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 October 5, 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
For a cash bet you already hold — formula (a) — the free hedge calculator sizes the hedge as you type, either to the same result both ways or to break even, with exchange fees taken off. 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.