A UUID v4 is a 128 bit number, but 4 bits are reserved to specify the version number and 2 more bits are reserved to specify the variant, which leaves 122 bits of randomness. That means it can take on 5 x 10^36 possible values. Following the birthday math, you'd have to generate about 103 trillion UUIDs to have a one-in-a-million chance of having a collision.