Arbitrage Calculator

Defaults are Odds 1 = 2.10, Odds 2 = 2.05, Total Stake = 1000. Submit. Arbitrage? Yes. Guaranteed Profit is 37.35. Stake Outcome 1 is 493.98. Stake Outcome 2 is 506.02. The inverse-odds sum is 1/2.10 + 1/2.05 ≈ 0.476190 + 0.487805 = 0.963995, which is less than 1, so a surebet exists. Each stake is total / odds_i / inv, which weights money toward the shorter price. 493.98 × 2.10 ≈ 1037.35 and 506.02 × 2.05 ≈ 1037.35. Minus the 1000 outlay leaves 37.35 either way.

If you flatten both odds to 2.00, inv = 0.5 + 0.5 = 1, Arbitrage? No, profit 0, while the stakes still split 500/500 as a Dutch book at fair prices. If you raise Odds 2 to 2.20 and keep 2.10, inv = 1/2.10 + 1/2.20 ≈ 0.47619 + 0.45455 = 0.93074, profit 1000/0.93074 − 1000 ≈ 74.40. Wider over-round inversion, larger locked profit. If you drop Odds 2 to 1.90 with Odds 1 at 2.10, inv ≈ 0.47619 + 0.52632 = 1.00251 > 1, Arbitrage? No, profit 0. The engine zeros profit whenever inv ≥ 1; it does not print a negative lock.

Total Stake is the combined outlay you are willing to freeze. It is not a stake on one side. Changing 1000 to 250 scales both legs and the profit by 1/4: about 123.49 / 126.51 and 9.34 profit when the 2.10 / 2.05 pair still arbs.

The two odds must be mutually exclusive exhaustive outcomes: home versus away in a two-way market, or yes versus no. A three-way football 1X2 needs three prices and a different tool. Mismatched markets (one book’s “draw no bet” against another’s three-way home) are not an arb even if the numbers look pretty.

Reload 2.10, 2.05, 1000 to recover Yes, 37.35, 493.98, 506.02. That 3.73% lock before commission, limits, and timing is the educational example, not a live ticket. If a 5% exchange commission applies on the winning side only, the locked 37.35 shrinks and can vanish; recompute with net odds rather than screen odds. Two prices that arb at 10:00 can be 1.002 inv at 10:01. The calculator timestamps nothing.

Arbitrage, surebets, or Dutch books in the betting-shop sense, exist when the implied probabilities of a complete outcome set sum to less than one after you pick the best price on each side. You then stake inversely to the odds so that every resolution returns the same amount, larger than the total outlay. The calculator detects that inversion on two decimal prices and splits a chosen total stake.

The mathematical ancestor is the Dutch-book argument in probability theory: if your prices (or the market’s) are incoherent, someone can arrange bets that profit in every state. Sportsbooks try not to be incoherent internally; they add overround. Arbs appear when two books disagree, when a stale line lags a goal, or when a promotional booster cheapens one side. Koopman-style and later quantitative treatments of surebets treat the problem as solving a linear stake vector against a payoff matrix.

Purpose: show the inventory split and the locked profit on a two-way. Recreational bettors hear “guaranteed profit” and miss the operational caveats: account limits, odds moving before the second leg lands, different settlement rules, voided bets, Asian-handicap versus three-way mismatches, and exchange commission that was not in the quoted decimal.

Limits: two outcomes only. No commission field. No stake-capping per book. Profit is forced to 0 when inv ≥ 1 even though the stake split is still computed. Those stakes at inv > 1 are a Dutch allocation at a loss (you lock a sure loss), which the profit row refuses to glorify by printing a negative “guarantee.” Timing risk is unmodelled. Currency conversion is unmodelled.

History on the high street: early surebet services in the 2000s scraped football 1X2 and tennis two-ways; books responded with delay, gubbing, and tighter limits. The identity 1/o1 + 1/o2 < 1 did not change. Use this tool as a pocket check on two numbers, not as a syndicate operations manual. A Yes on 2.10 and 2.05 at 1000 units is arithmetic. Clearing both tickets at those prices is a different profession.

Arbitrage in the betting-shop sense, also called a surebet or a Dutch book against the market, exists when the implied probabilities of a complete outcome set sum to less than one after you pick the best price on each side. You then stake inversely to the odds so that every resolution returns the same amount, larger than the total outlay. The two-way identity is elementary. Let o1 and o2 be the two decimal prices and S the total stake. Inverse-odds sum inv equals 1/o1 plus 1/o2. An arbitrage exists when that sum is less than one. Stake on side i equals S divided by o_i divided by inv, which forces both payouts equal to S / inv. Guaranteed profit equals S / inv minus S when inv is less than one, and is reported as zero when inv is at least one so that a locked loss is not dressed up as a lock.

The published defaults are 2.10 and 2.05 with a total stake of 1,000. Inverse sum equals 1/2.10 + 1/2.05 ≈ 0.476190 + 0.487805 = 0.963995, which is less than one, so a surebet exists. Stake on outcome one equals 1,000 / 2.10 / 0.963995 ≈ 493.98. Stake on outcome two equals 1,000 / 2.05 / 0.963995 ≈ 506.02. Common payout equals 1,000 / 0.963995 ≈ 1,037.35. Profit equals 1,037.35 − 1,000 = 37.35. Check: 493.98 × 2.10 ≈ 1,037.35 and 506.02 × 2.05 ≈ 1,037.35. The locked return on investment is 1/inv − 1 ≈ 3.735 percent. Money is weighted toward the shorter price, here 2.05, which is why 506.02 exceeds 493.98.

Flatten both odds to 2.00 and inv equals 0.5 + 0.5 = 1, profit 0, stakes 500 and 500: a fair Dutch at even money. Raise the second price to 2.20 and keep 2.10: inv ≈ 0.47619 + 0.45455 = 0.93074, profit ≈ 1,000 / 0.93074 − 1,000 ≈ 74.40. Wider inversion, larger locked profit. Drop the second price to 1.90 with the first at 2.10: inv ≈ 0.47619 + 0.52632 = 1.00251, which exceeds one, so the worksheet reports no arbitrage and profit 0 rather than a negative lock of about −2.51. That clamp is a reporting choice, not a claim that overround books are unpriceable.

The intellectual ancestor is the Dutch-book argument in probability: if prices are incoherent, someone can arrange bets that profit in every state. Sportsbooks try not to be incoherent internally; they add overround. Arbs appear when two books disagree, when a stale line lags a goal, or when a promotional booster cheapens one side. Koopman-style and later quantitative treatments treat the problem as solving a linear stake vector against a payoff matrix. This page is the two-by-two case.

Assumptions: two exhaustive mutually exclusive outcomes, both backs at the typed decimals, full matching, no commission, no push. Three-way football needs a third price and a different split. Exchange commission on a lay replaces a decimal with a net price. Limits and latency can prevent the 493.98 / 506.02 fill. The worksheet detects the inversion and splits the stake. It does not search books and it is not a prompt to arb.