Do large collections cost less per card?
In short: Collection appraisals are priced as a set, tiered by the number of items, rather than as a stack of single-card fees. The written quote shows the tier your collection falls in.
A collection report shares work across items (one scope, one definition of value, one set of research), so it is quoted as a single flat fee by tier, not per card. The remote clinic works the same way: collections are quoted as a set.
For insurance, insurance documentation is a flat fee for the whole collection. Either way, the quote tells you the exact number before you decide.
What decides the tier
The number of items sets the tier, and the scope states it. If you add cards after the quote, I tell you and re-quote before doing the extra work; see can a quote change after I agree to it?.
What stays the same
The fee is never a percentage of what the collection is worth, so a valuable collection does not cost more simply because it is valuable. Payment is by invoice after the engagement letter; see how do I pay?.