Counting curves in algebraic varieties is a subject of long history. It is particularly intriguing to count open curves, i.e. curves with boundaries. In my thesis, I studied the counting of open curves in log Calabi--Yau surfaces. Since the construction involves virtual fundamental classes, the counting numbers are a priori rational numbers. In this talk, I will explain a recent observation joint with Sean Keel, that the counting numbers are actually positive integers.