What one academic paper documented about complementary-price extraction on Polymarket

Suggested hed: What one academic paper documented about complementary-price extraction on Polymarket

Dek: Saguillo et al. (AFT 2025) classified complementary-price, NegRisk, and combinatorial extraction on markets that resolved 1 April 2024 to 1 April 2025 and reported $39,587,585.02. That is a pre-fee, dated measurement — not “bots made $40 million,” and not a claim the same gaps are still there in 2026.

Public write-ups about complementary prices on Polymarket often skip the paper and keep the folklore: bots printed tens of millions on books that failed to add to a dollar, and the same trade is sitting there now.

One academic paper measured a version of that activity. It is Saguillo, Ghafouri, Kiffer, and Suarez-Tangil, Unravelling the Probabilistic Forest: Arbitrage in Prediction Markets (AFT 2025 / arXiv:2508.03474). This note states what that paper documents. It is not a method for repeating the measurement.

The sample is a year of resolved markets, ending 1 April 2025

The authors collect historical bids on markets that resolved 1 April 2024 to 1 April 2025. They count 8,659 single-condition markets and 1,578 NegRisk (multi-condition) markets, 17,218 conditions in all.

That window is the fact. It is not a statement about books on 14 August 2026.

They classified historical fills. They did not publish a how-to.

They label two activity classes.

Market rebalancing is their name for intra-condition or intra-market complementary-price gaps: YES and NO of one condition, or the YES set of a mutually exclusive NegRisk market, summing to less than or more than $1.

Combinatorial is their name for logically dependent market pairs — for example, a winner market and a margin market on the same election — where the prices of dependent subsets disagree.

Those are labels on a historical tape. They are not instructions, and they are not a claim that a person clicking two buttons had a risk-free lock. The authors write that the legs are non-atomic: one side can fill and the other can fail.

The number on the page is $39,587,585.02. Read the assumptions.

In §7.4 they write that the combined amount extracted from all strategies they present totals $39,587,585.02, assuming ε = $1 profit per trade. The abstract rounds that to “40 million USD.”

They do not subtract fees. They write that Polymarket did not charge per trade executed in the sample they measured.

They required at least $0.05 of profit on the dollar before they counted an opportunity. They dropped bids below $2. They grouped one address’s fills inside a 950-block (~1 hour) window and called that one opportunity. That hour is a method parameter. It is not a hold-time finding.

They also write that because they average executed prices (VWAP), they underestimate the margin a filler could have realized.

So the headline number is a realized estimate under those rules, on that tape, before fees they say were not charged then. It is not “bots made $40 million.”

The buckets they publish

On single-condition books, they score $5,899,287.427 from buying when YES + NO sat below $1, and $4,682,074.77 from the path they describe as selling when the sum sat above $1.

On NegRisk books: buy YES $11,092,286.31; sell YES $612,188.83; sell NO $4,264.33; buy NO $17,307,113.81.

On combinatorial pairs: they kept 13 dependent U.S.-election pairs and found executed extraction in 5. They itemize four totals — pair 2 $60,236.71; pair 4 $18,472.31; pair 1 $15,818.53; pair 3 $629.16. The fifth pair total is not on the page.

Of 17.2k conditions, 7,051 had at least one intra-condition opportunity they counted. Those observed intra-condition opportunities were all long (YES + NO < $1). They still record executed profit on the over-$1 path. Of 1,578 NegRisk markets, 662 had at least one opportunity they counted, and those books showed both under-$1 and over-$1 gaps.

Politics and Sports dominate market counts in the sample. The exploited single-condition profit they plot is Sports-heavy. The extracted NegRisk profit they plot is Politics-heavy. That is where this classification sat in 2024–25. It is not a general menu of “what winners prefer.”

Table 1 exists. It is not a cast list.

The paper publishes Table 1: the top ten accounts by their classified extraction, as truncated hex, with a dollar total and a transaction count. The first row is $2,009,631.76 over 4,049 transactions (0xd218e474776403a3301422… as printed).

They write that some of the large accounts show “bot-like behaviour in the number of bids.” They do not prove those addresses are bots. They do not identify the people. This note does not invent biographies for the rows.

They also name @Tutaaa91, who they say bought both YES and NO for less than $0.02 each in a single trade they score at $58,983.36, plus two other high-return trades they do not itemize. That is one paper-reported fill. It is not a profile.

What this paper does not say

It does not say the same gaps are still there in 2026. UNKNOWN.

It does not say those gaps still clear costs after current fees. The authors’ no-fee sentence is about the sample they measured. This note did not re-open a fee schedule. Whether the gaps survive current fees is UNKNOWN.

It does not say the Table 1 addresses are bots. UNKNOWN.

It does not say how long a position was held. The ~1 hour figure is a bid-grouping window. UNKNOWN.

It does not say how to join Table 1, how to run a bot, or how to take a complementary-price gap.

If you came here because a thread offered a $40 million bot story, the useful move is smaller than picking up the story or picking up a recipe: keep the dated measurement, keep the assumptions on the same line as the dollar figure, and refuse the folklore until another primary replaces the 1 April 2025 end date.