Four Billion Positions

About $2^{21}$, roughly two million, from the birthday bound $\sqrt[3]{2^{64}}$. A 32-bit key collides after only about $2^{11}$, roughly two thousand.

About $2^{32}$, roughly four billion, from the birthday bound $\sqrt{2^{64}}$. A 32-bit key collides after only about $2^{16}$, roughly 65 thousand.

About $2^{64}$, roughly 18 quintillion, from the per-pair probability $2^{-64}$. A 32-bit key collides after only about $2^{32}$, roughly four billion.

About $2^{63}$, roughly nine quintillion, from the pigeonhole bound $2^{64}/2$. A 32-bit key collides after only about $2^{31}$, roughly two billion.