The independent-leg calculation
If two independent legs each have a 50% chance, both occur together 25% of the time under those assumptions: 0.50 multiplied by 0.50. Add a third 50% leg and the combined probability falls to 12.5%.
Four independent legs estimated at 55% each combine to about 9.15%. The individual picks can each look more likely than not while the complete ticket remains unlikely to hit.
Why a weak leg matters twice
A weak leg reduces the chance that every condition is satisfied. If that leg is also offered at a worse price than the broader market, it can reduce expected value as well. The payout may rise when the leg is added, but a larger payout does not automatically compensate for the added risk.
Reviewing the ticket without its weakest leg is a useful stress test. Compare the new combined probability and price rather than focusing only on the lower headline payout.
Price the ticket, not just the hit rate
A 10% estimated probability corresponds to fair decimal odds of 10.00, or approximately +900, before margin. If the offered price is materially shorter, your estimate and the payout are out of balance.
This comparison is only as good as the leg probabilities beneath it. Using raw sportsbook implied probabilities without removing margin can double-count cost when evaluating a full parlay.
When multiplication is the wrong shortcut
The multiplication rule above assumes independence. Outcomes from the same game may share pace, scoring environment, weather, playing time, or game script. Their joint probability can be higher or lower than the independent estimate.
That is why correlation deserves a separate review. It is not a reason to assume free value; it is a reason to check how the book repriced the combination.