Accidents and sagacity
Walpole's own definition, quoted by the Online Etymology Dictionary and the American Heritage Dictionary alike, pairs two things: accidents and sagacity. Serendipity is the faculty of making happy discoveries you were not looking for — the sagacity is the noticing. That is a narrower claim than “pure luck,” and it is the one the coiner's letter actually supports.
AHD's word history adds the texture: Walpole called his source “a silly fairy tale, called The Three Princes of Serendip,” while still drawing the name from it, and described his knack for finds as a kind of “talisman.”



