Key takeaways
- A cancelled leg is an economic outcome. Polymarket US describes a fair-price multiplier; OG describes a volume-weighted price. Neither description amounts to simply deleting the component and retaining the original maximum payout. The replacement value becomes part of the position's economics.12
- A combo can lose money without a leg resolving against its holder. In our illustrative three-leg position, 1,000 contracts bought for $200 pay $150 when one leg wins and two settle at 0.60 and 0.25 under a product rule. The $50 loss comes from fractional settlement, before fees.
- The combination has terms of its own. Kalshi's 5 October 2026 FOOTBALLSTATS amendment introduces a whole-contract Fair Price for nonbinary components. Its general help page continues to describe multiplication. An instrument review must identify the applicable terms, not choose a formula from the brand name.34
- Multiplying final payouts and multiplying current probabilities are different operations. Two events with assumed probabilities of 60% and 50% can have a joint probability anywhere from 10% to 50%. Their product, 30%, is the independent case. A combination's price therefore reflects both the relationship between the events and the rules used when an event cannot settle normally.
1. The component can disappear without the position disappearing
A multi-leg contract turns several conditions into one position. The familiar description is that every selected outcome must occur for the contract to pay its full amount. That describes the ordinary binary case. A cancellation introduces another question: what replaces an outcome that can no longer be decided?
Polymarket US's published combo FAQ provides a concrete answer. A component that cannot resolve receives a last fair market price, determined by the Settlement Committee, and that value enters the combination's payout. The FAQ names cancellations, walkovers, nonparticipation and certain postponements as examples.1
The financial distinction is easiest to see in cash. Assume a holder buys 1,000 three-leg contracts at 20¢ each, spending $200 before fees. Each contract has a maximum payout of $1. Two different things can now happen: the position can be unwound for its original cost, or it can remain outstanding and receive a fractional settlement. Those are different transactions.
| Assumed final component values | Settlement per contract under the product rule | Receipt on 1,000 contracts | Gain or loss against the $200 entry cost |
|---|---|---|---|
| 1.00 × 1.00 × 1.00 | $1.00 | $1,000 | +$800 |
| 1.00 × 1.00 × 0.60 | $0.60 | $600 | +$400 |
| 1.00 × 0.60 × 0.25 | $0.15 | $150 | −$50 |
| 1.00 × 0.00 × 0.60 | $0.00 | $0 | −$200 |
| Full reversal at original cost, a different assumed rule | $0.20 returned | $200 | $0 |
Source: Predict Here calculations. All quantities and component values are illustrative assumptions, not observed trades or settlements. Product-rule receipts equal quantity × the component-value product. Fees, financing and taxes are excluded. The reversal row illustrates a different contractual mechanism; it is not attributed to a venue.
The third row is the important one. No component has settled at zero, yet the holder receives less than the amount paid. Calling the two affected legs “void” would hide the mechanism. They have been assigned financial values, and those values multiply.
Deleting a leg would produce a different result again. If the two surviving legs both pay one, deleting the third multiplier leaves a product of one. Assigning that third component 0.60 leaves a product of 0.60. For the position above, the difference is $400. The word “cancelled” does not tell the reader which calculation applies.
This is the next step after identifying the terms of a single event contract. A combination requires the terms for each component and a rule for how their results become one payout.
2. Three settlement mechanisms sit behind similar interfaces
The official materials reviewed for this paper describe distinct approaches. Some specify a mathematical product of component values. Another permits a determination for the combination as a whole. A price used inside the product can itself come from different measurement procedures.
| Document and scope | Treatment described | Evidence needed to reconstruct the amount |
|---|---|---|
| Polymarket US, combo FAQ | Multiply by the affected leg's last fair market price | Committee determination and the other component values |
| OG, combo guide; linked Crypto.com cancellation guidance | Multiply component settlement values, including a cancelled leg's VWAP | Calculation window, eligible trades and any fallback determination |
| Kalshi, general combo help page | Product of component payouts, including scalar values | Each component's applicable terms and final value |
| Kalshi, FOOTBALLSTATS amendment filed 5 October 2026 | Whole-contract Fair Price when a component is nonbinary; product fallback if the exchange does not determine that price | Applicable contract version and the exchange's determination |
| Polymarket International, combinatorial-position documentation | Describes conjunction and complement for normal binary outcomes | Exact product and exceptional-resolution terms for any nonbinary case |
Sources: the named official documents, read 31 October 2026.125436 This is a document comparison, not a census of settled positions. The Kalshi rows deliberately preserve the difference between the two publications.
