution is the demonstration that this second number has its own arithmetic, and that the arithmetic is not intuitive.

More edge does not mean more money

Take a bet you win 55% of the time, paying even money — a modest but real edge. If you bet a fixed fraction of your account each time and let the results compound, your long-run growth rate depends on that fraction like this.

The shape is the entire lesson. Growth is not a straight line you climb by betting more. It rises, tops out, and comes back down through zero — and past the crossing point, a bet with a genuine statistical advantage loses money with certainty over enough repetitions.

The formula, and what each part of it is doing

f* = (bp − q) / b — the fraction to bet is your edge divided by your odds.

For an even-money bet, where b is 1, the formula collapses to something you can do in your head: *f\ = 2p − 1**. Win 55% of the time and you bet 10%. Win 60% and you bet 20%. Win 51% and you bet 2% — which is the first uncomfortable result, because a 51% edge is the kind most people believe they have.

Note what the formula does not contain: how confident you feel, how good the setup looks, or how much you lost last week. It takes two numbers, both of which have to come from a record rather than a memory. That is why this and a trade journal are the same project.

Overbetting is not aggression — it is a different outcome

Here is the same sequence of twenty bets — eleven wins, nine losses, the 55% edge showing up exactly as advertised — run at three different sizes.

The endpoints are checkable without simulation, because with a fixed fraction the order does not matter: the account ends at (1+f)¹¹ × (1−f)⁹. At 5% that is +7.8%. At 10%, +10.5%. At 20%, −0.3%. The doubled bet turned a winning run into a flat one.

Half Kelly, and why practitioners use it

Betting half the Kelly fraction keeps about three quarters of the growth and halves the size of the swings.

Read that trade as a price: you give up a quarter of the theoretical growth and buy back half the volatility. For anyone who has to live through the equity curve rather than read about it afterwards, that is a good price — and the growth you give up is theoretical anyway, because it assumed your inputs were exact.

The input you cannot measure is the one that decides everything

Everything above assumes you know p. You do not. You have an estimate from a sample of trades, taken in a market that has since moved on. Here is what a six percentage-point overestimate does.

This is the asymmetry that makes half Kelly the default rather than a compromise. Underbetting costs you a slice of growth. Overbetting can cross the zero line, and you cannot tell which side of it you are on from inside the sample that produced the estimate.

Four things Kelly does not handle, and one of them matters daily

1. 1Correlated positions. Kelly sizes one bet. Five positions that all fall together are one bet wearing five names, and sizing them independently means you are quietly at five times the fraction you think.
2. 2Continuous outcomes. A trade is not a coin flip with a fixed payout. Applying the formula needs your average win and loss in R multiples, which is another estimate with its own error.
3. 3A changing edge. The formula assumes p is stable. Market conditions that produced your sample end without announcing it.
4. 4How it feels. Kelly optimises the growth rate of money and is completely indifferent to whether you can sit through a 40% drawdown. You are not indifferent, and abandoning a correct system mid-drawdown is the most common way this ends.

What to do with this

The value of Kelly for someone starting out is not the number it produces. It is the discovery that a size can be too big for an edge that is real — a fact no amount of research into what to buy will ever surface.

So use it as a ceiling, not a target. Compute it from your own record once you have one, halve it, then compare it to the fixed percentage you were going to use anyway. If your habitual size is above half Kelly, the formula has just told you something worth knowing. See where to set a stop loss for the other half of the sizing decision.