Okay, well, math is not my forte, but I think we can use the "complement rule" to solve this, which states that the probability of the event happening is equal to 1 minus the probability of the event not happening.

In this, case since you're assumed to miss 999 of 1,000 throws, we get the following:

1-(.999)¹⁰⁰⁰ ≈ 1 - .367 ≈ .632

There's a .1% chance it happens on each throw, but a 63% chance it happens after 1,000 throws.