OG's guide says a cancelled component remains in an unsettled combo at its settlement value. The cancellation guidance it links to defines a one-week volume-weighted average before the cancellation determination, with an alternative fair-settlement process if the average is unavailable or unsuitable.25
A last fair price and a week-long average can differ even when both are calculated correctly. The former asks for a value associated with a particular moment; the latter aggregates transactions over a period. If information moved the component's price sharply before cancellation, the two procedures could retain different parts of that history. This is an analytical consequence of the definitions, not a measured gap between the venues.
The Kalshi document pair introduces a separate distinction. The amended FOOTBALLSTATS terms allow Fair Price to reflect the combo's earlier trading, quotes, related contracts and the exchange's assessment. The product of component values is not compulsory when that determination is made.3 Its contract-store PDF still presents the earlier product formulation.7
The economically relevant question is therefore two-stage. First, what value does the exceptional component receive? Second, does the combination multiply that value into its payout, or does its own rule substitute a value for the whole position? A screen that displays only the component's adjusted number may answer the first question while leaving the second unanswered.
3. Multiplying settlements does not mean multiplying prices
Suppose two components settle normally. Let A equal one when the first selected outcome occurs and zero otherwise. Define B the same way for the second. A contract paying A × B pays one only when both occur. That multiplication is a statement about the final payoff.
Its expected payout is the probability that both outcomes occur together. Multiplying their separate probabilities gives that answer only when the events are independent. Separate prices, even treated as perfect probabilities for the purpose of an illustration, do not establish independence.
Assume the probability of A is 60% and the probability of B is 50%. A and B must overlap by at least 10 percentage points because their probabilities add to 110%. They cannot overlap by more than 50 points because the joint event cannot be more frequent than B itself. Every joint probability between those bounds is compatible with the same two marginal probabilities.
| Illustrative relationship | Both occur | A only | B only | Neither | Expected payout of a $1 joint claim |
|---|---|---|---|---|---|
| Minimum overlap permitted by the marginals | 10% | 50% | 40% | 0% | $0.10 |
| Independence | 30% | 30% | 20% | 20% | $0.30 |
| B always occurs inside A | 50% | 10% | 0% | 40% | $0.50 |
Source: Predict Here arithmetic on assumed probability distributions. Each row totals 100%; A occurs in 60% and B in 50% of the cases. Expected payout excludes discounting, risk premia, transaction costs and exceptional settlement. These are distributions constructed to demonstrate an identity, not estimates of actual markets.
The bounds follow directly from counting the outcomes. The general expression is max(0, pA + pB − 1) ≤ P(A and B) ≤ min(pA, pB). Independence supplies one point within that interval, pA × pB. It does not turn the interval into a single answer.
This matters when comparing a combo quote with the product of its displayed component prices. A gap can reflect dependence between the events. It can also reflect spreads, fees, different observation times and the exceptional-payout rules. The quote-minus-product calculation alone cannot separate those effects.
A simple economic example makes the dependence intuitive. If one selected condition is a team winning and another is that same team winning by a substantial margin, the second entails the first under matching game and settlement definitions. The joint event is the narrower condition. Multiplying two separate probabilities would count an additional uncertainty that the logical relationship has already removed.
The same reasoning applies outside sport. Two policy decisions may share an underlying political condition, or a corporate action may require an earlier approval. The details of the relationship matter. Putting the two conditions in the same list does not establish how often they occur together.
4. The opposite of a combination is not a combination of opposites
Another error appears when the overall position is labelled NO. Under the ordinary binary conjunction, NO to “A and B” pays when at least one selected condition fails. It is not the same as selecting NO on A and NO on B and requiring both selections to succeed.
Polymarket International's combinatorial documentation explicitly distinguishes the YES conjunction from its complementary NO position. Its description concerns normal binary resolution and also explains compression when some components have resolved and others remain open.6
| A | B | YES to A and B | NO to A and B | YES to not-A and not-B |
|---|---|---|---|---|
| Occurs | Occurs | 1 | 0 | 0 |
| Occurs | Does not occur | 0 | 1 | 0 |
| Does not occur | Occurs | 0 | 1 | 0 |
| Does not occur | Does not occur | 0 | 1 | 1 |
Source: Predict Here binary truth table. The formulas are A × B, 1 − A × B, and (1 − A) × (1 − B), respectively. Values are dollars per assumed $1 contract; the example excludes exceptional settlement.
