This article explains the Kelly criterion and fractional Kelly as concepts. It is educational and general, not personalised investment advice, and nothing here is a recommendation to buy, sell, or size any position at any particular fraction. The Kelly formula is a mathematical result about long-run growth, not a prescription for how much anyone should risk.
The Kelly criterion is the closest thing gambling and investing have to an optimal bet size, a single formula that answers “given my edge, how much of my capital should ride on this?” The surprising part is that the mathematically optimal answer is almost always too aggressive to actually use. Here is what the Kelly criterion is, the growth-versus-survival tradeoff it exposes, why full Kelly produces drawdowns most people cannot stomach, and why nearly every serious practitioner bets a fraction of it.
The short version
The Kelly criterion is a formula for the bet size that maximises the long-run growth rate of capital when you have a known edge. It sizes each bet in proportion to your edge divided by the odds: the bigger your advantage and the shorter the payoff odds, the more you stake. Betting more than Kelly lowers long-run growth and raises risk; betting a fraction of Kelly (commonly half or less) sacrifices a little growth for a large reduction in volatility and drawdown.
Where the criterion comes from
The result was published in 1956 by John L. Kelly Jr., a physicist at Bell Labs, in a paper titled “A New Interpretation of Information Rate.” Kelly had no casino in mind. He was working out how much of a bankroll a gambler with a private information advantage, a noisy wire tip on a horse race, should stake to grow it fastest over many bets. His answer was elegant: stake the fraction that maximises the expected logarithm of wealth, which turns out to be exactly the fraction that maximises the long-run compound growth rate. Maximising expected log wealth and maximising long-run growth are the same problem.
The idea moved from information theory to the real world through Edward O. Thorp, the mathematician who used Kelly sizing to make card counting in blackjack actually profitable, then carried the same logic into markets through his hedge funds. Thorp is the reason Kelly is spoken of in the same breath as investing rather than staying a footnote in a signals-engineering journal. Later, Ralph Vince generalised the practical machinery for traders under the name optimal f, the fraction of capital that maximises geometric growth given a distribution of trade outcomes rather than a single fixed-odds bet, and documented just how punishing that optimum is to sit through.
How the formula works: edge over odds
The cleanest way to hold the Kelly criterion in your head is the phrase edge divided by odds. For a simple bet, the Kelly fraction rises with your edge, how much the bet is expected to make on average, and falls with the odds, how much you can win relative to what you stake. A large edge at short odds calls for a big fraction; a thin edge at long odds calls for a tiny one. If the edge is zero or negative, Kelly says stake nothing: there is no bankroll fraction that grows money on a bet with no advantage. That last property is worth dwelling on. Kelly only tells a genuinely advantaged bettor how hard to press, and no amount of clever sizing rescues a game with no advantage in it.
A crucial feature is that Kelly sizing is proportional to current capital, not to a fixed dollar amount. You bet a percentage of what you have now, so after a loss the next bet is smaller and after a win it is larger. That proportional rule is what makes ruin mathematically impossible under idealised full-Kelly betting: you can bleed the bankroll down toward zero, but scaling every bet to a fraction of what remains means you never stake the whole thing. The catch, as the next section shows, is that “never quite zero” still permits drawdowns savage enough to end most people’s tolerance long before the math would end their capital.
The growth-versus-survival tradeoff
Kelly’s optimum has a strange, useful shape. Plot long-run growth rate against bet size and you get a hump: growth rises as you size up from timid, peaks exactly at the Kelly fraction, then falls as you press past it. Bet more than Kelly and you get the worst of both worlds, lower growth and higher variance, which is why over-betting is the cardinal sin the framework warns against. Past a point (roughly twice Kelly for the classic even-money case) expected growth turns negative: you are now mathematically destined to go broke despite having a real edge, purely because your bets are too big for it.
The subtle part is on the other side of the peak. The hump is asymmetric and nearly flat just below the top. Backing off from full Kelly costs you very little growth, but it cuts variance and drawdown sharply, because volatility falls faster than return as you shrink the bet. This is the entire case for fractional Kelly: you give up a sliver of the theoretical growth rate to buy a large, disproportionate reduction in how violent the ride is. In compounding, a smoother ride is part of the return itself, the reason volatility drag makes two strategies with the same average return end at very different wealth.
Why full Kelly is too aggressive for real trading
On paper full Kelly maximises growth and never ruins you. In practice almost nobody bets it, for two blunt reasons.
The first is the drawdowns. Full-Kelly betting is astonishingly volatile. A well-known rule of thumb is that under full Kelly, a drawdown of fifty percent of peak capital is routine, something to expect repeatedly over a long betting career. Halve your money, recover, halve it again: mathematically survivable, psychologically brutal, and for anyone managing money on behalf of others, professionally fatal. The optimum that maximises long-run growth is calibrated for a bettor with infinite patience and no career risk, which describes no actual human.
