The Kelly criterion answers one specific question: what fraction of your bankroll should you stake on every bet with this edge to maximise long-term growth? It is a good answer to that question. It is a much less useful answer to "what should I actually stake?" and the gap between those two questions is why very few people who use Kelly sizing bet full Kelly.
The formula
f* = (b × p − q) ÷ b
where b is the decimal odds minus one, or the profit per dollar staked, p is your true win probability, and q is 1 − p.
Take a coin you believe is biased. The odds are even money, with decimal odds of 2.00 and therefore b = 1, and you estimate a 55% chance of winning rather than 50%.
f* = (1 × 0.55 − 0.45) ÷ 1 = 0.10 — stake 10% of bankroll
On a $1,000 bankroll, that is $100 per bet, recalculated after every result because the bankroll itself keeps changing. Half Kelly would be $50 and quarter Kelly would be $25.
Growth-optimal is not the same as survivable
"Maximises long-run growth rate" is a specific mathematical property, not a promise about what any particular run of results will look like.
The growth rate at stake fraction f, for a repeated even-money bet, is:
g(f) = p × ln(1 + f) + q × ln(1 − f)
At full Kelly, where f = 0.10, with our 55%/45% edge, that works out to about 0.501% expected growth per bet.
Halve the stake to 5% and growth drops to about 0.375% per bet. That is 75% of the full-Kelly rate, for half the stake size and roughly half the swings in bankroll along the way.
Quarter Kelly, at 2.5%, grows at about 0.219% per bet. That is 44% of full Kelly's rate, for a quarter of the stake and a much shorter list of bad nights.
That trade, giving up part of the growth rate in exchange for much smaller swings, is the main reason half Kelly is the default choice for many serious bettors. Full Kelly is optimal in the sense that no other fixed fraction grows the bankroll faster over an infinite number of trials. It is also the fraction that produces the largest and most frequent drawdowns of the options that still have positive growth, because the formula only cares about the eventual growth rate, not how difficult the path is along the way.
Why nobody actually bets full Kelly
- The formula assumes you know p exactly. You do not. Every real probability estimate carries error, and the Kelly stake scales directly with your edge - overestimate p by a small amount and you overstake by a proportional amount. The formula has no way to tell a real 5% edge from a mistaken one; it just bets as if the number you typed in is exact.
- Overbetting is punished harder than underbetting. Stake beyond roughly twice the true Kelly fraction on a bet and the growth rate turns negative - you can be right about which side has the edge and still be staking so aggressively that you are mathematically expected to go broke. Underbetting only ever costs you growth rate, never the whole bankroll. That asymmetry is why fractional Kelly is a hedge against being wrong about your own edge, not just a comfort blanket for variance.
- Large drawdowns are not a bug. Even a bettor with a real, correctly-estimated edge, betting full Kelly, will hit stretches that look like a broken model, purely from variance. Growth-optimal describes the destination over an infinite number of trials, not the shape of the road - and it is entirely possible to be on the growth-optimal path and still watch a third or more of the bankroll disappear before it recovers.
- Bets are rarely as clean as the formula wants. Kelly assumes a known, fixed, repeatable edge on independent events. Real edges drift, get priced out as markets sharpen, and correlate with each other more than the formula accounts for - betting several related markets each at their own "full Kelly" stake understates the combined risk, because it treats them as independent when they are not.
When Kelly correctly says: don't
The formula is just as useful when it produces a small or negative number.
Take a 3.00 decimal price, where b = 2, and estimate the true probability at 30%. That is below the market's implied probability of 33.3%, meaning you think the bet is actually worse than the price suggests:
f* = (2 × 0.30 − 0.70) ÷ 2 = −0.05
Negative. Kelly staking floors that at zero. There is no edge, so there is no stake.
Compare that with the same 3.00 price rated at a genuine 40%: f* = (2 × 0.40 − 0.60) ÷ 2 = 0.10
That gives you a real 10% stake.
The two probability estimates are only ten percentage points apart, yet one produces "don't bet" and the other produces a full-sized stake. That sensitivity is not a flaw in the formula. It is the formula refusing to create an edge from a probability estimate that does not actually beat the market price. That is precisely the discipline that flat staking does not enforce.
The bankroll is a moving target, on purpose
Kelly stakes a fraction of your current bankroll, recalculated after every result. It is not a fraction of the bankroll you started with. That design means that after a loss, the bankroll shrinks and the next stake shrinks with it. After a win, both the bankroll and the next stake increase. Under the pure Kelly model, with correctly estimated probabilities, this makes the staking process self-adjusting without the need for a separate stop-loss rule. Flat staking has no equivalent adjustment. A fixed dollar stake becomes a larger fraction of a shrinking bankroll after every loss, which is the opposite of what a variance-aware approach would do.
This self-correcting property is also why full Kelly never actually reaches zero during a finite losing run. Every stake is a fraction of what remains, so there is always something left to stake, however small. That does not make large drawdowns comfortable, but it is the mathematical reason Kelly staking cannot completely bankrupt the bankroll through a finite sequence of losses when the stakes are always calculated as a fraction of the remaining bankroll.
What this means in practice
Full Kelly is the mathematically correct answer to a question that is narrower than the one most bettors are actually asking. Half Kelly gives up some growth in exchange for a substantial reduction in how severe the bad stretches can be. That is why it is so often used as a practical default, while quarter Kelly can make sense when there is more uncertainty around the probability estimates.
Run your own edge and bankroll through the Kelly criterion calculator to see the full, half and quarter stakes side by side. The difference between them is often the most useful number the calculator produces.