Rare books?

When you're a book collector, you always want a "first", i.e. first edition, first printing. But when the publisher has "a first printing of 10.8 million copies" does that really allow the "first" to be worth anything? The first rule of collecting (anything) is scarcity. So, if there's a second printing of (only) 500,000 copies, and therefore more scarce, does that make the second printing more valuable?