Kelly Criterion Explained: How Much Should You Bet on Your Best Ideas?
Everyone obsesses over which bets to make. Almost nobody thinks carefully about how much to bet. The Kelly Criterion is a formula that answers that second question, and it is arguably more important than the first.
The Origin Story
In 1956, a physicist named John Kelly at Bell Labs published a paper on information theory and gambling. His question was simple: if you have an edge (you know something the odds do not reflect), what fraction of your bankroll should you wager to maximize long-term growth?
Kelly worked this out mathematically, and Claude Shannon (the father of information theory) helped refine it. But the formula stayed mostly theoretical until Ed Thorp, a mathematics professor, used it to beat blackjack casinos in the 1960s. Thorp later applied the same framework to options trading and ran one of the most successful hedge funds in history. The Kelly Criterion was his sizing engine the entire time.
The Formula
For a simple bet with two outcomes (win or lose), the Kelly fraction is:
Where f* is the fraction of your bankroll to bet, p is the probability of winning, q is the probability of losing (1 minus p), and b is the net odds (how much you win per dollar risked).
Let us work through an example. You find an investment where you believe there is a 60% chance of doubling your money and a 40% chance of losing it entirely. So p = 0.60, q = 0.40, b = 1 (you stand to win $1 for every $1 you risk).
Kelly says to put 20% of your bankroll on this bet. That probably feels aggressive, and your instinct is correct. We will get to that.
Why Most People Bet Too Much
The Kelly Criterion maximizes the long-run growth rate of your bankroll. That sounds great, and it is mathematically optimal. But "long-run optimal" comes with terrifying short-term volatility.
Full Kelly sizing means you will regularly see drawdowns of 30% to 50% of your portfolio. In simulations, a full Kelly bettor with a genuine edge will occasionally lose half their bankroll before the math catches up. Most people cannot stomach that, and they should not have to.
This is why practitioners almost universally use what is called half-Kelly or fractional Kelly. Instead of betting the full Kelly fraction, you bet some fraction of it, typically 25% to 50%. In our example above, half-Kelly would mean betting 10% instead of 20%. You sacrifice some long-term growth in exchange for dramatically smoother returns and a much lower risk of ruin.
Beyond Gambling: Kelly for Real Decisions
The Kelly framework is most associated with casinos and trading, but the underlying principle applies to any decision where you are allocating scarce resources under uncertainty.
Startup investments. If you are an angel investor deciding how much to put into your next deal, Kelly thinking forces you to be honest about both the probability of a good outcome and the magnitude of the payoff. Most angels over-concentrate in their highest conviction deal when the math says they should be more diversified.
Career decisions. Considering leaving your job to start a company? Kelly thinking asks: what is the probability this works (be honest), what is the upside if it does, and how much of your financial runway should you commit? The answer is almost never "everything."
Product bets. A product manager deciding how many engineers to put on a risky new feature is making a Kelly decision whether they know it or not. The probability of the feature succeeding times the value it creates should inform the resource allocation, not just gut excitement about the idea.
The Catch: Garbage In, Garbage Out
Here is the thing nobody talks about when explaining Kelly. The formula requires a probability estimate as input. If that estimate is wrong, the output is wrong. And not just a little wrong. Kelly is extremely sensitive to the probability input.
If you think your probability of winning is 60% but it is actually 50%, Kelly tells you to bet 10% of your bankroll on what is actually a coin flip. Do that repeatedly and you will go broke.
This is why calibration is a prerequisite for Kelly. Before you can meaningfully size your bets, you need to know whether your probability estimates are any good. If your 60% predictions actually come true 60% of the time, great, Kelly will serve you well. If your 60% predictions come true 45% of the time because you are overconfident, Kelly will amplify that error.
The combination of calibration measurement (via the Brier score) and Kelly sizing is what makes systematic decision tracking so powerful. First you learn whether your probability estimates are accurate, then you use those accurate estimates to size your commitments.
Are Your Probability Estimates Good Enough for Kelly?
Kelly only works if your inputs are calibrated. Take our free Calibration Challenge to find out if your confidence levels match reality. 10 questions, 2 minutes, instant results.