Learning outcomes
- Reproduce the mathematical or scenario analysis.
- Explain contract, execution, and settlement assumptions.
- Identify when the apparent opportunity is not reliably actionable.
Why coverage comes before the odds
Arbitrage is a relationship between contracts. It means that a portfolio of positions has a positive theoretical net payout in every possible resolution of a precisely defined event, subject to fills, valid quotes, grading and costs. Two prices pointing in opposite directions are not enough: the positions must cover all mutually exclusive and collectively exhaustive outcomes. A two-way tennis match winner market may have two results for settlement purposes, but a three-way soccer regulation-result market includes home, draw, away. Buying home and away without accounting for draw is not a complete hedge.
Use decimal prices and reciprocal sums
For a matched market with decimal odds d1... dn, let S = Σ(1/di). If S < 1, the offered combination is a theoretical full-coverage arb before costs; if S = 1, the equal-payout combination breaks even; if S > 1 it loses money if equalized. Decimal odds include the stake in total return. At +110, decimal odds are 2.10; at -120, decimal odds are 1+100/120 = 1.8333.
Worked example: a three-way event
Imagine a hypothetical regulation-time soccer result quoted at: home 2.80, draw 3.60, away 3.20. Reciprocals are 0.357143, 0.277778 and 0.312500. Their sum is 0.947421. This is a mathematical candidate for a full-coverage arb if all outcomes mean the same thing, prices are attainable, and no costs change the result. A $100 hypothetical portfolio equalizes gross returns at $100/0.947421 = $105.55. Theoretical net return is $5.55 (5.55% on aggregate stake). The next lesson calculates the allocation.
The market-equivalence checklist
Compare league and teams, event identifier, start date, regulation versus overtime, draw/void rules, settlement provider, pitcher/player participation clauses, and markets suspended or repriced. For a live match, add score and game clock. Different scoring or settlement criteria can leave a hole in what looked like full coverage.
Guided drill
Make a paper table of outcomes as rows and positions as columns. Write the payout for each cell. Include 'draw', 'void', 'abandoned', and any other relevant state, not merely the expected sporting results. If a state has no matched offsetting payout, the position isn't a comprehensive real-world hedge.
Errors to catch
A missing third soccer outcome; comparing different line thresholds; overlooking settlement exceptions; relying on delayed screenshots; mistaking an arb's theoretical return for certain execution; ignoring fees. An arb scanner is a candidate detector, not proof of executable profit.
Practice / answer key
A three-way market has decimals 3.00, 3.00 and 3.00. Is there a positive arb? No: 1/3+1/3+1/3 = 1, exactly break-even before costs. Two outcomes at 2.10 each? Yes, mathematically: 2/2.10 ≈ 0.95238 < 1, assuming fully matched terms. A market with home and away but a possible draw? Not complete.
Takeaway
First prove outcome coverage. Only then test the prices.
Applying the lesson in Sharp
Use archived, verifiable research snapshots from the Arb comparator and Odds screens where available. ARBAI is an optional conversational tutor; this article is the authoritative instructional source after editorial approval.
Editorial release checks
Independently verify arithmetic; confirm product rules and geographic availability; add authoritative references and screenshots for the current Sharp UI; review legally required disclosures. Do not imply profits are certain.
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Sharp App surfaces +EV opportunities from public sportsbook data. We do not place, accept, or facilitate wagers. 21+ where legal. If betting stops being fun, call 1-800-GAMBLER or visit ncpgambling.org.
