A lay bet is a bet that something will not happen. On a betting exchange you can take the bookmaker's side of any market: offer odds, accept a backer's stake, and pay out if the outcome wins. The arithmetic is a mirror image of backing, and once you see the mirror, every lay bet becomes an ordinary back bet in disguise — which is what makes hedging and arbitrage against bookmakers solvable with the same formulas.
The four numbers of a lay
When you lay at odds L against a backer's stake B:
- Backer's stake (B) is what the other side risks. It is also what you win if the outcome loses.
- Liability is what you risk: B × (L − 1). If the outcome wins, you pay this.
- Profit if the outcome loses is B, minus commission on it.
- Odds (L) are the price you are offering, which the exchange shows in decimal form.
liability = B × (L − 1) profit if outcome loses = B × (1 − c) (c = commission on net winnings)
loss if outcome wins = liability
Lay 100 at 2.10, 5% commission
Liability: 100 × 1.10 = 110. If the outcome loses: +95 (100 minus 5%). If it wins: −110. You are risking 110 to win 95.
Exchanges usually ask you to enter the backer's stake and show the liability; sometimes you can enter the liability instead. The calculators on this site treat the liability as "the stake" of a lay, because that is the money you put at risk and the number the equal-profit equations need.
The mirror: a lay is a back on the complement
Risking 110 to win 95 is exactly what a back bet does. Which back bet? One on "not this outcome", with a stake of 110 and a profit of 100 before commission. Its decimal odds are (stake + profit) / stake = 210 / 110 = 1.909. In general:
back odds on the complement = L / (L − 1) 2.10 → 1.909 1.50 → 3.00 3.00 → 1.50 1.05 → 21.0 stake
of that back bet = liability
Two things follow. First, laying a short price (1.05) is backing a long one (21.0) — laying heavy favourites is a longshot bet with a big liability, which surprises people who think of it as "safe". Second, commission applies to the profit of the equivalent back bet in the normal way, so the effective odds are 1 + (L/(L−1) − 1) × (1 − c).
Lay 2.10 at 5% as a back
Equivalent back odds: 2.10 / 1.10 = 1.909. After 5% commission: 1 + 0.909 × 0.95 = 1.864. Break-even for "not this outcome": 1/1.864 = 53.7%. So laying at 2.10 is profitable in the long run if the outcome happens less than 46.3% of the time.
Hedging a bookmaker bet
The classic use. You backed a team at a bookmaker at 2.20 and can now lay it on an exchange at 2.10. Treat the lay as a back on "the team does not win" at 1.909 (1.864 after 5% commission) and solve for equal profit.
S = 1/2.20 + 1/1.864 = 0.4545 + 0.5366 = 0.9911 ROI = 1/S − 1 = 0.90% bookmaker stake = total ×
0.4545 / 0.9911 = 45.9% of total exchange liability = total × 0.5366 / 0.9911 = 54.1% of total
On a total of 100, that is 45.9 at the bookmaker and a liability of 54.1 on the exchange, which corresponds to a backer's stake of 54.1 / 1.10 = 49.2. If the team wins: bookmaker pays 45.9 × 1.20 = 55.1 profit, exchange loses 54.1, net +0.9. If it loses: bookmaker loses 45.9, exchange pays 49.2 × 0.95 = 46.8, net +0.9. The arbitrage calculator reports both the liability and the backer's stake to enter on the exchange.
Usually the bookmaker bet is already placed, so its stake is fixed. Use fixed-leg mode with the bookmaker stake locked, and the calculator sizes the lay around it.
Laying to lock in profit or cut a loss
The same equations apply when the bet was not an arbitrage to begin with. Suppose you backed at 4.00 and the price has since fallen to 2.00 because your team scored. Laying at 2.00 now locks in a profit whatever happens; laying at a price higher than you backed at locks in a loss but reduces the variance. The equal-profit lay for a back stake b at odds d, laying at L with commission c, is:
backer's stake to lay = b × d / (L − c × (L − 1) − c + 1) (with no commission: b × d / L)
Back 100 at 4.00, lay at 2.00, no commission
Backer's stake to lay: 100 × 4 / 2 = 200. Liability: 200. If the team wins: +300 from the back, −200 from the lay = +100. If it loses: −100 from the back, +200 from the lay = +100. A locked 100 either way. With 5% commission the lay stake becomes slightly larger and the locked profit slightly smaller; the calculator handles the exact figure.
