MoneyKey number

Kelly criterion: sizing bets by edge

The Kelly criterion says what share of your bankroll to bet when you have an edge. The formula is edge divided by odds. If you have no edge, Kelly says bet nothing. Most bettors use half Kelly or less.

Reviewed Oct 15, 2026

Answer first

90s

01Kelly share = (b × p − q) ÷ b.
02A 55% bet at even money gets 10% of bankroll.
03Half Kelly cuts swings a lot for a small loss in growth.

Key numbers

Kelly examples

10%Full Kelly55% at even money

5.5%Full Kelly55% at -110

0%No edgeBet nothing

HalfKelly fractionCommon choice

In short

Key takeaways

Kelly needs a real edge to work.
Bet size grows with edge and falls with long odds.
Overestimating your edge leads to over-betting.
Fractional Kelly is safer in practice.

Progress

From edge to bet size

1
Your chance
p
2
Payout odds
b to 1
3
Losing chance
q = 1 − p
4
Kelly share
(b × p − q) ÷ b
5
Bet
Share × bankroll

Uses decimal profit per $1 staked as b.

Kelly share by chance and price

Your chance	Price	b	Full Kelly	Half Kelly
52%	Even money	1.00	4%	2%
55%	Even money	1.00	10%	5%
55%	-110	0.909	5.5%	2.7%
40%	+200	2.00	10%	5%
30%	+200	2.00	0%	0%

Our own calculations; 30% at +200 has no edge.

How the formula works

Let b be the profit per $1 staked, p your chance of winning and q your chance of losing. Kelly says bet (b × p − q) ÷ b of your bankroll. At even money b is 1, so a 55% chance gives 1 × 0.55 − 0.45, or 10%.

At -110 you win $0.909 per $1. With the same 55% chance the edge is 0.909 × 0.55 − 0.45, or about 0.05, and dividing by 0.909 gives about 5.5%. The worse price halves the bet.

John Kelly, a researcher at Bell Labs, published the idea in 1956. It maximises the long-run growth rate of a bankroll, if your chances are right.

A $1,000 bankroll, 55% bets at even money

Strategy	Bet	After a win	After a loss
Full Kelly	$100	$1,100	$900
Half Kelly	$50	$1,050	$950
Quarter Kelly	$25	$1,025	$975
Flat 2%	$20	$1,020	$980

Kelly bets are re-sized as the bankroll changes.

Why most people use half Kelly

Full Kelly gives the fastest growth over a very long run, but the swings are large. A full Kelly bettor has about a 50% chance of seeing the bankroll halve at some point. Half Kelly keeps about three quarters of the growth with far smaller drops.

The bigger problem is guessing p. If you think you win 55% but really win 52%, full Kelly makes you bet more than double the right size. Over-betting by twice Kelly or more removes the growth entirely. A fraction of Kelly gives room for error.

Sequence

Using Kelly sensibly

Step 01
Estimate your chance
Use real records, not hopes.
Step 02
Convert the price
Find b for the odds.
Step 03
Run the formula
Get the full Kelly share.
Step 04
Take a fraction
Half or a quarter.
Step 05
Resize often
Use your current bankroll.

Kelly and real betting

Sportsbook prices include vig, so most bets have a negative edge and Kelly says skip them. Kelly only helps if you can show over many bets that you beat the closing line or the market.

Casino games with a fixed house edge, such as roulette or slots, always give a Kelly share of zero. No bet sizing can change a negative edge into a positive one.

Floor rules

Kelly terms

Know before you sit

Edge: Expected profit per $1 bet.
Bankroll: Money set aside only for betting.
Fractional Kelly: Betting a share, like half, of the Kelly amount.
Drawdown: A fall from a bankroll peak.

Common mistakes

Guessing your win rate: Use records from many bets.
Using full Kelly: Swings are often too big.
Kelly on house-edge games: The answer is always zero.
Not resizing: Bets should follow your bankroll.

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After the 90 seconds

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01Basics

What is the Kelly criterion?

A formula for the share of bankroll to bet when you have an edge: (b × p − q) ÷ b, where b is profit per $1, p your chance to win and q your chance to lose.

What does Kelly say with no edge?

Bet nothing. If b × p is not above q, the formula gives zero or a negative number.

Who came up with it?

John L. Kelly Jr., at Bell Labs, in a 1956 paper on information theory. Rules differ between licensed sportsbooks, so read the house rules.

02Using it

What is half Kelly?

Betting half the full Kelly amount. It keeps most of the growth while cutting swings and the harm of a wrong estimate.

How do I know my chance?

Only from a long record or a proven model. Many bettors compare their prices with the closing line to check.

Should I use Kelly on parlays?

Parlays have long odds and big vig, so Kelly shares are tiny or zero for most bettors.

03Risks

Can Kelly lose my whole bankroll?

In theory a true Kelly bettor never bets it all, but large drops are common, and over-betting can wipe out growth.

Does Kelly work for slots?

No. Slots have a house edge, so Kelly always says zero. Rules differ between licensed sportsbooks, so read the house rules.

Is flat betting simpler?

Yes. Many bettors use 1% to 2% flat units because it is easy and limits risk. Rules differ between licensed sportsbooks, so read the house rules.

Sources

Wikipedia — Kelly criterion Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Formula and fractional Kelly
Wizard of Odds — Sports betting Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Sports betting math
American Gaming Association — Sports betting Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026US legal sports betting data
National Council on Problem Gambling — Help and resources Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Free, confidential help: call or text 1-800-GAMBLER