Arbitrage Math
Definition: An arbitrage (surebet) exists when the combined implied probabilities across bookmakers are below 100% for mutually exclusive outcomes.
Core Check
arb% = (1/O1 + 1/O2 [+ 1/O3]) × 100 — if arb% < 100, there is a theoretical profit.
Stake Split (Decimal Odds)
For 2-way outcomes with bankroll B and odds O1, O2:
S1 = B × (O2 / (O1 + O2)) S2 = B × (O1 / (O1 + O2)). Equalised return ≈ B × (O1×O2)/(O1+O2).
Three-Way Conversion (1X2 → Two-Way)
Many football arbs resolve via draw-protected markets (DNB, Asian +0). Convert to the market that fills faster and offers higher limits.
Worked Examples
Example 1 — DNB Arb
- Book A: Home DNB @ 2.05
- Book B: Away DNB @ 2.05
Implied sum: 1/2.05 + 1/2.05 = 0.9756 → < 1. For B=200, S1=S2=100. Return =205 regardless → profit 5.
Example 2 — Asian +0 vs 1X2
Neutralise draws by pairing Asian +0 with the opposing 1X2 side. Confirm both legs’ acceptance speed before committing.
Execution Workflow
- Scan for opportunities (filter football, reputable books, target ROI 1–2%).
- Pre-fund accounts and enable instant payments.
- Place the slower-moving leg first; confirm acceptance; place the hedge leg immediately.
- Log screenshots and fills. Track arb%, ROI, time-to-fill, limits.
Risks & Mitigation
- Price moves / delays: Use faster books; avoid exotic props; operate in lower-latency windows.
- Stake limits: Split across books or reduce stake; prioritise high-limit markets.
- Voids / palpable errors: Wait for acceptance; read rules; avoid error-prone markets.
- KYC & payments: Verify early; diversify balances; prefer instant rails.
- Profiling: Mix bet types, maintain device/network hygiene, respect laws and terms.
Bankroll, Records & Review
- Use a dedicated bankroll; keep unit size small and consistent.
- Ledger columns: Date · Books · Market · O1/O2 · S1/S2 · arb% · ROI · Fill time · Notes.
- Weekly review: hit rate, average ROI/arb, time-to-fill, % voids, recurring issues.
Scanner & Utility Stack
- Arb scanners with football filters, alerts, and regional book support.
- Odds screeners for line shopping and CLV tracking.
- Stake calculators (including partial-fill helpers).