Same-game parlays: a price you cannot decompose

A same-game parlay combines legs from one event into a single bet. Its price is not the product of the leg prices: it is the output of a correlation model that reprices each leg conditional on the others already on the slip. The same three legs will carry different prices at different books because the models disagree.

Multiplication assumes the legs are independent, and inside one game they never are. So the engine has to compute the joint probability of the whole combination, which means the resulting price cannot be split back into per-leg components. There is no leg price on the slip because there is no longer a leg price.

The repricing runs both ways. A leg the model judges to fight the others gets a longer in-parlay price than its single, so the engine is sometimes paying rather than taking. Doing the division tells you which is happening; assuming it is always taking is as unfounded as assuming it never is.

And that is the trap. SGP prices get compared across books by leg count, which compares nothing. Only the identical leg set is comparable, and even then a large gap is two correlation models disagreeing rather than a mispricing you can verify — neither book will show you its assumptions.

What to do with it. Add legs one at a time, divide each running price by the one before it, and read the implied in-parlay cost of every leg you add.