If there are N IDs to draw from and M videos on YouTube, then P(ID used) = M/N if the ID is drawn from a uniform distribution, and P(At least one of K IDs used)

If there are N IDs to draw from and M videos on YouTube, then P(ID used) = M/N if the ID is drawn from a uniform distribution, and P(At least one of K IDs used) = 1 - (1 - M/N)^K (not accounting for replacement). If M ≈ 1e9 and N ≈ 1e18, and you sample K = 1000 URLs, then it's about one in 1e-09 that you hit a used ID.