The second reason is more insidious: estimation error. The Kelly formula assumes you know your edge and your odds exactly. Real traders never do; they estimate them from finite, noisy, backward-looking data, and those estimates are optimistically biased more often than not. Kelly sizing is dangerously sensitive to that error, because it sits at the very peak of the growth curve where over-betting turns toxic. Overestimating the edge even modestly sails a bettor past the true Kelly point into the region where growth is negative. Since the penalty for over-betting is far worse than the penalty for under-betting, and the inputs are uncertain, the framework implies deliberately under-betting, treating the fraction as a shrinkage on a number nobody is sure of. Backtested edges in particular flatter themselves; why they overstate the real advantage is its own study, and it is a direct argument for sizing below the number the backtest implies.
Fractional Kelly: betting a slice of the optimum
Fractional Kelly is exactly what it sounds like: compute the Kelly fraction, then bet some proportion of it. Half-Kelly is the most cited choice, but the practice spans a wide range, and quieter fractions are common among professionals who value survival over speed. The appeal is the asymmetry described above. Because the growth curve is flat near its peak but variance falls quickly, a half-Kelly bettor keeps most of the long-run growth while roughly halving the volatility and dramatically softening the drawdowns. It is one of the rare places in finance where giving something up is nearly free.
Fractional Kelly also does double duty as a hedge against the estimation problem. If your edge estimate is inflated, betting a fraction pulls you back from the cliff of over-betting, so a fraction of a slightly-wrong Kelly number is far safer than the full amount of it. In that light, fractional Kelly is an honest acknowledgement that the inputs are uncertain and the cost of over-confidence is asymmetric.
Full versus fractional Kelly at a glance
| Property | Full Kelly | Fractional Kelly (e.g. half or less) |
|---|---|---|
| Long-run growth rate | Maximum (by definition) | Slightly lower, but most of it retained |
| Volatility of the ride | Very high | Much lower (falls faster than growth) |
| Typical drawdowns | Severe, deep pullbacks are routine | Materially shallower |
| Sensitivity to a wrong edge estimate | Dangerous, over-betting turns growth negative | Forgiving, the fraction cushions the error |
| Who it suits | A bettor with exact odds and infinite patience | Anyone with uncertain edges and real risk tolerance |
The limits: what Kelly does and does not tell you
Kelly is a growth-optimality result, not a complete risk framework, and it comes with real caveats. It optimises the long run, and the long run can be very long: over any finite horizon a full-Kelly bettor can underperform a more conservative one and endure drawdowns that end the experiment early. It assumes you can size continuously and re-bet proportionally, which real markets, with minimum sizes, gaps, and illiquidity, only approximate. It says nothing about your actual tolerance for volatility, which is a preference, not a mathematical fact, and a bettor who maximises growth may still be sizing far outside what they can psychologically hold. And it is silent on correlation: sizing several positions each at their individual Kelly fraction can add up to a portfolio far more aggressive than any single bet suggests, because the bets move together. The formula is a ceiling and a discipline, not a substitute for judgement about how much risk a given account can bear. How ruin arises when sizing ignores that ceiling is the subject of risk of ruin.
How a systematic, risk-first process treats this
The Kelly framework is the cleanest formal argument for a principle that good systematic operators arrive at independently: size for survival first, growth second. Shishin sizes risk-first, deciding how much risk a candidate may carry before anything about expected upside enters, which is a fractional, survival-weighted posture in the spirit of fractional Kelly rather than a press-the-edge one. It sizes by risk, not by conviction, so a name the model likes more does not automatically get a bigger stake, precisely the over-betting-on-a-favourite trap Kelly warns against when the edge estimate might be wrong. How that risk-first rule is set per position is described in risk per trade, and why sizing by conviction rather than by risk is the more fragile choice is the argument of position sizing by conviction. The connection to Kelly is conceptual, not a claim that the system bets any particular fraction; the shared idea is that staying in the game through the drawdowns is what lets the edge compound at all.
So, what is the Kelly criterion?
It is the mathematically optimal bet size for long-run growth, edge divided by odds, sized as a proportion of current capital, and it is one of the genuinely deep results in the theory of betting and investing. It is also, at full strength, too aggressive for almost anyone to actually use, because it maximises growth at the cost of drawdowns few can survive and it assumes an edge nobody knows exactly. The practical lesson is not the formula but its shape: over-betting is ruinous, under-betting is nearly free, and the sensible place to live is a fraction below the optimum. Kelly tells you where the ceiling is. The discipline is in choosing to stay well beneath it.
Sources & further reading
- Kelly, J. L. (1956). “A New Interpretation of Information Rate.” Bell System Technical Journal, 35(4), 917 to 926. The original derivation of the growth-optimal bet fraction.
- Thorp, E. O. (2006). “The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market,” in The Kelly Capital Growth Investment Criterion. The practitioner’s account of applying Kelly to real markets.
- Vince, R. The Mathematics of Money Management. Introduces optimal f and how punishing the geometric-growth optimum is to trade.
- For how this connects to per-position risk and to ruin, see risk per trade, risk of ruin, and compounding and volatility drag. Shishin’s live, attested record is at the track record and the verification log.