Why Complementary Prices Should Add Up to About a Dollar

Complementary prices should add up to about a dollar because complementary claims are two sides of one dollar of collateral. On a well-formed yes-no market, exactly one side pays a dollar if the rules say that side happened, and the other side pays nothing. The pair is minted from a dollar and can be merged back into a dollar. That is the machine. A screenshot where the two numbers do not add to $1.00 is a fact about prices, not a fact that the event is "wrong."

What this page does not claim. It does not claim that books are usually over a dollar, or usually under. It does not tell you to buy the cheap complete set, sell the rich one, or run a program against the gap. It does not claim a gap is risk-free. The $0.60-and-$0.40 mint example below is a documentation example published by one venue, retrieved 2026-08-15T00:40Z, not a live order-book quote. How many addresses are in profit, and which named wallets a 2024–25 paper classified as extracting gaps, are separate pieces.

### Complementary claims

A claim is complementary to another when they cannot both pay, and — if the set is complete — they cannot both fail. Yes and No on one condition are the simple case. "Trump wins this market" and "Trump does not win this market" are complementary if that is actually the rule. In a winner-take-all event with several named outcomes, the complete exclusive Yes set is the complement: exactly one of those Yes tokens is supposed to pay a dollar.

Official docs on the venue this guide uses (retrieved 2026-08-15T00:40Z) put that in tokens. Each binary market has two ERC-1155 outcome tokens. Yes redeems $1.00 if the event occurs. No redeems $1.00 if it does not. Every Yes/No pair in existence is backed by exactly $1 of collateral locked in the conditional-token contract.

### What the official machine does with a dollar

Three operations move money between collateral and the pair.

Split: $1 of collateral becomes 1 Yes and 1 No. The docs' own scale example is $100 → 100 Yes + 100 No.

Merge: 1 Yes and 1 No become $1 of collateral again.

Redeem: after resolution, each winning token becomes $1 and each losing token becomes $0.

There is a fourth path that looks like a trade and is actually a mint. The prices-and-orderbook page (retrieved 2026-08-15T00:40Z) says a buy-Yes at $0.60 can match a buy-No at $0.40 because those two bids add to $1.00. The dollar is locked; one Yes and one No are created; each buyer receives their token. That $0.60 / $0.40 pair is a documentation example, not a live fill. Matching is off-chain; settlement is on-chain. Every user-facing order is a limit order.

### "About a dollar" is a band, not a tick

In frictionless theory the identity is exact. Tsang and Yang (arXiv:2603.03136v1, HTML retrieved 2026-08-15T00:40Z) write δ = P_YES + P_NO − 1, and say that in a frictionless market with instantaneous arbitrage δ would be identically zero. In the same section they say on-chain settlement costs and execution delays create a no-arbitrage band, and that the size and persistence of δ is their efficiency measure.

Official docs describe matching when complementary bids sum to $1.00. They do not say the live best bid and best ask always sum to $1.00. An earlier section of the same paper says split and merge "force" the sum to always equal $1.00. Their efficiency chapter is the one this guide follows: the target is a dollar; the screenshot is allowed to miss.

### One documented over-$1 book — not a 2026 law

On the 2024 Trump election market, Tsang and Yang observe a persistent **positive** δ: Yes + No traded above $1. Their sample is 2024-01-05 00:00:00 UTC to 2024-11-06 06:46:00 UTC. They read that as sustained demand on both sides that minting could not absorb instantly — temporary overpricing of the *pair*, not a verdict that the event forecast was wrong. They also write that the Harris book saw large δ swings in late July 2024 around the nominee shock, then quieter as liquidity deepened, and that the magnitude of δ shrank as volume grew. The HTML we retrieved does not print a table of δ values. The size of that gap is UNKNOWN from the text. Do not invent one.

A different paper, Saguillo, Ghafouri, Kiffer, and Suarez-Tangil (AFT 2025 / arXiv:2508.03474, HTML retrieved 2026-08-15T00:40Z), looked at markets that resolved from 2024-04-01 to 2025-04-01. Of 17.2 thousand conditions, they counted 7,051 with at least one intra-condition opportunity under their filters (at least five cents of gap per dollar, no token above $0.95, prices from executed-bid VWAP). Every intra-condition opportunity they flagged was **long**: Yes + No **under** $1. On multi-outcome (NegRisk) books they saw both sides: 662 of 1,578 such markets had at least one opportunity they counted.

Those two findings can both be true. They are different samples, different price constructions, and different market types. They are not a 2026 census. Whether books are "usually" over $1 on this venue now is UNKNOWN. This page will not say they are.

