This matched betting calculator performs one narrow job: it applies the published back-and-lay stake formulas to figures you enter, and reports the lay stake, the liability, and the position you would be left in under each of the two outcomes. It is arithmetic on your inputs. It is not a recommendation to place any bet, and it does not tell you that any bet is worth placing.
Arb Digital publishes free calculators across maths, money and everyday life. This one carries more caveats than most, because matched betting is a gambling technique, it is frequently presented online as free money, and that presentation is how people end up losing money they could not afford to lose. The arithmetic below is real. The assumptions it depends on very often are not.
Read This Before the Numbers
Gambling is age-restricted and regulated, and the rules differ by jurisdiction. Nothing on this page is advice to gamble, an endorsement of any operator, or a suggestion that betting can be a source of income. It is not a way to make a living, and treating it as one is a recognised route into serious harm.
If gambling is causing difficulty for you or someone close to you, help exists and is free. In the United States, the National Council on Problem Gambling's National Problem Gambling Helpline operates call, text and chat services around the clock and refers to local support. In Great Britain, the Gambling Commission's public and players section lists safer gambling tools, consumer protections and free 24-hour helpline numbers. Most other countries have an equivalent body.
This page names no bookmaker, lists no offers, promotes no service and carries no affiliate arrangement of any kind. It offers no strategy, no selection advice and no view on which markets to use. It computes stakes from numbers you type in, and stops there.
What This Calculator Does
Matched betting refers to placing a back bet with a bookmaker and an opposing lay bet on a betting exchange, sized so the two positions offset. The published formulas for that sizing are not secret and not disputed; they follow directly from the definitions of decimal odds, lay liability and exchange commission. This tool implements them for three cases: a qualifying bet placed with your own stake, a free bet where the stake is not returned with any winnings, and a free bet where the stake is returned.
You enter the back stake, the back and lay odds in decimal form, the exchange's commission rate, and your available exchange balance. It returns the lay stake, the liability that lay stake creates, the position under each outcome, and the commission charged in the lay-wins case. Every figure is a consequence of your inputs: if the odds you enter are not the odds you actually get, the results describe a bet that does not exist.
How to Use It
- Choose the bet type from the operator's own terms. Whether a free bet returns the stake changes the lay stake formula outright, and assuming the wrong one produces a badly mismatched position.
- Enter the back stake and back odds in decimal form. If your bookmaker shows fractional odds, convert them first — our odds and probability converter handles fractional, decimal and moneyline.
- Enter the lay odds shown at the exchange, and the exchange's commission rate for your account. Commission rates differ between exchanges and sometimes between accounts.
- Enter the balance you actually hold at the exchange. Liability is withheld in full when a lay bet is matched, and an unfunded liability means the lay bet never gets placed.
- Read both outcome figures. They are the two ways the event can resolve, and neither is more likely to be the one that happens because of anything on this page.
The Formula / How It's Calculated
Write the back stake as S, back odds as B, lay odds as L and commission as c expressed as a decimal. For a qualifying bet, and for a free bet whose stake is returned, the lay stake is (B × S) ÷ (L − c). For a free bet whose stake is not returned, it is ((B − 1) × S) ÷ (L − c). In both cases the liability — the amount the exchange withholds — is lay stake × (L − 1).
If the back bet wins, you collect S × (B − 1) in bookmaker winnings and pay the liability, giving S × (B − 1) − liability (for a stake-not-returned free bet the stake itself is not returned, so this expression is unchanged). If the lay bet wins, the exchange pays the lay stake less commission and the bookmaker keeps your stake, giving lay stake × (1 − c) − S, or simply lay stake × (1 − c) where the stake was a free bet that cost you nothing.
Worked example, matching the defaults. A £10 qualifying bet at back odds of 3.0, laid at 3.2 with 2% commission. Lay stake = (3.0 × 10) ÷ (3.2 − 0.02) = 30 ÷ 3.18 = 9.43. Liability = 9.43 × 2.2 = 20.75. If the back bet wins: 10 × 2 = 20 collected, minus 20.75 liability, leaves −0.75. If the lay bet wins: 9.43 × 0.98 = 9.25 from the exchange, minus the £10 stake lost at the bookmaker, leaves −0.75. Both outcomes land on the same figure, and that figure is a loss of 75 pence. That loss is the ordinary and expected result of a qualifying bet, and it is what the technique's own literature calls the qualifying loss.
What Goes Wrong in Practice
The arithmetic above is exact. It is exact about a situation that frequently fails to occur, and the failures are not rare edge cases — they are the normal texture of the activity. It is worth being specific about them.
Bets get voided. A non-runner, a market settled under a rule you did not read, an abandoned fixture or a palpable-error price can void one leg and leave the other live. When only one side stands, you hold a plain unhedged bet at whatever odds you took, and the loss is the full liability or the full stake rather than a small qualifying loss.
Accounts get limited or closed. Bookmakers monitor betting patterns and restrict stakes or close accounts of customers they identify as unprofitable. This is written into standard terms and is entirely at the operator's discretion. It commonly happens without warning and sometimes while funds or unsettled bets are in the account.
Terms get misread. Minimum odds, qualifying markets, expiry dates, maximum stakes and whether a free bet stake returns are all terms that void a promotion when breached, and none of them are standardised between operators.
Odds move between the two legs. You place the back bet, switch to the exchange, and the lay price has moved against you. The position you end up with is not the one this calculator described, and in a fast market the drift can be large. Partial matching at the exchange creates the same problem in a different form: half a lay bet is not a hedge.
