A trader should put more weight on Shi and Zhai's first-fill result than on their $2.50M headline. The price inconsistencies they find across Polymarket contracts are real; the larger figure assumes quotes stay as observed after earlier simulated trades.
How the trade works
Polymarket lists binary contracts on the same event in separate order books. Its matching engine does not enforce coherence between those books or offer an atomic multi-leg order. An "over 3.5 goals" bid can therefore exceed an "over 2.5 goals" ask, although the first outcome implies the second. In the paper's example, fee-adjusted quotes on that pair are 0.9267 and 0.7789. Selling the first and buying the second locks in $0.1479 per pair at resolution, whatever the score. Shi and Zhai call a portfolio that profits under every admissible joint resolution combinatorial arbitrage.
The authors extend the idea to a system of related contracts. Coherent prices lie inside the convex hull of the payoff vectors permitted by the logical relations; the ℓ1 distance to that set gives the best guaranteed profit per unit position. With real order books, an arbitrage exists when no coherent price fits inside every fee-adjusted spread. Finding the relations takes more work. Venue-asserted relations come from Polymarket's negative-risk groups, which the venue treats as mutually exclusive baskets. Venue-derived relations place sports contracts on a shared score grid. Semantic-inferred relations come from text parsers and five open-weight LLMs. Two frontier audit models must agree on an LLM proposal's type and direction before it is kept; parser relations undergo rule checks. The reduced system contains 573,024 relations across more than 255,000 contracts.
From 23 June to 3 August 2026, the authors collected 73.22 billion live order-book messages and 227 million on-chain fills. Fee-adjusted best quotes produced 491,939 arbitrage windows, periods when a portfolio offered positive guaranteed profit. Their simulated arbitrageur traded in 125,095 windows; 112,376 had settled. The accumulated result is $2.50M guaranteed on $113.7M committed, or 2.2% net of spreads and taker fees. At resolution it is $3.63M (3.2%).
The first take is the better dollar figure
The $2.50M adds every simulated execution within each window. Later executions use observed quotes without allowing the arbitrageur's earlier trades to change them. The authors state that assumption plainly and call the accumulated take an upper bound. Their lower bound counts only the first execution per window: $1.10M on $40.6M, or 2.7%. The abstract leads with the accumulated figure, while the conclusion places $2.50M next to the unchanged-quote assumption and follows it with $1.10M. In venue-derived windows, accumulated take is about 2x first take.
Returns tell a different part of the story. The first take guarantees 2.7% against 2.2% for the accumulated take, and both return 3.2% at resolution. My objection concerns the dollar total. The $113.7M repeatedly counts capital as it is redeployed; estimated peak capital outstanding is $11.1M for the accumulated take and $3.5M for the first. A median window guarantees 0.5% on capital. Weighted by profit, the median rises to 6.5% for the accumulated take and 10.4% for the first.
Reconstructed best quotes agree with the venue's in 97.2% of 13.3 billion comparisons. The authors caution that this check cannot establish whether depth at other price levels is complete. Simulated size beyond the best level consequently depends on depth the comparison cannot verify. Two checks are reassuring: excluding cancelled-and-re-posted depth for up to 120 seconds leaves guaranteed profit at 100.0% to 100.7% of baseline, while a cap of 50% of displayed depth retains 56.5% of profit and raises the guaranteed return to 2.5%.
Can all the legs fill?
This is the test that matters.
Resubmitting every order after 100 ms cuts profit at resolution to 91.4% of baseline; 14.2% of orders lose money. At one second, 54.3% of orders fill in full and 84.0% of quantity fills. Resolution profit falls to 79.3% of baseline, with 22.1% of orders losing. Unequal fills erase the guarantee. The authors accordingly report these delayed results at resolution, the right way to describe a position that has become a bet. Among settled orders, it still paid 91.4% of baseline at 100 ms and 79.3% at one second.
Speed alone does not explain the dollar total. Windows shorter than 0.3 seconds account for 47% of executed windows but 8% of accumulated take. Competition is visible nonetheless: a median of 2.6 seconds elapses before one taker has traded every leg in the arbitrage direction. Only 854 addresses ever do that, and the top 10 account for 77.5% of matched windows. As the paper cautions, a directional match does not establish execution at simulated prices and quantities. The matching window extends to 30 seconds after an arbitrage window closes. For venue-asserted trades, the median time to complete every leg is 2.7 seconds, though the median executed venue-asserted window lasts 0.2 seconds. Many matched trades therefore arrive after the window closes. Those wallets may be taking the simulation's first fill; these matches cannot prove it.
Text-inferred relations last longer
Parsers and LLMs together supply 7% of guaranteed profit in the semantic layer: $179K accumulated and $35K first take. Parsers account for 21,744 of its 29,097 executed windows. Among windows lasting at least 0.3 seconds, semantic windows persist for a median 30.8 seconds, versus 2.9 for venue-asserted windows. With controls, LLM-found windows last about 15x as long. A matched trade appears in only 8.8% of semantic windows, compared with a 0.3% placebo. The authors acknowledge that "these comparisons do not isolate discovery costs from execution costs." Semantic positions also hold capital for a median of 7 days, against about 3 hours for venue-derived positions.
The documented relation failure occurs in this layer. An audit after the replay found six invalid parser relations. Removing them eliminated 9,172 executions; 82 affected windows had settled at a profit anyway. The authors say the episode shows "why profitable settlement does not validate an ex-ante guarantee." Their footnote nevertheless offers zero settled windows below guaranteed profit as consistent with relation validity. The audit makes that evidence less persuasive.
Why we could not replicate the trade
We could not replicate this. Our data have no prediction-market contracts, resolution text or settlements, and their finest interval is one-minute bars. This trade depends on full-depth books. The median executed venue-asserted window lasts 0.2 seconds, or 2.9 among windows lasting at least 0.3 s.
Beyond the World Cup sample
The sample spans 42 days on one venue during the 2026 FIFA World Cup; the paper's examples include group matches such as Algeria vs. Austria. Sports make up 50,603 of 69,698 daily active contracts. The sports taker fee rose from 0.03 to 0.05 on 10 July, mid-sample, and we did not find results split by fee regime.
For this edge to persist, depth beyond the best quote must be available, latency must stay near 100 ms, the top 10 wallets must leave room for a first fill, and profit must survive the 0.05 fee rate. A second sample outside tournament season, with first take still near 2.7% on settled windows, would convince me the edge outlasts the tournament.