The middle two rows carry the difference. When exactly one event occurs, the overall NO position pays one. A position requiring both opposite outcomes pays zero. A record that stores only the names of the events and the word “NO” is therefore incomplete. It must retain the side of each component and the side of the combination itself.
That distinction also matters for comparison across venues. Two positions can contain the same events yet expose their holders to different parts of the outcome space. Matching titles or counting common components will not identify that difference. The operator linking the components—“all,” “any,” or a more specific condition—is part of the instrument.
5. The reference price becomes a settlement input
Fractional settlement promotes a market price from an observation to an input in the payout calculation. The change is consequential. While trading is open, a price records an offer, execution or estimate at a moment. Once incorporated into settlement, the selected value determines cash received by every affected position.
For a product-rule combo with one scalar component s and all other selected components paying one, the payout per contract is s. A one-point difference in s changes receipts on 1,000 contracts by $10. If another component also settles at 0.25, the same one-point change moves the payout by only $2.50. Both results follow from the multiplication rule; neither needs a forecast of the underlying events.
More generally, the sensitivity of the product to one component equals the product of the others. This gives a precise way to explain which determination matters to a position. A component's price can be material before another leg resolves and irrelevant after a different component becomes zero under the same product rule.
The time selected for a reference price matters as much as the price measure. A value before a cancellation announcement and a value after it can describe different information sets. A transaction average can also be influenced by where trading was concentrated during its window. Recording the final scalar without its fixing convention prevents a reader from reconstructing why that value was used.
Whole-contract determination adds another object to the record. The final value F must be retained as the combo's own settlement input, with the source of that determination. Replacing F with the product of the visible components would be a new analytical assumption. It may happen to produce the same number, but numerical agreement does not establish that the same rule was applied.
6. A dependency map is needed before a price comparison
A useful combo record has three levels. The first identifies each underlying event and the exact component contract. The second identifies the side selected and the component's possible settlement values. The third records how the combination turns those values into one payment.
Polymarket US's API documentation already treats the combination as its own instrument. A canonical set of components maps to an instrument symbol within a product, and the component definitions retain their sides.8 The instrument therefore needs its own record even when every component already appears in a database.
| Record | What it answers |
|---|---|
| Combo identifier, venue and product/version | Which instrument and terms governed this position? |
| Component identifiers and selected sides | Which exact underlying claims were combined? |
| Overall side and combination operator | Is the holder exposed to the conjunction, its complement or another expression? |
| Component contingencies | What happens after cancellation, nonparticipation, postponement or other exceptional events? |
| Combination-level override | Does the combo multiply component values or use a separate determination? |
| Reference-price procedure and timestamps | Which trades, quotes, time window and decision produced a scalar value? |
| Component results, combo result and cash-receipt time | What resolved, what became payable and when was it received? |
Source: Predict Here proposed analytical record, derived from the distinct reconstruction questions in this paper. This is a research proposal, not a claim that every field is available from every venue or implemented in Predict Here's current product.
A change to one underlying contract can affect several combinations. The data problem is consequently a dependency problem: identify every combination that references the component, then establish which rules apply to each. Updating the component's current description alone does not preserve what an earlier position referenced.
Predict Here's published methodology already separates event mapping from semantic verification and names explicit relationship states.9 The extension proposed here is to retain the full combination rule alongside those component relationships. “These contracts concern the same events” is a weaker conclusion than “these positions pay the same amount in every relevant state.”
The second conclusion is the one that supports a payoff comparison. If a reviewed exceptional state produces different payments, the positions are different instruments even if their ordinary outcomes match perfectly.
7. Settlement time belongs to the combination too
The component results and the cash-receipt date are separate facts. Polymarket US's CAOC filing ties the latest scheduled expiration to the latest constituent expiration, while allowing acceleration when a component settles against its specified side.10 Kalshi's help page describes an additional period after the final component resolves.4
That creates an asymmetry in the ordinary product-rule case. One known zero can determine the final product immediately. A positive payout generally requires the remaining relevant components to be determined. A delay in the last component can therefore retain uncertainty in the positive branch even after several other components have finished.
For recordkeeping, “last event ended,” “last component determined,” “combo determined” and “cash received” should remain separate timestamps. Collapsing them into a single settlement date makes operational delay look like event uncertainty and makes event uncertainty look like an accounting delay.
