Fractional Kelly: Why Half Kelly Is the Smart Default

Full Kelly tells you the bet size that maximises the long-run geometric growth rate of your bankroll, assuming you know your true edge. For a simple binary bet, the formula is f* = (bp - q) / b, where b is the decimal odds minus one, p is your true probability of winning, and q = 1 - p.

Fractional Kelly is just k · f*, where k is some fraction less than 1. Half Kelly (k = 0.5) is by far the most common, followed by quarter Kelly (k = 0.25) and, occasionally, three-quarter Kelly. Some funds run as low as eighth Kelly when their edge is highly uncertain.

The reason this rule even exists is that the math behind Kelly is fragile in a specific way. If your real edge is slightly smaller than you think - which it almost always is - full Kelly stops being optimal and becomes catastrophic. Fractional Kelly is a robustness adjustment, not a correction to a mistake in the formula.

The Kelly fraction maximises log-utility - the expected logarithm of terminal wealth. This is exactly the right objective if you're an immortal bettor with perfect information and no path-dependent constraints. In the real world, three properties of full Kelly make it intolerable.

First, the variance is huge. Under full Kelly, the standard deviation of your bankroll growth is equal to your edge. That means a strategy with a 2% edge per bet will swing wildly between gains and losses on any short horizon, even though it's profitable in expectation.

Second, drawdowns are extreme. A well-known result is that under full Kelly, the probability of seeing your bankroll cut in half at some point before doubling is exactly 50%. The probability of an 80% drawdown is 20%. These aren't tail events - they are the typical experience of a full-Kelly bettor.

Third, the strategy is acutely sensitive to estimation error. If you overestimate your edge by even a small amount, the optimal-feeling bet size becomes systematically too large, and the strategy can be worse than not betting at all. This connects to a deeper idea in ergodicity: a time-average outcome can diverge brutally from an ensemble-average outcome when variance is high, and full Kelly maximises a quantity that only makes sense in the ensemble.

There's an elegant closed-form result for fractional Kelly drawdowns. Under continuous-time Kelly betting with fraction k, the probability of drawing down by a factor of x before doubling is approximately x^(2(1-k)/k) for k between 0 and 1.

That formula does a lot of work. It says that halving the Kelly fraction doesn't just halve the drawdown probability - it transforms the exponent. Below is what that looks like for common drawdown thresholds, assuming a stable edge:

The cost of that risk reduction is surprisingly small. Geometric growth rate under fractional Kelly scales as k(2-k) times the full-Kelly growth rate. Half Kelly captures 75% of full Kelly's growth, and quarter Kelly captures 43.75%. So half Kelly gives up a quarter of the upside to slash the chance of a 50% drawdown from a coin-flip to a one-in-four event, and the chance of an 80% drawdown from one-in-five to one-in-twenty-five.

That asymmetric trade-off - small reduction in growth for a large reduction in volatility - is why half Kelly is the default among practitioners who can do the math.

Half Kelly is recommended whenever three conditions hold. The edge is real but estimated with normal uncertainty. The bettor will keep betting for a long time and cares about geometric growth rather than a single-period payoff. And there is no external constraint (margin call, withdrawal, deadline) that would make a transient drawdown ruinous.

Those conditions describe most serious sports betting, value investing, and quantitative trading. They are also approximately what a poker bankroll-management framework looks like - see expected value in poker for the parallel logic about how aggressively to play with a given edge.

The reason half Kelly works as a default is that it's robust to the most common mistake: overconfidence in your own edge. If your true edge is half of what you think it is - which is approximately what you should assume for any model you didn't already calibrate against years of out-of-sample data - then half Kelly on your estimated edge equals full Kelly on your true edge. You're back at the theoretical optimum, by accident, by being humble.

Quarter Kelly is appropriate when your edge estimate is itself a wide distribution rather than a point estimate. This is the norm in two situations.

The first is any new strategy that hasn't yet accumulated thousands of bets of out-of-sample evidence. A backtested model on historical data is notorious for overstating its real-world edge - a backtest with a 4% edge often has a real edge closer to 1–2%, and sometimes none. Quarter Kelly buys you survival during the period when you're discovering this.

The second is bets in regimes with structural shifts. Sports betting markets sharpen rapidly, financial markets reprice persistent inefficiencies, and what was a 3% edge last season can be a 0.5% edge this season. Quarter Kelly lets a strategy degrade gracefully rather than vaporise.