Laying in multi-way markets
In a three-way market a lay on one outcome pays if either of the other two happens. Treated as a back, it is a back on the set of both other outcomes. That is still one leg in the equal-profit equations: it wins on two outcomes and loses on one. The calculator's solver handles legs that win on any subset of outcomes, which is why a 1X2 position with a lay on the draw and backs on home and away can be sized for equal profit like any other.
Commission on turnover
Most exchanges charge on net winnings, and everything above assumes that. If commission is charged on turnover instead, the lay's equivalent back bet has commission on both its win and its loss side, and there is no single effective price. The calculators apply the turnover charge to the liability and warn that this is an assumption, since real exchanges with turnover charges define the base differently.
Common errors
- Confusing stake and liability. On a lay, your risk is the liability, not the backer's stake. At 5.00 a backer's stake of 100 puts 400 at risk.
- Forgetting commission is on the backer's stake. Your lay profit is B × (1 − c), not B.
- Laying short prices casually. Laying 1.10 is a 10-to-1 bet against; one upset costs ten wins.
- Using displayed lay odds in the arbitrage test directly. Convert to L/(L−1) first; the implied probability of the lay leg is (L − 1)/L, not 1/L.
Laying to trade: green up and red out
Exchange traders rarely hold a bet to settlement. They back at one price and lay at another, or the reverse, and the difference is the profit or loss, equalised across outcomes so it no longer depends on the result. "Greening up" is equalising a profit; "redding out" is equalising a loss to stop it growing.
The equalising trade is the equal-profit lay from the section above. Back 100 at 3.00; the price drops to 2.50. Lay 100 × 3.00 / 2.50 = 120 at 2.50 (liability 180). If the outcome wins: +200 − 180 = +20. If it loses: −100 + 120 = +20, before commission on the 20. The profit is locked. Had the price risen to 4.00 instead, the equalising lay would be 75 (liability 225): win +200 − 225 = −25, lose −100 + 75 = −25. A locked loss of 25, which is the position's value at the new price and smaller than the 100 at risk if the outcome loses.
The general rule: profit on the trade is the back stake times (back price / lay price − 1), spread across outcomes by the lay. Prices that move in your favour after a back (they shorten) or after a lay (they lengthen) produce a green book; the other way produces a red one. Commission applies to the net profit in the market, so a green book of 20 pays about 19 at 5%.
Liquidity and partial matches
A lay only exists once someone backs against it. The exchange shows, at each price, how much is available to back and to lay; a lay of 120 at 2.50 needs 120 of backers' money at 2.50 or better, and if only 80 is there the rest waits unmatched. Unmatched money can be left in the market at your price, moved to the current price, or cancelled. For a hedge that must be complete before the event starts, place the lay early enough to be matched, or lay at a slightly worse price where there is depth.
The equal-profit formulas assume the full amount is matched at the stated price. A partial match at one price and the remainder at another is two lays, and the position's profit is no longer equal across outcomes. Fixed-leg mode in the calculator, with the matched amounts locked, recomputes the rest around what actually went through.
Rounding and minimum stakes
Exchanges enforce a minimum backer's stake and round liabilities to the cent, so the exact equal-profit lay is rarely placeable. The practical approach is to round the backer's stake to something the exchange accepts, recompute the two outcomes, and accept a small difference between them; the arbitrage calculator's rounding mode does the recomputation and shows the worst outcome. On a hedge worth a few units, a rounding difference of a few cents is noise; on a thin arbitrage it can be the whole margin, which is one more reason to leave the thinnest positions alone.
Summary
A lay at L with liability X is a back on the complement at L/(L−1) with stake X. Apply commission to that back bet's profit, then use every ordinary formula: implied probability, effective odds, equal-profit stakes. The exchange shows you B and L; the maths wants liability and L/(L−1); the calculators translate between the two.