Lay Hedge Calculator

The Lay Hedge Calculator equalizes a back on a sportsbook with a lay on a betting exchange, after commission. Defaults: Back Stake $100, Back Odds 2.50, Lay Odds 2.20, Commission 5%. You backed a selection at 2.50 for $100; you now offer to lay the same selection at 2.20 and the exchange will take 5% of net winnings on the lay. The engine solves the lay stake that makes the two settlement states nearly equal once that 5% is deducted.

Denominator is lay odds minus commission times (lay odds − 1): 2.20 − 0.05 × 1.20 = 2.14. Lay stake is (back × back odds) / denom = 250 / 2.14 = $116.82. Liability is 116.82 × 1.20 = $140.19. Profit if back wins: 100 × 1.50 − 140.19 = $9.81. Profit if lay wins: 116.82 × 0.95 − 100 = $10.98.

The two profits differ by a little over a dollar because commission is charged only on the winning lay, so the equalizing formula targets the back-win state via the 2.14 denominator and leaves a small residual on the lay-win state. That is expected, not a rounding bug. The four result rows are Lay Stake $116.82, Liability $140.19, Profit If Back Wins $9.81, Profit If Lay Wins $10.98. Confirm you have at least $140.19 of available exchange funds before offering the lay; unmatched liability is not a hedge.

Zero commission is a useful sanity check. Set commission to 0 and denom becomes 2.20, lay stake 250 / 2.20 = $113.64, liability $136.36, both profits $13.64. The 5% haircut on the default therefore costs about $3–$4 of locked profit relative to a commission-free lay at the same 2.20. If a second sportsbook still offers 2.20 as a back on the other side, a two-back hedge (partial-hedge engine) avoids exchange commission entirely but needs the opposing selection rather than a lay of the same selection.

A second numeric walk: back $100 at 2.50, lay 2.05, commission 5%. Denom = 2.05 − 0.05 × 1.05 = 1.9975, lay stake = 250 / 1.9975 ≈ $125.16, liability ≈ $131.41, back-win profit ≈ $18.59, lay-win profit ≈ $18.90. Tighter lay odds (closer to the back) increase both profits; wider lay odds eat them. If lay odds exceed back odds, the “hedge” can lock a loss. The calculator will still print the four numbers. It does not advise you to lay, to hold, or to wait for a closer 2.20.

Laying is the exchange-native way to hedge a sportsbook back: you become the bookmaker on the same selection. Betfair opened that retail door in 2000; later exchanges copied the back/lay order book and the commission-on-net-winnings model. Before exchanges, the only retail hedge was an opposing back at another book. After exchanges, a single-selection ticket could be flattened without finding the other side of a two-way. That is why this calculator exists next to, not instead of, the two-way partial hedge tool.

Commission is the entire reason the formula is not “lay stake = back × back odds / lay odds.” Exchanges typically charge on net winnings, not on turnover, and only on the winning side of your matched bets. A 5% rate on the default 2.20 lay means you keep 95% of the lay’s gross profit when the selection loses. The 2.14 denominator capitalizes that haircut into a slightly larger lay stake ($116.82 versus $113.64 commission-free) so the back-win column stays close to the lay-win column.

The default lock is modest: about $10 either way on $100 back plus $140.19 liability reserved. The edge comes from the 2.50-to-2.20 gap, a 12% shortening of the decimal, which is a typical in-play move after an early goal or a shortened favorite. It is not “free money”; it is the crystallization of a price move you already captured on the back. If the 2.50 was itself −EV, locking $10 does not retroactively make the opener +EV. The calculator is silent on true probability.

Operational traps dominate this product. Liability must be available as exchange funds, not as “I have $116.82.” A lay at 2.20 for $116.82 risks $140.19. Partial matching leaves you with a leftover naked back. Minimum lay sizes, suspended markets, and in-play delay can prevent the hedge from landing at 2.20. Some exchanges charge commission on the net of a market, not per bet, which this single-market formula still approximates if you have no other bets in that market.

Related pages: free-bet hedge uses the same commission-adjusted denominator but a different numerator because free-bet stake is not returned. Partial hedge is the two-back analogue without commission. Cash-out versus hedge compares a book’s button with a two-way back hedge, not with a lay. Use the lay engine when you actually intend to lay the same selection. Educational output, not a recommendation to open an exchange account or to lay into a thinning book.

Equalising a sportsbook back with an exchange lay after commission uses a haircut denominator. Subtract the commission rate times (lay odds minus one) from the lay odds. Lay stake is then back stake times back odds, divided by that denominator. Liability is lay stake times (lay odds minus one). If the selection wins, profit is back net minus liability. If it loses, profit is lay stake times one minus the commission, minus the back stake. Defaults are a 100 dollar back at 2.50, lay odds 2.20, commission five percent.

Denominator is 2.20 minus 0.05 times 1.20, which is 2.14. Lay stake is 250 over 2.14, about 116.822, displayed as 116.82 dollars. Liability is 116.82 times 1.20, about 140.184, displayed as 140.19 dollars. Back-win profit is 100 times 1.50 minus 140.19, namely 9.81 dollars. Lay-win profit is 116.82 times 0.95 minus 100, namely 10.98 dollars. The 1.17 dollar gap is expected: with a positive commission a one-parameter cover cannot force both columns equal. At zero commission both would print 13.64 dollars, because profit then equals back stake times (back odds over lay odds minus one).

Positive lock requires laying at a shorter decimal than you backed. Laying at a longer decimal locks a loss of back stake times (one minus back odds over lay odds). Shortening the lay from 2.20 to 2.10 raises the denominator to 2.045, lay stake to about 122.25 dollars, liability to about 134.47, back-win 15.53, lay-win 16.14. A commission bump from five to six percent only lifts lay stake from 116.82 to about 117.48. Sensitivity to the lay price dominates the rate.

Retail laying became possible after betting exchanges opened a back-and-lay book around 2000, with commission typically charged on net winnings rather than turnover. Before that, the only retail flatten was an opposing back at another shop. Liability must be available as exchange funds: a 116.82 dollar lay at 2.20 risks 140.19, not 116.82. Partial matching leaves a leftover naked back. Rule-4 after a non-runner and dead-heat on a place market both break the pre-race numbers.

Assumptions: one back and one lay on the identical selection and market; commission as a fraction of net winnings on the lay only; no other bets in the market netting that commission; full match at the typed lay odds; no void. Zero commission is the sanity check that recovers the schoolbook cover. The four printed quantities are arithmetic on the four inputs, not advice to lay into a thinning book.