Combos: Simulation-Based Pricing for Correlated Multi-Leg Contracts

Combos are the most requested and least well priced product in event markets. A combo is a single position built from several legs that all have to come true, usually on the same event. Team wins and the total goes over. Driver finishes on the podium and sets the fastest lap. Three specific players each clear a performance threshold.

They are popular for an obvious reason. Almost nobody has a view that is purely about one binary outcome. Views are shaped, and a combo is how a shaped view gets expressed precisely. That is as true of an institutional counterparty positioning around a tournament as it is of a retail customer building a same game parlay.

They are also where most pricing systems quietly fall apart.

The Problem Is Correlation

The intuitive way to price a combo is to multiply the probabilities of its legs. Two legs at 50 percent each becomes 25 percent. This is correct only when the legs are independent, and legs on the same event are almost never independent.

A team winning and its strongest player posting a high individual statistic tend to happen together. A match staying low-scoring and a particular player clearing a performance line tend not to. In Formula 1, a driver finishing on the podium and that driver leading laps are tightly linked. In cricket, a high team total and a specific batter passing a runs threshold move together. None of these relationships are subtle, and none of them survive an independence assumption.

What makes this dangerous is not that the answer is wrong. It is that the answer is wrong in a consistent, predictable direction for any given structure. Positively correlated legs get underpriced. Negatively correlated legs get overpriced. A counterparty who works out which structures fall on which side has a repeatable edge, and they will take that exact structure in size for as long as it is quoted. Random error is a cost of doing business. One-sided error is an invitation.

Two Workarounds, Both Bad

The industry has two standard responses to this, and it is worth being honest that both are defensive rather than correct.

The first is to restrict what can be combined. Block the legs known to be correlated and only allow combinations the system can price under independence. This is safe and it removes exactly the combinations customers most want, since the appealing combos are appealing precisely because the legs relate to one another. It is also a public admission that the correlation is not being priced.

The second is to apply a blanket haircut, some fixed correction factor applied to every multi-leg position. This manages to be wrong in both directions at once. Genuinely independent combos come out overpriced and uncompetitive, so the good flow goes elsewhere. Strongly correlated combos remain underpriced, so the informed flow stays. The result is a book that loses the business it wants and keeps the business it does not.

What a Simulation-Based Architecture Does Instead

Rimble does not estimate correlation. It never computes a correlation coefficient at any point, which is the part that tends to surprise people.

The models simulate each event a large number of times and retain the full result set, so what exists at the end is not a set of probabilities but a set of complete simulated outcomes. Each one records everything that happened in that run: who won, the final margin, what every participant did.

Pricing a combo against that is a counting exercise. Take every simulated run, check which ones satisfy all the legs simultaneously, and divide by the total. That share is the probability of the combo. Nothing else is required.

Correlation is handled because it was never separated out in the first place. In the simulated runs where the team wins comfortably, its best player has already tended to have a strong game, for the same underlying reasons that produce the correlation in reality. The relationship is embedded in the outcomes rather than bolted on as an adjustment afterwards. Ask the question and the correlated answer comes back automatically.

Why This Scales to Any Structure

The practical consequence is that combo complexity stops mattering.

Approaches that model correlation explicitly face a combinatorial problem. Two legs need one pairwise relationship. Eight legs need twenty-eight, plus the higher-order interactions between them, each estimated from limited data and each contributing its own error. It becomes intractable quickly, which is the real reason leg limits exist on most products.

Counting simulated runs does not care. Eight legs is the same operation as two legs, evaluated against the same result set. Independent legs, positively correlated legs, and mutually exclusive legs are all handled by the same computation, and mutually exclusive legs correctly return zero rather than a small positive number. There is no structure the method has to refuse.

This is why Rimble's bet builder is unrestricted rather than a menu of pre-approved combinations. The absence of restrictions is not a commercial concession. It is what falls out of the architecture, described further in our piece on the in-house stack.

The Same Machinery at Institutional Size

A retail same game parlay and an institutional correlated basket are the same object. One is small and arrives through an operator's app; the other is large and arrives directly. The pricing question is identical, and it is answered the same way.

This matters because combos are where institutional demand concentrates and where institutional liquidity is thinnest. There is no public order book for an eight-leg correlated basket on a specific match. Each structure is effectively bespoke, so there is nothing to sweep and nothing to work into. Bilateral quoting is not one option among several. It is the only route to getting the position on.

Rimble quotes these on request, two-way, with a firm price covering the entire position. The counterparty gets one level for the whole structure rather than a sequence of partial fills at deteriorating prices, and nothing is signalled to a public venue in the process.

The quote is backed by Rimble's own capital. The desk is not matching two counterparties against each other; the position moves onto Rimble's book and is managed there. That is what allows a price to be firm on request rather than contingent on somebody else appearing on the other side.

Combos Concentrate Risk

The same correlation that makes combos hard to price makes them hard to risk-manage, and for the same reason.

A correlated basket is one bet, not several. When a book holds a number of positions across a single match, summing their notional will understate the true exposure, because those positions resolve together. A book that appears diversified across twenty positions may be holding a single concentrated bet on one outcome, and no amount of position-level reporting will reveal it.

Rimble measures exposure against the joint distribution rather than by adding positions together. Because the risk layer reads the same simulation output that produced the prices, this happens natively instead of through a reconciliation between two systems that model the event differently. Quotes then skew to favour the side that reduces existing exposure, which lets ordinary two-way flow flatten the book without a separate hedging trade.

What Gets Quoted, and for Whom

Coverage follows the sports Rimble already prices: esports, Formula 1, cricket, and kabaddi. Within those, the desk quotes combos across match outcomes, totals and handicaps, and participant or player performance thresholds, in any combination and at any leg count.

Sportsbook operators use this to offer unrestricted combos without carrying the correlated exposure that results, moving part of the position rather than restricting customers or defensively shading their own lines. Funds and proprietary desks use it to express a shaped view on an event in a single structure instead of legging into it and taking execution risk on each part. Venues launching combo products use it to have prices available before organic two-way flow exists.

Enquiries go to support@rimble.io. Existing pricing clients can reach the desk through their usual contact, and the underlying markets remain available through the standard API.

Frequently Asked Questions

1. What is a combo and why is it hard to price?

A combo is a single position made up of several legs that must all come true, usually on the same event. It is hard to price because those legs are correlated. A team winning and its strongest player posting a high individual statistic tend to happen together, so multiplying the individual probabilities produces a systematically wrong answer rather than a randomly wrong one.

2. How does simulation-based pricing handle correlation between combo legs?

Rimble simulates each event many times and keeps the full result set. Pricing a combo means counting the share of simulated runs in which every leg came true at once. Correlation is already present in those simulated outcomes, so it never has to be estimated as a separate parameter. The method returns the same answer whether the legs are independent, positively correlated, or mutually exclusive.

3. Can Rimble quote combos at institutional size?

Yes. Rimble quotes combos two-way with its own capital and carries the resulting positions on its own book. Combos have almost no public order book liquidity because each structure is effectively bespoke, so pricing is done bilaterally on request, with a firm price covering the whole position rather than a series of partial fills.