S - TERM

Sum-to-one arbitrage

/sʌm tə wʌn ɑːrˈbɪtrɑːʒ/ · noun · trading strategy
arbitrage prediction markets CLOB YES / NO

The trade where you buy YES and NO on the same binary market for a combined price strictly less than $1.00 - guaranteeing $1.00 of return on a less-than-$1.00 outlay, regardless of which side resolves.

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:

Condition arb = 1 − (a_y + a_n)
a_y + a_n < 1.00→ arbitrage exists
a_y + a_n = 1.00→ market is fair
a_y + a_n > 1.00→ no arb (spread & fees pay the bookmaker)

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.

P&L breakdown $420 size
Cost - YES leg−$205.80
Cost - NO leg−$205.80
Polygon gas (2 txs)−$0.006
Maker/taker fees (40bps total)−$1.64
Guaranteed payout at resolution+$420.00
Net realized+$6.75 · ≈1.6%

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.

06Where this appears at Predikted

First indexed Jan 2024 · Last edited May 11, 2026 by Camille M. · v3 · Source code on Github ↗