01In plain English
Every binary prediction market resolves to one of two outcomes: YES at $1.00 or NO at $1.00. The two outcomes are mirror images - by construction, exactly one of them will pay. So if at some moment you can simultaneously buy YES at $0.49 and NO at $0.49 on the same market, you've spent $0.98 to be guaranteed $1.00. That 2¢ is the arbitrage.
The discrepancy exists because YES and NO are quoted as separate orderbooks with separate buyers and sellers. They drift apart momentarily when one side gets hit hard without a matching counter-order. A bot's only job is to be there in that moment, before another bot is.
02Formal statement
For any binary market M with complementary outcomes YES and NO, and let a_y, a_n be the current best-ask prices on the two books. A sum-to-one arbitrage exists when:
03Worked example
Market: "Trump approval > 45% in May". Best-ask on YES is $0.49 with $420 of size. Best-ask on NO is $0.49 with $420 of size. Fees: 0.20% per leg. Polygon gas: $0.003.
04Constraints that limit the strategy
- Book depth. The arb price almost never has institutional depth. You can usually fill $200-$2k at the touch; larger sizes eat the gap.
- Latency. The opportunity exists for hundreds of milliseconds, not seconds. By the time a slow bot fills, the book has moved.
- Leg-failure. Roughly 3-7% of attempts fill only one side, leaving directional exposure. The reconciler logic is the part most DIY bots get wrong.
- Edge decay. Every new operator narrows the gap. Liquid markets had 2%+ opportunities ~480 times/week in Q3 2024; ~120/week by Q1 2026.