Kelly criterion calculator: stake size, edge and half Kelly

Kelly criterion calculator

Your edge: -
Full Kelly stake: -
Suggested stake: -

Key facts

Kelly stake as a share of your bank = (p x odds - 1) / (odds - 1), where p is your estimated chance of winning.
At $2.50 with a 45% estimate, your edge is 12.5% and full Kelly is 8.33% of the bank: $83.33 from $1,000.
No edge means no bet: at $2.50 Kelly stakes nothing unless you rate the chance above 40%.
If your 45% is really 42%, full Kelly leaves a typical $1,000 bank at about $905 after 100 bets, while half Kelly grows it to about $1,081.

How to use the Kelly criterion calculator

Enter the decimal odds you can get, your own estimate of the chance in percent, and the size of the bank you set aside for betting. Choose full, half or quarter Kelly. The calculator shows your edge, the full Kelly stake and the stake for the fraction you picked. If there is no edge at that price, it tells you so and shows the price you would need.

The chance has to be your estimate, not the bookmaker's. Typing in the implied probability of the price always gives a Kelly stake of zero, because at that point you have no edge.

The Kelly criterion formula

The Kelly criterion stakes a share of your bank, f, equal to your edge divided by the profit odds:

f = (p x odds - 1) / (odds - 1)

Here p is your chance of winning as a decimal and odds is the Australian decimal price. The top line, p x odds - 1, is your edge: the average profit per $1 if your estimate is right. The bottom line, odds - 1, is the profit per $1 when the bet wins. The textbook version, (b x p - q) / b with b = odds - 1 and q = 1 - p, gives the same answer.

Worked example: $2.50 with a 45% estimate

You can get $2.50 on a team you rate a 45% chance, and your betting bank is $1,000.

Edge: 0.45 x 2.50 - 1 = 0.125, so 12.5% per dollar staked.
Profit odds: 2.50 - 1 = 1.5.
Full Kelly: 0.125 / 1.5 = 0.0833, or 8.33% of the bank.
Stakes: full Kelly $83.33, half Kelly $41.67, quarter Kelly $20.83.

Price $2.50 implies 40%. Your estimate is 5 points higher, and that gap is the whole reason to bet. Rate the team at 40% or less and Kelly says stake nothing; your estimate of 45% only has value at prices longer than $2.22. The expected value calculator shows what that edge is worth on average per bet.

How the Kelly stake moves with your estimate

Kelly is very sensitive to the chance you type in. Here is the same $2.50 price and a $1,000 bank with different estimates.

Your estimate	Edge	Full Kelly	Full Kelly stake	Half Kelly stake
38%	-5.0%	No bet	$0	$0
40%	0.0%	No bet	$0	$0
42%	5.0%	3.33%	$33.33	$16.67
45%	12.5%	8.33%	$83.33	$41.67
48%	20.0%	13.33%	$133.33	$66.67
50%	25.0%	16.67%	$166.67	$83.33

Moving your estimate from 42% to 48% quadruples the stake. If you cannot tell a 42% chance from a 48% chance, full Kelly is betting on the precision of your guess.

Why most punters use half or quarter Kelly

Kelly maximises the long-run growth of your bank only when your estimate is right. When it is too high, full Kelly over-bets. The table shows the typical result, using the long-run growth rate, of 100 bets at $2.50 starting from $1,000, sized for a 45% estimate.

Staking	Stake per bet	True chance 45%	True chance 42%	True chance 40%
Double Kelly	16.67%	$1,014	$300	$134
Full Kelly	8.33%	$1,673	$905	$601
Half Kelly	4.17%	$1,473	$1,081	$879
Quarter Kelly	2.08%	$1,255	$1,074	$968

Three lessons sit in that table. Betting double Kelly grows almost nothing even when you are right. Full Kelly shrinks the bank if you are only 3 points too optimistic. Half Kelly gives up $200 of the $673 best-case profit but stays in profit at 42%, and loses far less when there was never an edge.

Pundit tip: if you are new to estimating chances, start at quarter Kelly and keep a record of your estimates against results. Move up only if your record shows a real edge over a few hundred bets.

Kelly at short and long prices

Kelly stakes are smaller on longshots, even when the edge is bigger, because the bet loses more often.

Price	Your estimate	Edge	Full Kelly
$1.50	70%	5%	10% of bank
$2.50	45%	12.5%	8.33% of bank
$11.00	10%	10%	1% of bank

The $11.00 bet has double the edge of the $1.50 bet, but Kelly stakes a tenth as much, since you expect to lose nine times out of ten.

What Kelly does not cover

Kelly assumes one bet at a time, a price that is fixed, and a bank you resize after every result. It does not handle several bets running at once, and it says nothing about how good your estimates are. It also cannot fix a price with a big margin built in; check the market with the implied probability calculator first, and use the odds converter for prices quoted in other formats.

Multis need extra care: a leg you rate highly still multiplies with the others, so size the whole slip, not each leg. The multi bet calculator gives the combined price to feed into Kelly. If you are unsure what a price means, read how to read odds first, and keep your betting bank to money you can afford to lose. Our gambling help page lists free support, and every tool is on the bet calculators page.

Frequently asked questions

What is the Kelly criterion?

It is a formula that sets your stake as a share of your betting bank, based on the odds and your own estimate of the chance. It stakes more when your edge is bigger and nothing when you have no edge.

How do you calculate a Kelly stake?

Multiply your chance by the decimal odds, subtract 1, and divide by the odds minus 1. At $2.50 and 45%: (0.45 x 2.5 - 1) / 1.5 = 0.0833, so 8.33% of your bank.

What is half Kelly?

Half Kelly stakes half the full Kelly amount. It grows a bank more slowly when your estimates are right, but it is far more forgiving when they are too optimistic, which is why many punters use half or quarter Kelly.

Does the Kelly criterion work for sports betting?

The maths works for any bet with a known price, including head to head and line bets. It is only as good as your estimate of the chance. If your estimates are not better than the market's, Kelly will tell you to bet nothing.

Can I use Kelly on a trifecta or other tote bet?

Not reliably. Kelly needs the price you will be paid, and a tote dividend is only known after the race. Use it on fixed odds bets.