What is full, half and quarter Kelly?

Full Kelly is the stake the formula returns. Half and quarter Kelly are that stake cut to one half or one quarter. They grow a bankroll more slowly but with smaller swings, which most bettors prefer.

Why does it sometimes say no bet?

When your win probability is too low for the price, the Kelly fraction is negative. A negative stake would mean betting the other side, so for this bet the correct stake is zero.

Why use a fraction instead of full Kelly?

Full Kelly assumes your probability is exactly right. Real estimates are not, and full Kelly punishes an overestimate harshly. A fraction protects the bankroll when the input is a little off.

What bankroll should I use?

The amount you have set aside for betting, not your whole balance. Kelly sizes each bet as a share of that number, so it should be money you can treat as a single, dedicated pool.

Free calculator

Kelly criterion calculator

Size a bet with the Kelly criterion. Enter the price, your win probability and your bankroll, then pick full, half or quarter Kelly. When the edge is not there, it tells you not to bet.

Price

Win probability

Bankroll

Kelly fraction

Stake (Half Kelly)

$41.67

Of bankroll

4.17%

Half Kelly

Full Kelly

8.33%

before fraction

For information only. Not betting advice.

How it works

The Kelly criterion sets the stake that maximizes the long-run growth of a bankroll. The full-Kelly fraction is (b × p − q) ÷ b, where b is the decimal odds minus 1, p is your win probability, and q is 1 minus p.

Multiply that fraction by your bankroll to get the stake. Many bettors scale it down to half or quarter Kelly, which gives up a little growth for much smaller swings. When the formula returns a negative number, there is no edge and the stake is zero: the calculator shows no bet.

Kelly is only as good as the win probability you give it. An overstated probability makes Kelly bet far too much, which is the main reason bettors use a fraction of it.

Worked example

At +150 with a 45% win probability, b is 1.50, p is 0.45 and q is 0.55. Full Kelly is (1.50 × 0.45 − 0.55) ÷ 1.50 = 0.0833, or 8.33% of bankroll. Half Kelly is 4.17%, which on a $1,000 bankroll is a $41.67 stake. If the win probability were 35%, Kelly would be negative, so the answer is no bet.

Questions

What is full, half and quarter Kelly?: Full Kelly is the stake the formula returns. Half and quarter Kelly are that stake cut to one half or one quarter. They grow a bankroll more slowly but with smaller swings, which most bettors prefer.
Why does it sometimes say no bet?: When your win probability is too low for the price, the Kelly fraction is negative. A negative stake would mean betting the other side, so for this bet the correct stake is zero.
Why use a fraction instead of full Kelly?: Full Kelly assumes your probability is exactly right. Real estimates are not, and full Kelly punishes an overestimate harshly. A fraction protects the bankroll when the input is a little off.
What bankroll should I use?: The amount you have set aside for betting, not your whole balance. Kelly sizes each bet as a share of that number, so it should be money you can treat as a single, dedicated pool.

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