Below is how the trade-offs stack up for the three most common fractions, assuming you're working with a true 2% edge per bet on even-money outcomes:

Three-quarter Kelly is occasionally defensible, but only in a narrow set of circumstances. The edge must be quantitatively measured against a deep out-of-sample dataset. The portfolio must be diversified across many uncorrelated bets, so that any individual loss has a small effect on total bankroll. And the bettor must have a documented psychological tolerance for drawdowns of 30-40%, because they will happen.

Full Kelly is almost never the right choice. Even Edward Thorp, who first applied Kelly to blackjack card-counting in the early 1960s, recommended in his retrospective writings that practitioners use fractional Kelly. His own hedge fund, Princeton Newport Partners, used a heavily fractional approach with strong diversification.

The signs that you should scale down from half Kelly are equally important. If your edge depends on a market condition that could change (a soft sportsbook, an underpriced volatility regime, a competitor not yet in the market), scale down. If you've had two consecutive losing months and are starting to doubt the model, scale down. If you've taken on outside capital with redemption rights, scale down. Drawdowns interact with your own behaviour in ways that the math doesn't capture - and the math doesn't have to face redemption calls.

The two most famous case studies of professional Kelly-style betting both used fractional, not full, Kelly.

Edward Thorp's blackjack work, published in Beat the Dealer in 1962, established the original real-world application of Kelly. By his own later accounts, his team used roughly half-Kelly sizing because the variance of full Kelly was unacceptable for a team operating with shared capital and limited tolerance for visible swings at the table. Thorp's subsequent hedge fund, Princeton Newport Partners, ran for nearly twenty years with returns of around 15% annually and very low volatility - possible only because of fractional sizing combined with broad diversification.

Bill Benter ran a quantitative horse-betting syndicate in Hong Kong from the mid-1980s and reportedly earned hundreds of millions of dollars over several decades. Public interviews and conference talks attribute his sizing approach to a Kelly framework, but applied conservatively - typically well below full Kelly, and dynamically reduced when the model's confidence was lower. Benter's writing on the topic emphasises that the marginal cost of being too conservative is far smaller than the marginal cost of being too aggressive, which is the core intuition behind fractional Kelly.

The pattern across both is consistent. Professional bettors with a measured edge, working over long horizons, with their own capital at stake, choose growth-volatility trade-offs much closer to half Kelly than full Kelly. The theoretical optimum is almost never the practical optimum.

The mechanical steps for using fractional Kelly look like this. First, calculate the full Kelly stake for the bet, using your honest estimate of edge and the offered odds. The Kelly criterion calculator handles the arithmetic for binary bets and multiple-outcome scenarios.

Second, multiply by your chosen fraction. If you're using half Kelly, halve it. Quarter Kelly, quarter it. Don't deviate session-by-session - the discipline of a fixed fraction is half the point.

Third, recompute your bankroll between bets. Kelly is a proportional rule, so the stake should be a fraction of the current bankroll, not the starting bankroll. This automatically scales up bets after wins and down after losses, which is part of why Kelly survives long drawdowns: the bet sizes shrink with the bankroll, so the percentage drawdown stays bounded.

Fourth, cap individual bets. Even half Kelly can recommend a 20% bet when the edge is high and the odds are short. Most practitioners impose an additional cap - typically 5% to 10% of bankroll per bet - to defend against model errors on outlier opportunities. For the systematic relationship between bet size, bankroll, and risk of ruin, see position sizing with the Kelly criterion.

Three errors recur in almost every retail attempt at Kelly betting.

Mixing fractions in the same portfolio. Using half Kelly on bets you feel confident about and quarter Kelly on speculative ones sounds prudent, but it interacts badly with the fact that your confidence is itself the most error-prone input. The bets you feel most confident about are statistically the ones most likely to embed an overestimation bias. A fixed fraction across the whole portfolio is more robust than a self-reported confidence-weighted one. This is closely related to the lesson of overconfidence bias: the bets you'd label highest-confidence are exactly where your edge estimate is most likely inflated.

Ignoring correlation between bets. Kelly assumes independent outcomes. If you have ten bets on related markets - say, ten football matches with overlapping injury and weather effects - fractional Kelly on each one ignores that they could all lose together. The fix is to compute Kelly on the portfolio joint distribution, or to use a smaller fraction (eighth Kelly is common in highly correlated books) as a practical proxy.

Treating Kelly as a precise number. The output of a Kelly formula carries the precision of its inputs, which usually aren't precise. Quoting a 3.247% stake suggests a precision you don't have. Round to the nearest meaningful unit - typically the nearest 0.5% of bankroll - and accept the residual error as below the noise of your edge estimate. For more on the gap between the precision a model offers and the precision an estimate deserves, see risk vs uncertainty.