### What under $1 and over $1 mean — mechanically

Say the numbers you are adding are the prices at which you could actually buy each complementary leg, at the same moment, in enough size.

If that executable sum is under $1, the book is offering a complete set — 1 Yes + 1 No, or 1 Yes of every mutually exclusive outcome — for less than the dollar that backs the set and that the winning side redeems. Merge (if you already hold both) or hold-to-redeem is the conversion the contracts describe. The gap is a dollar difference only after you subtract fees, gas, and the cases where one leg does not fill.

If that executable sum is over $1, the complete set is more expensive to buy than a dollar. The mechanical inverse the papers describe is to lock a dollar, mint the pair, and sell the pair for more than a dollar — again before fees and fill risk. Tsang and Yang's persistent positive δ is this side of the identity: both legs trading rich relative to the collateral.

Neither reading says the market is wrong about the event. Neither reading is a risk-free lock. The venue's matching is not atomic across two legs. Saguillo state that execution risk explicitly.

This page does not tell you to take either side.

### The numbers you add up may not be the numbers that trade

On the venue that published the prices-and-orderbook page retrieved 2026-08-15T00:40Z, the displayed price is the midpoint of the best bid and the best ask, unless the spread is wider than $0.10, in which case the last trade is shown. Their own example is a $0.34 bid and a $0.40 ask, which displays as $0.37. A buyer pays the ask. A seller receives the bid.

Add two mids and you can get a sum near $1 while the two asks — the prices a person buying both legs would pay — sit above $1 by about the two half-spreads. Add two last trades and you can be adding prints from different times. Saguillo's δ-like flags use executed-bid VWAP, not the number on the button. If you cannot see bid, ask, time, and whether the figure is mid or last, you do not know which sum you are looking at.

### Fees move the band

As of the fees page retrieved 2026-08-15T00:40Z, takers on most categories pay `fee = C × feeRate × p × (1 − p)`. Makers are not charged. The USDC fee peaks at a 50¢ price. Geopolitics is listed as fee-free. Documented taker rates on that page: Crypto 0.07; Sports, Economics, Culture, Weather, and Other 0.05; Finance, Politics, Mentions, and Tech 0.04. The same page's 100-share tables (documentation, not an invoice) peak at $1.75, $1.25, and $1.00 per 100 shares at 50¢ for those three rate groups.

Qin and Yang (arXiv:2606.04217v1, HTML retrieved 2026-08-15T00:40Z) date the 2026 fee reform as staggered: Crypto in January 2026, Sports in February 2026, other categories in March 2026. Saguillo's sample ends 2025-04-01. They write that they ignored fees because the venue charged none then. That sentence does not travel into fee-on books in 2026. A gap that is smaller than two taker fees plus the spread plus the chance one leg misses is not the frictionless δ in the papers.

Whether any given 2026 book still shows an executable complementary gap after those costs is UNKNOWN. This page does not claim the 2024–25 gaps are still there.

### When there are more than two outcomes

If the event is winner-take-all and the venue has turned on negative risk, the $1 rule has a second door. Official docs (retrieved 2026-08-15T00:40Z): 1 No on one outcome can be converted into 1 Yes on every other outcome. Tsang and Yang's Table 1, same retrieval: in a three-candidate race, 1 No on A plus 1 No on B pays the same at resolution as 1 Yes on C plus $1. That is the inter-outcome complement.

If negative risk is off, each Yes/No pair is its own $1 identity. There is no official conversion bridge between outcomes. Adding Yes prices across independent markets and expecting $1 is a different claim, and this page does not make it.

### The binary-option analogy — and where it stops

A Yes token that pays a dollar if a defined event happens, and nothing if it does not, has the same *payoff shape* as a cash-or-nothing claim with a one-dollar payout. People call that shape a binary option. The analogy is useful for one sentence: you are looking at a yes-or-no payoff, not a share of a company.

The analogy stops there. This page does not claim the token is a listed binary option, that option-pricing formulas apply, that the venue is an options exchange, or that a 65-cent Yes "is" a 65-delta option. Payoff shape is not product identity.

### What to do with a screenshot that does not add to a dollar

Read which numbers were added. Mid, last, bid, and ask are different objects. Check whether the set is actually complementary — same condition, or a complete exclusive Yes set on a neg-risk event, not two related headlines. Remember that a miss of a few cents can be spread, fees, or a stale print rather than a story about the election. The 2024 Trump book in one paper traded rich as a pair for months. A 2024–25 paper's intra-condition flags went the other way. Neither finding is a rule for a book you have open tonight.

Wallet profitability, and the named wallets a paper measured against historical gaps, are separate pieces. They are not evidence that you should take the under-$1 side.