What is the Kelly Criterion and how does it work?

The Kelly Criterion, from John L. Kelly's 1956 paper, computes the fraction of your capital that maximizes long-run compound growth when you have an edge: f* = W − (1 − W) / R, where W is your probability of being right and R is the ratio of average gain to average loss. Bet more when your edge or payoff is bigger; bet nothing without an edge.

Is the Kelly Criterion applicable to investing, not just betting?

Yes. It originated in information theory and was popularized in gambling, but investors including Ed Thorp applied it to markets. For stocks, W is the probability your thesis plays out and R the ratio of expected upside to downside. Because those inputs are estimates rather than known odds, investors almost always use fractional Kelly.

Should I use full Kelly, half Kelly, or quarter Kelly?

Full Kelly maximizes growth but the drawdowns are violent (a 50% loss of capital is routine), and it assumes your probability estimates are exactly right. Half Kelly delivers about 75% of the growth with half the volatility, which is why most practitioners size at half or quarter Kelly. Overestimating your edge at full Kelly means systematic over-betting.

What does a negative Kelly result mean?

It means the numbers you entered describe a losing proposition: your win probability is too low for the payoff on offer. The formula's answer is to take no position at all, not a smaller one.

How do I calculate my win probability for the Kelly Criterion?

In sports betting you can compare your estimate against bookmaker odds; in investing there is no posted line, so W comes from your own base rates: how often theses like this one have worked for you historically. Track your decisions over time and be conservative. Uncertain probabilities argue for fractional Kelly rather than precision you don't have.

Does the Kelly Criterion guarantee profits?

No. It optimizes how much to risk given an edge; it cannot create one. With honest inputs it maximizes long-run growth and mathematically avoids total ruin (you never stake everything), but if your true edge is zero or negative, Kelly sizing just controls how fast you lose.

What's the difference between Kelly and fixed-percentage position sizing?

Fixed-percentage sizing (say 5% per position) ignores how attractive each opportunity is; Kelly scales the position to your edge and payoff, so a high-conviction, asymmetric idea gets more capital than a marginal one. The cost is sensitivity to estimation error, which fractional Kelly mitigates.

Who invented the Kelly Criterion?

John Kelly, a Bell Labs physicist, published the formula in 1956. Professional gamblers adopted it for blackjack and sports betting; value investors and hedge funds later applied the same math to position sizing.

What is the difference between Kelly and fixed-fraction position sizing?

A fixed-fraction rule risks the same stake size on every idea regardless of edge. Kelly sizing scales the Kelly fraction up when your edge and win probability are high, and down when they are marginal, so the stake matches the quality of the opportunity. In practice, many investors run half Kelly on their best ideas and cap any single position — combining Kelly betting logic with portfolio-level risk limits, and leaving the free betting tools to the sportsbooks.

Kelly Criterion Calculator for Stock Investors

How much of your portfolio one idea deserves: full, half and quarter Kelly.

Win probability (W)

How often theses like this one work out for you

Average gain when right

Average loss when wrong

Portfolio value (optional)

Full Kelly: the growth-maximizing position size

25.0%

A full Kelly this large tolerates brutal drawdowns and assumes perfect estimates. Most investors run half or quarter Kelly, because estimation error compounds faster than returns.

Half Kelly (common in practice): 12.5% · $12,500
Quarter Kelly (conservative): 6.3% · $6,250
Payoff ratio (R): 1.50

How to size a position with Kelly

Estimate your win probability honestly: how often have theses like this one worked for you?
Enter the average gain when you're right and the average loss when you're wrong.
Read full Kelly as a ceiling rather than a target. It assumes your estimates are exact.
Size at half or quarter Kelly; add your portfolio value to see the dollar amounts.
A negative result means no position. The formula never says "just size it smaller."

How this was calculated

f* = W − (1 − W) / R

W is the probability your thesis works out and R is the payoff ratio: average gain when right divided by average loss when wrong. f* is the fraction of capital that maximizes long-run compound growth for those inputs. Half and quarter Kelly scale it down, because with estimated rather than known probabilities, over-betting costs more than under-betting, so most practitioners size fractionally. A negative f* means the edge is negative and the correct position is zero. These are educational estimates, not investment advice.

Kelly for sports betting vs. Kelly for investing

The Kelly Criterion was popularized in sports betting, where a bettor sizes each wager as a fraction of their bankroll based on the betting odds and their edge. A sportsbook quotes decimal odds; a disciplined bettor estimates the true win probability, strips out the vig to get a no-vig fair price, and only stakes when the expected value (EV) is positive. The same mathematical formula that gives a blackjack player or sports bettor the optimal bet size — a percentage of your bankroll — gives an investor the optimal stake in a stock: your portfolio is the bankroll, your edge comes from analysis instead of odds, and the fraction of your bankroll at risk is your position size. Investing outcomes are not binary bets, so investors apply the formula more conservatively than bettors.

Full Kelly, half Kelly, or quarter Kelly?

Full Kelly maximizes the long-term growth rate of capital, but the ride is violent: deep drawdowns are expected and normal. Most practitioners use a fractional Kelly multiplier — half Kelly cuts volatility dramatically while keeping about three quarters of the growth rate, and quarter Kelly is common when your edge is uncertain. A smaller multiplier also protects against over-betting when your win probability estimate is wrong, minimizing the risk of ruin while still letting you maximize long-term growth.

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Frequently asked questions

The Kelly Criterion, from John L. Kelly's 1956 paper, computes the fraction of your capital that maximizes long-run compound growth when you have an edge: f* = W − (1 − W) / R, where W is your probability of being right and R is the ratio of average gain to average loss. Bet more when your edge or payoff is bigger; bet nothing without an edge.
Yes. It originated in information theory and was popularized in gambling, but investors including Ed Thorp applied it to markets. For stocks, W is the probability your thesis plays out and R the ratio of expected upside to downside. Because those inputs are estimates rather than known odds, investors almost always use fractional Kelly.
Full Kelly maximizes growth but the drawdowns are violent (a 50% loss of capital is routine), and it assumes your probability estimates are exactly right. Half Kelly delivers about 75% of the growth with half the volatility, which is why most practitioners size at half or quarter Kelly. Overestimating your edge at full Kelly means systematic over-betting.
It means the numbers you entered describe a losing proposition: your win probability is too low for the payoff on offer. The formula's answer is to take no position at all, not a smaller one.
In sports betting you can compare your estimate against bookmaker odds; in investing there is no posted line, so W comes from your own base rates: how often theses like this one have worked for you historically. Track your decisions over time and be conservative. Uncertain probabilities argue for fractional Kelly rather than precision you don't have.
No. It optimizes how much to risk given an edge; it cannot create one. With honest inputs it maximizes long-run growth and mathematically avoids total ruin (you never stake everything), but if your true edge is zero or negative, Kelly sizing just controls how fast you lose.
Fixed-percentage sizing (say 5% per position) ignores how attractive each opportunity is; Kelly scales the position to your edge and payoff, so a high-conviction, asymmetric idea gets more capital than a marginal one. The cost is sensitivity to estimation error, which fractional Kelly mitigates.
John Kelly, a Bell Labs physicist, published the formula in 1956. Professional gamblers adopted it for blackjack and sports betting; value investors and hedge funds later applied the same math to position sizing.
A fixed-fraction rule risks the same stake size on every idea regardless of edge. Kelly sizing scales the Kelly fraction up when your edge and win probability are high, and down when they are marginal, so the stake matches the quality of the opportunity. In practice, many investors run half Kelly on their best ideas and cap any single position — combining Kelly betting logic with portfolio-level risk limits, and leaving the free betting tools to the sportsbooks.