Arbitrage betting (arbing / sure betting) means staking all mutually exclusive outcomes of the same market across different prices so that, if every stake is accepted at those prices, the return is the same whichever selection wins — and that return is above your total stake.

That “if” is doing the work. An arb on paper is a math identity. In live books it is a race against odds moves, stake limits, voided legs, and account risk. It is not free money and it is not the same product as value betting or matched betting.

Related: Is arbitrage betting legal?, Back and lay, Getting limited.

When an arb exists (the % test)

For a complete market with decimal odds O₁, O₂, …, Oₙ (one price per mutually exclusive outcome, usually taken from different books):

arb = 1/O₁ + 1/O₂ + … + 1/Oₙ
  • arb < 1 → an arbitrage exists at those prices.
  • arb = 1 → fair combined book (zero edge before fees).
  • arb > 1 → overround; you are paying the market, not locking a cross-book edge.

Often people quote arb % as arb × 100. Below 100% means the same thing as arb < 1. Use the decimal arb in stake formulas — do not divide by 95.24 if you meant 0.9524.

Two-way tennis example (illustrative only — not a tip):

Book Selection Decimal odds
Book A Player A 2.10
Book B Player B 2.10 
arb = 1/2.10 + 1/2.10 = 0.952381  (≈ 95.24%)

Under 1 → arb. Profit on turnover if filled at these prices:

profit_rate = 1/arb − 1 = 1/0.952381 − 1 ≈ 5.00%

Unequal two-way (still illustrative):

Book Selection Odds
Book A Home 2.05
Book B Away 2.10 
arb = 1/2.05 + 1/2.10 ≈ 0.963995
profit_rate ≈ 3.73%

Three-way 1X2 only arbs when the best home, draw, and away prices you can actually get still sum under 1. Example of prices that do:

Outcome Best available odds
Home 2.50
Draw 3.80
Away 3.40 
arb = 1/2.50 + 1/3.80 + 1/3.40 ≈ 0.9573

If the best three add to more than 1, there is no full-market arb — shopping one long price is not enough.

Stake formulas (equalised return)

You pick a total stake T (cash at risk across all legs). Stakes must be proportional to each selection’s implied share of arb:

stake_i = T × (1/O_i) / arb

Then for every i:

return_i = stake_i × O_i = T / arb
profit   = T / arb − T = T × (1/arb − 1)

All winning legs pay the same cash return (before fees / tax / FX). That is the whole point of sizing.

Worked two-way (£100 total)

Odds 2.10 / 2.10, arb = 0.952381:

stake_A = 100 × (1/2.10) / 0.952381 = £50.00
stake_B = 100 × (1/2.10) / 0.952381 = £50.00
return either way = 50 × 2.10 = £105.00
profit = £5.00

Odds 2.05 / 2.10, arb ≈ 0.963995, T = £100:

Leg Stake If this side wins — return Net
Home @ 2.05 £50.60 £103.73 +£3.73
Away @ 2.10 £49.40 £103.73 +£3.73

Stakes rounded to 2dp; one cent of rounding noise is normal — re-check both returns before you click.

Worked three-way (£100 total)

Odds 2.50 / 3.80 / 3.40, arb ≈ 0.957276:

Outcome Stake Return if that outcome
Home @ 2.50 £41.79 £104.46
Draw @ 3.80 £27.49 £104.46
Away @ 3.40 £30.72 £104.46

Profit ≈ £4.46 if all three bets stand at those prices.

Formula that looks similar and is wrong

Some old write-ups use:

stake = ((1/odds) / arb_percentage) × T with arb_percentage = arb × 100 (e.g. 95.24).

That under-stakes by a factor of 100. Always divide by the decimal arb (0.9524), not by 95.24.

Back/back vs back/lay

Back/back: every outcome is a back at a bookmaker (or exchange back). Classic multi-book arb above.

Back/lay: one outcome backed at a book, laid on an exchange (you are the book on that selection). Mechanically this is the same equalisation idea, with liability and usually commission on exchange net winnings. See back and lay betting.

