Free Bet Hedge Calculator

The Free Bet Hedge Calculator converts a stake-not-returned free bet into an approximate locked cash amount by backing at a sportsbook and laying on an exchange. Defaults: Free Bet $50, Back Odds 4.00, Lay Odds 3.60, Commission 5%. A free bet that does not return stake pays only the profit portion on a win: $50 × (4.00 − 1) = $150.00, not $200. That $150 is the quantity you lay off. The engine then uses the same commission-adjusted denominator as the lay-hedge tool.

Denominator = 3.60 − 0.05 × (3.60 − 1) = 3.60 − 0.05 × 2.60 = 3.60 − 0.13 = 3.47. Lay stake = backProfit / denom = 150 / 3.47 = $43.23. Liability = 43.23 × 2.60 = $112.39. Profit if the back (free bet) wins: 150 − 112.39 = $37.61. Profit if the lay wins: 43.23 × 0.95 = $41.07 (the free bet expires worthless, you do not lose the $50 because it was not your cash). Average of the two profits is $39.34. Conversion is that average divided by the free-bet face: 39.34 / 50 = 78.67%.

The highlighted Conversion row therefore prints 78.67%, with Lay Stake $43.23 and Locked Profit $39.34 (the average). The two sides are not identical — $37.61 versus $41.07 — for the same commission reason as in the lay hedge. Matched-betting worksheets often quote the average as “the” conversion. If you need the worse column as a floor, use $37.61, which is a 75.22% conversion on the $50 token.

Higher back odds usually raise conversion because more of the token sits in (odds − 1), but they also widen the typical spread. Back 3.00 / lay 2.80 / 5%: backProfit = $100, denom = 2.71, lay = $36.90, conversion ≈ 68.6%. The default 4.00 / 3.60 pair is more efficient on paper. Type the actual pair; a 4.00 back with a 4.10 lay is not a hedge.

Eligibility rules sit outside the formula. Some tokens exclude odds below 2.00, in-play, or certain sports; some are stake-returned (SR) rather than stake-not-returned (SNR). This engine is SNR only. An SR token would use backProfit = freeBet × backOdds and would require subtracting the returned stake from a different identity — use the ordinary lay-hedge calculator with back stake equal to the token. The numbers here are a worked SNR example, not advice to request free bets or to convert them.

Free-bet conversion is the retail name for locking a promotional token into cash by backing and laying the same selection. The industry that grew around it — matched betting — treats the token as a wasting asset whose expected value is conversion% × face, not face. A $50 SNR token at 78.67% is $39.34 of cash in the default model, provided both sides are matched and the book pays the free-bet win as profit-only. That last clause is the whole game: SNR means a winning $50 at 4.00 credits $150, not $200.

Why SNR exists: the book wants the token to look like $50 of stake while costing closer to $50 × (1 − 1/O) in expected payout at typical odds, plus the overround. Hedging on an exchange transfers most of that cost into a near-certain debit the book still pays you, which is why terms bar “obviously hedged” play and why accounts get limited. The calculator does not model gubbing, delays, or voided tokens. It models the two cash-flows if both bets settle as entered.

History is recent. UK and European books scaled free-bet acquisition offers in the 2000s; Betfair-style exchanges made the lay half mechanical; spreadsheet communities standardized the SNR formula this engine uses. The denom L − r(L − 1) is the same commission adjustment Joseph Buchdahl and the matched-betting manuals popularized. Armand’s 19th-century Dutching is a cousin (equal profit across outcomes) but Dutching is several backs; free-bet conversion is one promotional back plus one lay.

The 78.67% default is not a universal constant. Tight back/lay spreads at low odds convert worse in SNR terms; long shots convert better on paper and worse in practice because of maximum-bet caps, in-play suspension, and place-term traps on horses. A $50 token laid into a $43.23 hole also needs $112.39 of exchange liability — more than twice the token — which is a liquidity requirement, not a rounding detail. If the exchange balance cannot cover $112.39, the conversion is fictional.

Related tools: lay hedge for real-money backs; partial hedge if you convert by backing the other side at a second sportsbook instead of laying; bonus-value calculators for wagering-requirement casino tokens, which are a different object. This page is sports SNR only, decimal odds, one back, one lay, one commission rate. Educational arithmetic. It does not recommend signing up for tokens, laying horses at 3.60, or treating 78.67% as a guaranteed yield.

Stake-not-returned conversion lays off only the profit portion of a promotional back. Back profit on a winning token is face times (back odds minus one), because the face is not returned. The lay denominator is lay odds minus the commission rate times (lay odds minus one), the same haircut as a cash lay. Lay stake is back profit over that denominator. Liability is lay stake times (lay odds minus one). If the selection wins, profit is back profit minus liability. If it loses, profit is lay stake times one minus the commission, and the token expires worthless without costing cash. Conversion percent is one hundred times the average of those two profits, divided by face.

Defaults are a 50 dollar token, back odds 4.00, lay odds 3.60, commission five percent. Back profit is 50 times 3, namely 150 dollars, not 200. Denominator is 3.60 minus 0.13, which is 3.47. Lay stake is 150 over 3.47, about 43.227, displayed as 43.23 dollars. Liability is 43.23 times 2.60, about 112.39 dollars. Back-win profit is 150 minus 112.39, namely 37.61 dollars. Lay-win profit is 43.23 times 0.95, namely 41.07 dollars. Average is 39.34 dollars. Conversion is 39.34 over 50, which is 78.67 percent. The worse column as a floor is 37.61 dollars, a 75.22 percent conversion.

Using a cash numerator of 200 over 3.47 would over-lay the token at about 57.64 dollars, crushing the back-win column and inflating the lay-win column. That is the characteristic stake-not-returned error. Treating a stake-returned token as stake-not-returned under-lays and leaves leftover variance. Zero commission recovers denominator 3.60, lay stake 41.67 dollars, both profits 41.67, conversion 83.33 percent, which is simply (odds minus one) over lay odds, here 3 over 3.60. Five percent therefore costs about 4.7 conversion points on this pair, not a flat five, because the rate hits only the lay-win column and because lay stake itself changes.

Matched-betting manuals after the 2000s standardised this haircut. Longer back odds raise paper conversion because more of the token sits in (odds minus one), but they also widen typical spreads. A 3.00 back against a 2.80 lay at five percent yields back profit 100, denominator 2.71, lay about 36.90, conversion near 68.6 percent. The default 4.00 against 3.60 is more efficient on paper. Liquidity is not a rounding detail: 112.39 dollars of liability is more than twice the 50 dollar face.

Assumptions: profit-only settlement of the token, identical selection on back and lay, commission on lay net winnings, full match, no minimum-odds breach, no void, no dead-heat. Eligibility rules sit outside the identity. The 78.67 percent and 39.34 dollar average are arithmetic on the four inputs, not a forecast of account limits.