Betting Math

Arbitrage

Betting both sides of a market across different books to lock in a guaranteed profit regardless of the outcome.

Also known as: arb, arbing, sure bet, risk-free bet

Definition

Arbitrage (arbing) exploits price differences between sportsbooks or prediction markets. When the combined implied probabilities across platforms sum to less than 100%, you can bet both sides and guarantee profit.

Example: Book A has Team X at +150, Book B has Team Y at +150. Implied probs: 40% + 40% = 80%. The 20% gap means you can distribute bets across both and profit no matter who wins.

Arbs are rare and short-lived. They require multiple funded accounts, fast execution, and careful sizing. Platform fees (especially in prediction markets) can eat into or eliminate the arb margin.

Formula

arbMargin = 1 - Σ(1/decimalOdds_i)
If arbMargin > 0, an arb exists.

Worked Example

Platform A: Yes at $0.45 (decimal 2.222). Platform B: No at $0.48 (decimal 2.083). Sum = 1/2.222 + 1/2.083 = 0.45 + 0.48 = 0.93. Arb margin = 7%.

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