Simple 0% commission equalisation: back stake B at odds O_b, lay at O_l:

lay_stake L = B × O_b / O_l
liability   = L × (O_l − 1)

Example: back £100 @ 2.20, lay @ 2.10, commission 0%:

L = 100 × 2.20 / 2.10 ≈ £104.76
liability ≈ £115.24
Result Back P/L Lay P/L Net
Selection wins +£120 −£115.24 +£4.76
Selection loses −£100 +£104.76 +£4.76

With 5% commission on lay net winnings, equalising needs a larger lay stake. One common form (commission only when the lay wins):

L = B × O_b / (O_l − c)     # c = 0.05

Same back £100 @ 2.20, lay @ 2.10, c = 0.05 → L ≈ £107.32, both nets ≈ +£1.95. Always use your exchange’s actual commission rules (some charge on net winnings per market, some have discount tiers).

Matched betting uses the same back/lay toolkit against promotions, not against raw odds gaps — different goal, overlapping maths: matched betting guide.

Arb vs value betting vs matched betting

Arbitrage Value betting Matched betting
Edge source Cross-book (or book vs exchange) price gap covering the market Your probability > implied by one price Book promo + covering bet
Outcome risk if fully filled Locked (math) Variance — +EV over many bets Near-locked once promo rules are met
Typical failure mode One leg not filled / odds move / void / limit Losing run / bad model Promo terms, gubbing, qualifying loss
Book attitude Hostile — patterns are obvious Hostile over time on softs Hostile once bonuses are farmed

Arbing removes selection risk only when the full set of bets is on at the modelled prices. It does not remove execution risk. Value betting keeps selection variance on purpose because that is where durable edge lives for most sharp operations once soft books stop paying arbers. Longer take: why stop arbing and value bet.

What actually breaks an arb

These are the reasons pros do not treat arbing as “guaranteed”:

  1. Odds move between clicks. You get the first leg on; the second shortens; arb flips above 1. You are left with a naked directional bet.
  2. Stake limits / “max bet”. The book accepts £5 of your £80 request at the shown price — or offers a worse price for the rest. Equalisation breaks.
  3. Delay / bet referral. Live and higher stakes often sit in a queue while the price changes.
  4. Voids, rule 4, score corrections, wrong market. One voided leg + one settled leg is not an arb; it is a one-sided position.
  5. FX, deposit/withdrawal fees, exchange commission. A 1.5% paper arb can be negative after costs.
  6. Account limits and closures. Soft books detect opposing-outcome patterns quickly. See how limits work.
  7. Incomplete market. Backing two of three 1X2 outcomes is not a full arb.

Do not invent ROI targets. Paper margins on live arbs are often thin; capacity is the binding constraint, not a spreadsheet % .

Practical checklist

  1. Confirm selections are mutually exclusive and exhaustive for the market you are covering.
  2. Compute arb from the prices you can still get, not from a scanner screenshot five seconds ago.
  3. Size with stake_i = T × (1/O_i) / arb, then verify both (or all) returns match before placing.
  4. Place the worse-liquidity / more likely to move leg first when you must sequence clicks — knowing that this is risk management, not a free lunch.
  5. Log rejected stakes and partial fills; those are losses in disguise.
  6. Count commission, FX, and payment fees in the edge.

Scanners and alerts help find gaps; they do not place risk-free bets for you.

FAQ

Is arbitrage betting risk-free?

No. The math locks profit only if every leg is accepted at the modelled odds and settles as assumed. Odds moves, limits, voids, fees, and account actions are real risks. Details: Is arbitrage betting legal?.

How do you calculate arb stakes?

arb = Σ (1/odds_i). If arb < 1, stake_i = T × (1/odds_i) / arb. Each winning return equals T / arb.

What is the difference between back/back and back/lay arbs?

Back/back covers outcomes with back bets at different books. Back/lay covers one outcome by backing at a book and laying on an exchange (watch liability and commission). See back and lay.

Can bookmakers limit you for arbing?

Yes — quickly on soft books. Opposing stakes and sharp pricing patterns get capped or closed. Limits guide.

Related

Arbing is a narrow execution trade on mispriced pairs (or full markets). For long-run edge against soft prices without needing a perfect opposing fill on every ticket, look at value betting with Trademate Sports.