The Kelly criterion, and why to halve it

There is a mathematically optimal bet size. It is also brutally unforgiving of an overestimated edge, which is why half of it is the working default.

There is a mathematically optimal bet size. It was worked out at Bell Labs in 1956 for signal transmission, adopted by gamblers almost immediately, and it is brutally unforgiving of an overestimated edge — which is why nearly everyone who uses it seriously bets a fraction of it.

The formula

f = (b × p − q) ÷ b, where b is the profit per unit staked, p is your probability of winning, and q is 1 − p. The answer f is the share of your bankroll to bet.

Sizing a real bet

The price is +120, so b = 1.20.
You believe the true chance is 50%, so p = 0.50 and q = 0.50.
f = (1.20 × 0.50 − 0.50) ÷ 1.20 = 0.10 ÷ 1.20.
= 0.083.

Full Kelly says 8.3% of the bankroll — $166 of a $2,000 roll. That is eight times a normal 1% unit.

That number should feel uncomfortable, and the discomfort is correct. Kelly maximises long-run *growth rate*, not comfort, and it assumes something that is never true.

The assumption that breaks it

Kelly is optimal only if your probability estimate is exactly right. It is not. Nobody's is.

The asymmetry is what matters. Underestimate your edge and you simply grow slower. Overestimate it and you overbet — and overbetting compounds against you, because the losses come off a shrinking bankroll. Bet twice the Kelly stake with no edge at all and the expected long-run outcome is zero.

Betting a multiple of Kelly, roughly
Stake	Growth rate	Swings	In practice
Quarter Kelly	~44% of maximum	Small	Conservative and very durable
Half Kelly	~75% of maximum	Moderate	The working default
Full Kelly	100%	Severe	Correct only with a perfect estimate
Double Kelly	0%	Extreme	Long-run growth of nothing

Half Kelly is the standard compromise for a reason: it keeps three quarters of the growth for roughly half the volatility, and it forgives an edge estimate that is somewhat too optimistic.

Practical corrections

Cap it. However confident you are, a hard ceiling of 2-3% of bankroll per bet prevents one bad estimate from mattering too much.
Shade your probability toward the market. If your number and the no-vig line disagree wildly, the market is usually closer.
Do not stack correlated bets. Three Kelly-sized bets on outcomes that move together is one much larger bet wearing a disguise.
Recalculate on the current bankroll, not the one you started the season with.

Kelly on a bad edge estimate is worse than flat betting

Kelly amplifies whatever you feed it. Given a well-measured edge it sizes better than any fixed rule; given wishful thinking it sizes the wishful thinking. If you have not yet measured your closing line value over a real sample, flat betting is the more honest choice.

Enter a price, your fair number and a bankroll — the calculator does full and half Kelly. Size a bet with Kelly.