Some structures also permit capital to be released without eliminating all remaining exposure. Polymarket International documents a collateral-return process that offsets compatible positions and leaves residual positions.11 An amount released through that process is therefore a distinct category from a final payout on a fully resolved combination. Reconstructing the position requires following what remains as well as what has been returned.
8. Our take
A combination needs its own terms review. Reading every component is necessary, but the composition rule is an additional contract term. The question is what the whole position pays after those components produce their results, including exceptional ones.
Treat fractional settlement as an outcome with a measurement method. A cancellation flag is not a payout. The record needs the assigned value, its source, its time convention and the formula through which it affects the combination.
Separate dependence from contractual differences. The product of marginal prices is a useful reference under a declared independence assumption. It is not a universal valuation, and a deviation from it is not automatically a pricing error. Before interpreting the deviation, establish what the components measure and what the combination pays.
Publish the route from components to cash. A reader should be able to trace the selected sides, the final component values, any whole-contract determination, the quantity held and the resulting receipt. This is a practical standard for research and reconciliation. It makes a surprising settlement explainable without requiring the reader to infer a financial rule from a short interface label.
Methodology, data and limitations
Source scope. This paper compares public primary documents read on 31 October 2026. It is a contractual and mathematical analysis, not a statistical study of executed combos. The sample was selected for explicit settlement mechanisms, not to estimate their prevalence.
Kalshi document difference. The 5 October filing, the contract-store copy and the general help article contain different formulations. The filing establishes what the amended text says. This review does not establish its effective application to every outstanding or newly listed combo, or the history of any particular settlement. The relationship between early-zero settlement and a later nonbinary determination also requires the applicable instrument's terms and sequence of decisions. The article does not resolve that hierarchy by assumption.
Polymarket venues. Polymarket US and Polymarket International are treated separately. The International material reviewed explains normal binary composition and position operations. It does not supply a complete exceptional-resolution formula for every combination, and the US FAQ is not substituted for that missing specification. The May US CAOC filing establishes the filed binary structure; the contemporary FAQ supplies the described fractional-settlement treatment.
Examples. All payout tables, probability distributions and sensitivities are author-created illustrations. They demonstrate arithmetic under explicit assumptions and do not estimate cancellation rates, fair market prices, attainable execution prices or realized returns. There is no claim that the illustrated scalar values occurred on a venue.
Comparisons. Help pages describe product behavior but are not a substitute for an applicable contract, rulebook, amendment or determination. A document mismatch does not establish a wrong payout. This research does not provide a legal opinion on the priority of those sources.
Reproducibility. The workpapers behind this paper retain source captures, retrieval results, hashes and exact-decimal calculations. Failed captures, if any, remain identified in the manifest; an accessed web source and a retained raw file are distinct evidence states.
Notes and references
- Polymarket US, Combos FAQs, sections “Payouts” and “When a leg cannot resolve”; read 31 October 2026. ↩
- OG, Combo, settlement section; read 31 October 2026. ↩
- KalshiEX LLC, FOOTBALLSTATS amendment submitted 5 October 2026, cover letter and Appendix A, PDF pages 7–8. Describes amended terms, not a verified migration of every live instrument. ↩
- Kalshi, Combos, “Settlement” and nonparticipation sections; read 31 October 2026. ↩
- Crypto.com, Sports Event Trading, “What happens if an Industry Event is postponed, canceled or not completed?”; linked by the OG guide and read 31 October 2026. ↩
- Polymarket International documentation, Combinatorial Positions, “What They Represent” and “Resolution”; read 31 October 2026. ↩
- KalshiEX LLC, FOOTBALLSTATS contract-store copy, payout criterion, PDF page 1; read 31 October 2026. ↩
- Polymarket US, Combos API Overview, instrument identity and component-side definitions; read 31 October 2026. ↩
- Predict Here, Methodology, event mapping, semantic verification and provenance; read 31 October 2026. ↩
- QCX LLC d/b/a Polymarket US, CAOC product self-certification, 20 May 2026, Attachment A, PDF pages 2–3. ↩
- Polymarket International documentation, Collateral Return, “How Collateral Return Works”; read 31 October 2026. ↩
Disclosures
This paper is general research published for information only. It is not investment, legal or tax advice. It does not recommend any position, venue or strategy, and is not tailored to any reader's circumstances. Its worked examples illustrate methods and express no view on any outcome. Predict Here is operated by Odyssea Research LLC. Predict Here does not list markets, hold client funds, take the other side of trades, or execute or route orders.
Persons associated with Predict Here may hold positions in event contracts, including on venues discussed in this report.