Commission eats the margin. The margins are small. A rate a couple of points higher than assumed turns a thin position into a losing one, and commission rules are set entirely by the exchange.
One mistyped stake outweighs several offers. This is the failure that people underestimate most. A stake entered with an extra zero, a lay placed as a back, or odds transposed between the two legs can lose more in a single click than a long run of correctly executed positions would have gained. There is no undo.
Why the Word "Guaranteed" Does Not Belong Here
You will see this technique described as risk-free or guaranteed. Neither word survives contact with the list above. A calculation can be exact while the situation it describes is uncertain, and the two are constantly confused. What the arithmetic guarantees is that if both bets are placed at exactly the odds entered, and neither is voided, and the terms are as assumed, and commission is as entered, then the two outcomes resolve to the figures shown. Those are four conditions, each outside your control once the bets are placed.
There is also a structural point that matters more than any operational risk. Promotional offers exist because they are profitable for the operators that run them, in aggregate, across everyone who takes them up. Any framing of this activity as reliable income is at odds with why the offers are made available at all. To understand betting markets properly rather than as a technique, the implied probability calculator converts odds into the probability a price implies, and the expected value calculator shows how an edge — or its absence — plays out over repeated trials.
Liability Is the Number People Underestimate
The most common practical shock for someone new to exchanges is liability. Backing a selection risks your stake. Laying a selection risks the amount you would have to pay out if it wins, which at long odds is many times the lay stake. In the default example a lay stake of 9.43 creates a liability of 20.75 — more than double. At lay odds of 11.0 the same lay stake would tie up ten times its own value.
Liability is withheld from your exchange balance the moment the bet is matched and stays withheld until the market settles. That is why this calculator asks for your balance: an account that cannot cover the liability will not match the lay bet, leaving you holding an unhedged back bet you did not intend.
What the Two Outcome Figures Mean
The two grid figures are the positions the arithmetic produces under each resolution of the event. For a correctly sized qualifying bet they will be equal or very close, and both will typically be slightly negative — that is the qualifying loss, and it is a cost, not a bug. For a stake-not-returned free bet they will also be equal, and positive, because the back stake was not your money.
Neither figure is a forecast. The event resolves one way or the other for reasons that have nothing to do with your stakes, and the arithmetic only says the two paths have been made to arrive at similar places. That is the whole idea, and also the whole fragility: it depends on both legs standing.
Arb Digital maintains a large library of free tools covering maths, probability, money and everyday planning. Have a look, or get in touch.
Browse Free Tools Contact Arb DigitalCommon Mistakes to Avoid
- Assuming a free bet returns the stake — the two cases use different formulas, and picking the wrong one leaves the position badly mismatched under one outcome.
- Entering fractional or moneyline odds in the decimal fields — 5/2 is not 5, and the resulting lay stake would be nonsense. Convert first.
- Ignoring liability against your balance — an unmatched lay leaves a plain unhedged bet.
- Using odds you saw a minute ago — prices move, and this position only exists at the prices you actually get.
- Treating any of this as income — gambling is age-restricted, regulated and not a way to make a living, and the promotional offers that make the arithmetic look attractive exist because they are profitable for the operators that run them.
Related Free Tools From Arb Digital
To convert between odds formats and the probability a price implies, use the odds and probability converter and the implied probability calculator. For the underlying mathematics, the probability calculator and expected value calculator are the general-purpose tools, the poker odds calculator applies the same reasoning to a different game, and the lottery odds calculator shows how quickly long odds become very long indeed. Everything else is in the free online tools hub.
Frequently Asked Questions
No. The arithmetic is exact, but it assumes both bets are placed at the odds entered, neither is voided, the terms are as you understood them and commission is as entered. Bets get voided, accounts get restricted, odds move between legs and terms get misread, and any of those leaves you holding an unhedged position.
No. Gambling is age-restricted and regulated and is not a way to make a living. Promotional offers exist because they are profitable for the operators running them across everyone who takes them up, and no calculator changes that. If gambling is causing difficulty, free help is available from national problem gambling services.
The small loss that a correctly sized qualifying bet produces under both outcomes, caused by the gap between back and lay odds plus exchange commission. In the default example it is 75 pence on a £10 stake. It is a cost of participating, not an error in the calculation.
Liability is what you must pay out if the selection you laid wins. It equals the lay stake multiplied by the lay odds minus one, so at odds of 3.2 a lay stake of about 9.43 creates a liability of about 20.75. The exchange withholds it in full from your balance until the market settles.
Rounding, mostly. A lay stake that cannot be placed to the exact penny, or odds that shift between the two legs, leaves the outcomes marginally uneven. If they differ by a lot, check that the bet type matches the operator's terms and that the odds entered are decimal.
No. It names no operator, lists no promotions, has no affiliate arrangement and gives no strategy or selection advice. It applies published stake formulas to figures you type in, and that is the entire scope of the tool.
Because the margins involved are small. Commission is charged by the exchange on net winnings in a market, at a rate the exchange sets, and a difference of a couple of percentage points is easily enough to move a thin position from marginally positive to negative.
This tool performs arithmetic on figures you enter. It is not gambling, betting, financial or legal advice, and it does not recommend placing any bet. Gambling is age-restricted and regulated, involves a real risk of losing money, and is not a way to make a living. If it is causing you or someone you know difficulty, contact a national problem gambling helpline such as those linked above.
