Definition
Complement arbitrage is the specific form of arbitrage based on the complement relationship in binary markets: YES and NO are complements that together always pay exactly $1.00. If YES wins, the YES contract pays $1.00 and the NO contract pays $0.00. If NO wins, the reverse. Either way, holding both pays exactly $1.00.
The mathematical basis
In an efficient single-market, YES + NO prices should sum to approximately $1.00 (accounting for fees). Across two separate platforms with independent liquidity, this constraint can break — the same event's YES and NO can be priced at a combined total below $1.00, creating a riskless profit opportunity.
Single-platform vs cross-platform
Single-platform complement arbitrage is rare — market makers quickly correct any YES + NO ≠ $1.00 divergence within the same order book. Cross-platform complement arbitrage between Polymarket and Kalshi is more common because the two order books are completely independent and don't self-correct.
Event matching requirement
Complement arbitrage only works when YES and NO refer to exactly the same event with the same resolution criteria. If the two contracts have different resolution dates, different interpretations of the outcome, or different oracle sources, they're not true complements — and the "arbitrage" carries directional risk.
Why it's the safest form of arbitrage
Unlike statistical arbitrage (which bets on correlations that can break) or triangular arbitrage (which involves multiple currency pairs), complement arbitrage profits are mathematically guaranteed once both legs fill at the quoted prices. The only residual risks are execution risk and resolution risk — both manageable with proper controls.