Kelly Criterion Position Size

For most people and most situations, fractional Kelly is the right choice, and half-Kelly is the standard compromise. Full Kelly is the mathematical optimum for the objective of "maximise long-run compound growth", but it is fragile to small errors in the probability estimate and it produces very large drawdowns along the way. A full-Kelly bettor with a 55% win probability and even money will routinely experience drawdowns of 40% or more before grinding to a new high. Half-Kelly cuts the expected growth rate by about 25% but roughly halves the volatility, which for most capital pools is a very worthwhile trade. Quarter-Kelly is defensible when your p estimate is uncertain.

Two adjustments. First, use the lower end of your confidence interval, not the midpoint. If your estimate is "60% ± 5%", use 55% as your Kelly input. Second, apply a Kelly multiplier less than 1 — half-Kelly or third-Kelly — as a safety margin against estimation error. Combined, these two adjustments make your betting much more robust. An honest assessment is that the estimate error dominates everything else in Kelly sizing: getting the odds and the bankroll right matters little if your p is off by 5 percentage points in a consistent direction.

Yes, with caveats. The Kelly criterion applies to any repeated bet with a known edge distribution — that includes speculative trades, options positions, and portfolio allocation decisions. But there are three practical problems when moving from a casino bet to a market trade. First, market outcomes are not binary; you don't win b or lose 1, you win or lose a continuous amount drawn from a distribution. Kelly extends to continuous distributions via the same log-utility framework, but the formula becomes the solution to an optimisation problem rather than a simple ratio. Second, the edge in markets is uncertain and usually small, so your estimate of p is a major source of error. Third, market trades are not independent — a losing streak in a correlated portfolio is far more brutal than in a set of independent coin flips. In practice, serious quant traders use fractional Kelly on estimates of continuous return distributions, not the binary formula shown here.

It means the bet has negative expected value: the edge per unit wagered (b·p − q) is negative. Taken literally, the Kelly formula says you should take the other side of the bet if such a side is available — the size of the negative fraction is the fraction to wager on the opposite outcome. In most practical settings, the honest interpretation is simply "do not make this bet." Kelly has no smaller positive size to recommend for a negative-edge situation; any positive stake still loses money in expectation, just more slowly. The one exception is if you can genuinely take the other side (bet that the event does not happen), in which case you should.

Because longer odds mean higher variance per unit wagered, and the Kelly criterion penalises variance through the logarithm. Consider two bets with identical edges: even money at 55% (edge +10%) and 9:1 at 12% (edge 9 × 0.12 − 0.88 = +0.20... actually different edge). Let's pick equal edges: even money at 55% (edge +0.10) and 9:1 at 11% (edge 9 × 0.11 − 0.89 = +0.10). Same edge, but the Kelly fractions are 10% and 0.10/9 = 1.11%. The long-odds bet has to be much smaller because the losing streak potential is far worse in log terms — a few losses in a row at 9:1 with a 10% stake would be catastrophic. Kelly therefore sizes bets in inverse proportion to the variance, which for a binary bet is roughly proportional to 1/b.

Flat betting means wagering the same amount on every bet regardless of edge. Kelly sizes each bet proportionally to the edge and inversely to the odds. Flat betting is simpler and less sensitive to estimation error, and it avoids the "over-bet when rich, under-bet when poor" dynamic of proportional sizing. But it also leaves growth on the table when the edge is large and it over-bets when the edge is small relative to bankroll. In practice, many professionals use a hybrid: flat betting at a fixed small stake for the bulk of their betting, with proportional Kelly only on the highest-conviction opportunities. The two are not mutually exclusive, and Kelly's main value is often as a sanity check on whether a proposed stake is reasonable.

The log-growth rate g(f) = p·ln(1 + b·f) + q·ln(1 − f) is the expected change in ln(bankroll) per bet when you bet the fraction f. It is exactly the quantity Kelly maximises, and its maximum occurs at f = f*. Because compounding is multiplicative, the long-run growth rate of your bankroll is governed by this quantity rather than by the arithmetic mean of gains and losses. A positive g means your bankroll grows geometrically; g = 0 means you are on a random walk with no drift; g < 0 means you shrink in the long run regardless of individual wins. Even a positive-edge bet with g < 0 is possible if you over-bet — this is the mathematical definition of an "over-bet".