The hedge bet formula, for cash, bonus bets, site credit and lays
Every equal-profit hedge comes from one step: write down what each outcome pays and set them equal. For a cash bet H = S × d₁ ÷ d₂; for a bonus bet H = B × (d₁ − 1) ÷ d₂.
Updated September 27, 2026 · TrueEdge Academy
The hedge stake that leaves you with the same result whichever side wins is H = S × d₁ ÷ d₂ for a cash bet, H = B × (d₁ − 1) ÷ d₂ for a bonus bet whose stake is not returned, and H = C × d₁ ÷ d₂ for site credit that returns its stake. For a lay on an exchange with commission c, the lay stake is L = S × d₁ ÷ (d₂ − c). Here d₁ is the decimal odds of the first bet and d₂ the decimal odds of the hedge. Below, each one is derived and worked, so you can check a calculator rather than trust it.
Why decimal odds
Decimal odds are the total return per $1 staked, stake included: +150 is 2.50, −125 is 1.80, −450 is 1.222. That makes every payout a single multiplication. To convert, plus odds become 1 + American ÷ 100, and minus odds become 1 + 100 ÷ |American|. If that is new, how to read betting odds covers it.
(a) A cash bet
You have S on outcome A at d₁ and want to bet H on outcome B at d₂. If A wins you collect S × d₁ and have paid S + H, so your result is S × d₁ − S − H. If B wins you collect H × d₂, result H × d₂ − S − H. Set them equal and the −S − H cancels: S × d₁ = H × d₂, so H = S × d₁ ÷ d₂. This is the formula for a qualifying bet, and for hedging any cash position.
- Bet: $100 on A at +150
- d₁ = 2.50
- Hedge price: B at −160
- d₂ = 1.625
- H = 100 × 2.50 ÷ 1.625
- $153.85
- A wins: $150.00 − $153.85
- −$3.85
- B wins: $153.85 × 0.625 − $100
- −$3.85
A small, equal loss either way. That is what a well-placed qualifying bet looks like.
(b) A bonus bet, stake not returned
A bonus bet of B pays only its winnings, B × (d₁ − 1), and costs nothing if it loses. If A wins your result is B × (d₁ − 1) − H. If B wins it is H × (d₂ − 1). Setting those equal: B × (d₁ − 1) − H = H × d₂ − H, so H = B × (d₁ − 1) ÷ d₂. The locked profit is H × (d₂ − 1).
- Bonus bet: $100 on A at +300
- d₁ = 4.00, pays $300
- Hedge price: B at −350
- d₂ = 1.2857
- H = 100 × 3.00 ÷ 1.2857
- $233.33
- A wins: $300.00 − $233.33
- +$66.67
- B wins: $233.33 × 0.2857
- +$66.67
- Conversion rate
- 66.7%
(c) Site credit that returns its stake
Some books issue credit that pays out the stake as cash when it wins. Then a win returns C × d₁, and a loss costs nothing you paid for. A wins: C × d₁ − H. B wins: H × d₂ − H. Setting them equal gives H = C × d₁ ÷ d₂, the same stake as a cash bet, and the profit is H × (d₂ − 1). Because the stake comes back, credit converts best near even money, where the pair's margin is smallest.
- Credit bet: $100 on A at +105
- d₁ = 2.05, returns $205
- Hedge price: B at −115
- d₂ = 1.8696
- H = 100 × 2.05 ÷ 1.8696
- $109.65
- A wins: $205.00 − $109.65
- +$95.35
- B wins: $109.65 × 0.8696
- +$95.35
- Conversion rate
- 95.3%
(d) A lay bet with commission
On an exchange you can lay A: accept a backer's stake L at lay odds d₂, risking a liability of L × (d₂ − 1). If A loses you win L, less commission c on that net win. Backing S at d₁ and laying L: A wins gives S × (d₁ − 1) − L × (d₂ − 1); A loses gives L × (1 − c) − S. Set equal and simplify: S × d₁ = L × (d₂ − c), so L = S × d₁ ÷ (d₂ − c). For a bonus bet, replace S × d₁ with B × (d₁ − 1): L = B × (d₁ − 1) ÷ (d₂ − c). Commission rates and how they are charged vary by venue — use your venue's published rate, not the illustrative 2% below.
- Back: $100 on A at +200
- d₁ = 3.00
- Lay A at 3.10, commission 2% (illustration)
- d₂ − c = 3.08
- L = 100 × 3.00 ÷ 3.08
- $97.40 lay stake
- Liability: $97.40 × 2.10
- $204.55
- A wins: $200.00 − $204.55
- −$4.55
- A loses: $97.40 × 0.98 − $100
- −$4.55
If you back the other side on an exchange instead of laying, use formula (a) or (b) with the hedge's odds reduced for commission on winnings: d₂ becomes 1 + (d₂ − 1) × (1 − c). That is how the Calculators screen applies its commission field. Venues that charge at fill rather than on winnings need their own adjustment; see lay betting explained.
Letting a calculator do it
The Bonus Bet Converter on Calculators runs formulas (a) and (b) — its Qualifying bet mode is the cash case — with an optional commission on the hedge. Arb Stake Sizing splits a total across two prices. Both take decimal odds you type; to have the prices found for you, use the Promo Optimizer. Calculators walkthrough.
Frequently asked questions
- What is the formula for a hedge bet?
- For a cash bet, hedge stake = original stake × original decimal odds ÷ hedge decimal odds. That makes both outcomes return the same amount.
- How do you calculate a hedge for a free bet?
- Use the winnings only: hedge = bonus × (bonus odds − 1) ÷ hedge odds, all in decimal. The stake is left out because a bonus bet does not return it.
- How does commission change the hedge?
- Commission on winnings shrinks the hedge's effective odds to 1 + (d − 1) × (1 − c), which raises the stake you need. For a lay, divide by (lay odds − commission) instead of the lay odds.
- Why do I need decimal odds?
- Decimal odds include the stake, so each payout is one multiplication. The formulas work with American odds only after converting them.