How Parlay Odds Are Calculated

A combined bet pays out only if every leg wins. Because the legs are settled together, the price is the product of the individual prices rather than the sum.

In decimal notation this is direct: multiply the legs. Two legs at 2.00 combine to 4.00. Three legs at 2.00 combine to 8.00. In fractional or moneyline notation the same operation requires converting to decimal first, which is one reason decimal is the sane internal representation for any system handling these.

The probability side works the same way, for independent events. If each leg has a genuine probability of one half, the combination has one quarter, then one eighth. The payout multiplies and so does the improbability, which is the property that makes these attractive to buyers and is not itself the interesting part.

The interesting part is what happens to the margin, because each posted price is not a fair price. It is a fair price with a load added, and the multiplication does not know the difference.

Take a single leg. Its posted price implies a probability slightly higher than the modeller's estimate of the true probability, and that difference is the margin.

Now combine several. The fair combined probability is the product of the fair probabilities. The implied combined probability is the product of the implied ones. Because each implied figure is inflated, multiplying them multiplies the inflation.

The result is that the gap between the combined posted price and a fair combined price is proportionally larger than the gap on any single leg, and it widens as legs are added. Two legs compound two margins. Five legs compound five.

This is arithmetic rather than a claim about anyone's intent. Nothing unusual is being done to combined markets; the ordinary per-leg margin is simply being applied multiplicatively because the settlement is multiplicative.

For anyone modelling these, the practical consequence is that comparing a combined posted price against a naive product of implied probabilities compares two quantities that are inflated to different degrees. De-margin each leg first, then multiply, and the comparison becomes meaningful. Doing it in the other order produces a number that looks like an edge and is mostly accumulated load.

Correlation breaks the multiplication

Store legs and combinations separately. A combined price is a derived quantity, and keeping it alongside the legs that produced it lets you recompute and check. Systems that store only the combined price cannot answer where a discrepancy came from.

De-margin before you multiply. The order matters, as above, and the method used should be recorded with the result so a later change of method does not silently invalidate historical comparisons.

Test dependence rather than assuming it away. Historical co-occurrence of leg outcomes is measurable. Where legs come from the same event, assuming independence is a modelling error with a known direction rather than an approximation.

Expect high variance in any evaluation. Combined outcomes are rare by construction, so a sequence of results carries very little information about whether a method works. Evaluating on realised outcomes over a short window is close to reading noise, which is why measuring against price movement is generally more informative than measuring against settlement.

Watch for stale legs. A combination priced from a leg that has since moved is not a live price, and in a normalization pipeline the freshness of the worst leg governs the freshness of the whole.

This page describes how these prices are computed and is not betting advice.