SOLVETUTORMATH SOLVER

Instrument MI-14-120 · Other

Matched Betting Calculator

Enter your back bet details and the exchange's lay odds, and this instrument works out exactly how much to lay off to hedge cleanly.

Instrument MI-14-120
Sheet 1 OF 1
Rev A
Verified
Type 14 — Betting & Gambling SER. 2026-14120

Lay stake ($)

19.31

lay stake = (back stake x back odds) / (lay odds - commission)

81.08 Liability ($)
-1.08 Profit if back bet wins ($)
-1.08 Profit if lay bet wins ($)
The working Every figure verified twice
  1. layStake = 20·5 ⁄ (5.2 − 2 ⁄ 100) = 19.31
  2. liability = 20·5 ⁄ (5.2 − 2 ⁄ 100)·(5.2 − 1) = 81.08
  3. profitIfBackWins = 20·(5 − 1) − 20·5 ⁄ (5.2 − 2 ⁄ 100)·(5.2 − 1) = -1.08
  4. profitIfLayWins = 20·5 ⁄ (5.2 − 2 ⁄ 100)·(1 − 2 ⁄ 100) − 20 = -1.08
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Matched betting is a technique for extracting the value from a bookmaker's free-bet or bonus offer by hedging it against a real-money bet at a betting exchange. You back an outcome (bet it will happen) at a bookmaker, and simultaneously lay that same outcome (bet it will not happen) for a calculated stake at an exchange, sized so that your overall result comes out close to identical whichever way the event actually goes. The bookmaker side wins if the outcome happens; the exchange side wins if it doesn't — between the two, the result is deliberately close to a wash, which is the whole point on the initial 'qualifying bet' that unlocks the free bet.

Lay stake is the amount you need to bet against the outcome at the exchange to properly hedge your back bet, and it depends on both odds and the exchange's commission rate. Liability is the amount you stand to owe the exchange if your lay bet loses — meaning the outcome you backed actually happened, so the exchange pays out on your lay bet's opponent side and you owe your counterparty (via the exchange) lay stake x (lay odds - 1). Liability is the real money at risk on the exchange side of a matched bet, separate from the stake itself.

Commission is why the lay stake isn't simply the back stake times the odds ratio: exchanges take a percentage cut of net winnings from a winning lay bet, so the lay stake has to be slightly larger than a commission-free calculation would suggest, fully offsetting the back bet either way. Even with perfectly equal back and lay odds, a nonzero commission introduces a small, symmetric guaranteed cost on both outcomes — the built-in price of hedging on a real exchange rather than a frictionless one, and worth checking before assuming a qualifying bet is entirely free.

This instrument computes the theoretical hedge math only — it doesn't guarantee a profit and isn't financial advice. Real matched betting involves genuine money staked upfront and real execution risk: odds can move between placing the back and lay bets, exchanges and bookmakers can restrict or close accounts they identify as running matched bets, and simple data-entry mistakes can turn a hedge into a real loss. Treat this as a bookkeeping aid for working out stakes accurately, verify current odds and commission before placing either bet, only stake what you can afford to lose if something goes wrong, and follow the terms and local laws that apply to your account and jurisdiction.

lay stake = (back stake x back odds) / (lay odds - commission%/100)
liability = lay stake x (lay odds - 1)
profit if back wins = back stake x (back odds - 1) - liability
profit if lay wins = lay stake x (1 - commission%/100) - back stake
back stake, back odds — your bet at the bookmaker · lay odds, commission% — the opposing bet at the exchange · lay stake — the amount to lay to hedge the back bet · liability — what you owe the exchange if the backed outcome happens.
  • Enter Back stake ($) and Back odds (decimal) — the bet you're placing at a bookmaker.
  • Enter Lay odds (decimal, exchange) and Exchange commission (%) — the opposing bet you'll place at a betting exchange.
  • Read Lay stake ($) — how much to lay at the exchange to hedge the back bet.
  • Read Liability ($) — the amount at risk on the exchange side if your back bet's outcome happens.
  • Compare Profit if back bet wins and Profit if lay bet wins — a well-matched qualifying bet keeps these two figures close together.

Worked example — a perfectly matched, commission-free hedge

Back $10 at odds of 5.0, and lay against the same outcome at an exchange also offering odds of 5.0, with 0% commission. Lay stake = (10 x 5.0) / (5.0 - 0) = $10.00. Liability = 10 x (5.0 - 1) = $40.00.

Profit if back bet wins = 10 x (5.0-1) - 40 = 40 - 40 = $0.00. Profit if lay bet wins = 10 x (1-0) - 10 = 10 - 10 = $0.00. Both outcomes land at exactly $0, which is precisely what a frictionless, equal-odds hedge should produce — no matter which side of the bet actually wins, the result is identical. This is the qualifying-bet pattern matched bettors rely on: the small guaranteed cost (or, with a genuine free bet instead of real cash on the back side, the retained value) comes from the specific offer being unlocked, not from the hedge math itself.

Questions

What is matched betting?

It's a technique for extracting the value of a bookmaker's free-bet or bonus offer with minimal risk, by backing an outcome at the bookmaker and simultaneously laying that same outcome at a betting exchange. The two opposing bets are sized so the result comes out close to identical whichever way the event goes — a hedge, not a prediction. It's a well-documented, widely practiced technique, generally legal where sports betting itself is legal, though it can trigger account restrictions from bookmakers that don't want to pay out on offers this way.

What does "liability" mean in a lay bet?

Liability is the amount you owe the exchange if the outcome you laid against actually happens — meaning your lay bet loses. It equals lay stake x (lay odds - 1), and it's the real money the exchange holds you accountable for, separate from and larger than the lay stake itself. When placing a lay bet, always check your account has enough available balance to cover the liability, not just the stake.

Why isn't my profit exactly $0 on both sides even with a well-matched hedge?

Exchange commission is almost always the culprit. Exchanges take a percentage cut of net winnings from a winning lay bet, so even with identical back and lay odds, a nonzero commission rate introduces a small, symmetric cost on both outcomes — for example, a 5% commission on an otherwise-perfect 5.0/5.0 hedge produces a small guaranteed loss of about 40 cents on a $10 back stake either way, rather than the $0/$0 result you'd get with 0% commission.

Is matched betting risk-free?

Not entirely, even though the underlying math is a genuine hedge. Odds can shift between placing your back bet and your lay bet, turning a planned hedge into a mismatched one if you're not fast enough; bookmakers can restrict, limit, or close accounts they identify as running matched bets; and manual data-entry mistakes (wrong stake, wrong odds) can turn a hedge into a real loss. This instrument computes the theoretical stake and liability math only — it doesn't account for execution risk, and it isn't financial advice.

What's the difference between backing and laying a bet?

Backing is the familiar kind of bet: you bet for an outcome at a bookmaker and win if it happens. Laying is the opposite, placed at a betting exchange rather than a bookmaker: you bet against an outcome, effectively acting as the bookmaker for that specific outcome, and win your opponent's stake if it doesn't happen — but if it does happen, you owe your liability, lay stake x (lay odds - 1), which is why liability is worth checking before laying.

References