How much to stake on a +EV bet
A +EV bet is a price. The stake is a second decision. You can take a good number and still size it so large that a normal losing run knocks you out, or so small that the edge never moves the bankroll.
This page is the Kelly criterion for sports betting: the formula for a +EV decimal-odds bet, why full Kelly is usually too much, and why fractional Kelly — quarter Kelly especially — is the usual start. How you run the whole process lives on the positive EV betting strategy page. This article owns the stake. It does not retell that process.
The price is not the stake
Expected value answers whether the quote is worth taking. It does not tell you how many units to put on it.
A 6% edge on a 1.85 favorite and a 6% edge on a 4.50 underdog are not the same ticket. Same sign. Different variance. Same “+EV” label. The stake has to follow the odds and the win probability, not a flat unit that ignores both.
The edge is an input. You get it from a fair probability and the offered decimal. That arithmetic is the EV calculator. This page takes the edge as given and asks how much of the bankroll belongs on the slip.
Finding the price is a different job. The manual method is in How to find positive EV bets. A value bet scanner runs the same comparison on a live board. Neither page sizes the bet. They flag a number. You still decide the stake.
People collapse the two questions because they feel related. They are sequential. First: is this +EV? Then: how much of the roll?
A flat 1% or 2% per ticket ignores the size of the edge and the length of the price. Kelly uses both.
The Kelly fraction
The Kelly criterion gives the fraction of current bankroll that maximizes the long-run growth rate of that bankroll, if you know the win probability and the payoff. John Kelly published it in 1956. For a single +EV decimal-odds bet that loses the whole stake, the standard form is:
f* = (b p − q) / b
where:
- f* is the full-Kelly fraction of bankroll
- b = decimal odds − 1 (the net odds: what you win on a 1-unit stake)
- p = true win probability
- q = 1 − p
If f* is zero or negative, you do not bet. There is no stake on a −EV number.
Fractional Kelly is that fraction scaled down:
quarter Kelly = 0.25 f*
half Kelly = 0.50 f*
One worked example. The decimals are made up so the arithmetic is visible. This is not a live card and not a claimed return.
True win probability is 0.50. A book is offering 2.25. Implied from the quote is 1 ÷ 2.25 ≈ 44.4%. The number is +EV.
- b = 2.25 − 1 = 1.25
- p = 0.50
- q = 0.50
- f* = (1.25 × 0.50 − 0.50) / 1.25 = (0.625 − 0.50) / 1.25 = 0.125 / 1.25 = 0.10
Full Kelly is 10% of the current bankroll. Quarter Kelly is 0.25 × 0.10 = 2.5%. Half Kelly is 0.50 × 0.10 = 5%.
On a €4,000 bankroll that is €400 full, €200 half, €100 quarter.
The same inputs give EV = (0.50 × 2.25) − 1 = 0.125, or 12.5% expected return per unit staked. Kelly used the edge and the odds. It did not use a flat percentage of roll.
| Multiplier | Fraction of bankroll | On €4,000 |
|---|---|---|
| Full Kelly (1.00) | 10% | €400 |
| Half Kelly (0.50) | 5% | €200 |
| Quarter Kelly (0.25) | 2.5% | €100 |
That is one ticket. After it settles, the bankroll has changed. The next f* is computed on the new roll, not the starting one.
p is the true probability, not the book’s implied. If you plug implied into Kelly you will size a number that has no edge as if it did, or you will under-size a real one. Get p from the fair, no-vig estimate you already used to call the bet +EV. Then run Kelly.
Why full Kelly is usually too much
Full Kelly is optimal only when p is known. In sports betting, p is an estimate. A sharp no-vig line is a good estimate. It is still an estimate. News the reference book has not taken, a thin market, a mismatched prop — the printed edge can be wrong.
If you overstate p, f* comes out too large. Overbetting Kelly is worse than underbetting it. Stake more than f* and you raise the chance of a deep drawdown while you lower the long-run growth rate. Extra variance, worse path. There is no prize for “more aggressive than optimal.”
Even with a correct p, full Kelly is loud. A 10% stake on a near-even number produces swings most people cannot sit through. A short losing run is not a failed process. It is the sample. Full Kelly makes that sample expensive enough that people abandon a sound book, or they start chasing the next card to get even.
The formula also assumes you can keep betting the same game, at the same edge, against only this bankroll. Real books have limits. That alone argues for a smaller fraction.
So: full Kelly is aggressive because the probability is an estimate, and because the path variance is large even when the estimate is good. Use it as the ceiling the math names, not as the default stake.
After you take the number, closing line value is how you check whether the prices were actually good. That is the next page. It is not a second staking formula.
Quarter Kelly, half Kelly
Fractional Kelly is the same formula, multiplied by 0.25 or 0.50.
Quarter Kelly (0.25) is the usual start. It keeps the logic — bigger edge or longer odds, bigger stake; smaller edge, smaller stake — and cuts the swings. You give up some growth rate. You keep more of the roll through a normal losing streak. That trade is the point.
Half Kelly (0.50) sits in the middle. Same direction, less reduction. Use it when you trust the probability more, not when last week was green.
Neither number is a published return. Quarter Kelly does not imply a standard ROI. It is a risk lever. Two people on quarter Kelly with different edges and different odds will not have the same month. Do not treat 0.25 as a performance forecast.
A few rules that follow from the formula, not from folklore:
- If f* is tiny, the stake is tiny. Do not round a 0.4% quarter-Kelly ticket up to a “respectable” unit. The formula already told you the edge does not justify the size.
- If several +EV numbers are live at once, you cannot full-Kelly each of them. The fractions add. Fractional Kelly leaves room for more than one ticket.
- If the price moves after you size it, the stake you calculated is for the old number. Recalculate or skip. Do not keep the old stake on a worse quote.
People ask for a single unit size they can reuse. Kelly will not give them one. That is the feature.
What EV Kings uses
EV Kings sizes from the bankroll you set and a Kelly multiplier.
Onboarding default is Quarter Kelly (0.25). That is the start because the probability on each card is an estimate — a sharper market used as the reference — and because full Kelly is too loud for a new book. You can raise the multiplier later. You should not start at 1.00 to get there faster.
You enter a bankroll. The feed uses that roll and the 0.25 default to print a stake on each betting card, next to the EV%. The public Kelly calculator is the same arithmetic on one ticket: bankroll, decimal odds, win probability, multiplier. Use it to see the number before you have a card in front of you. This page will not walk the fields.
The edge input is the same fair probability you already used. If you are checking a quote by hand, run it through the EV calculator first, then Kelly. If you are on the feed, the card has already done both.
The bankroll you type should be the betting roll, not household cash. Kelly assumes the figure you give it is the figure you can lose tickets against. Inflating it to print a bigger stake is just full Kelly by another name.
Log the bet at the price you took. Leave the result. A week of P&L does not rewrite f*. The performance guarantee is about the subscription, not the staking rule. It does not cover betting losses.
The calculator confirms a single stake. The feed is where the next +EV number is. Size, then go there.
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