Why 37%, Exactly

The magic number is really 1/e, about 0.368, where e is the constant 2.718. It comes straight from calculus. Reject too few candidates and you barely know what good looks like; reject too many and the best one is probably already gone. Balance those two risks, set the math to its peak, and 1/e falls out. The clean lesson: the right amount of exploring is something you can calculate, not just guess.