How unique is UUID?

by

Very safe:

the annual risk of a given person being hit by a meteorite is
estimated to be one chance in 17 billion, which means the
probability is about 0.00000000006 (6 × 10−11), equivalent to the odds
of creating a few tens of trillions of UUIDs in a year and having one
duplicate. In other words, only after generating 1 billion UUIDs every
second for the next 100 years, the probability of creating just one
duplicate would be about 50%.

Caveat:

However, these probabilities only hold when the UUIDs are generated
using sufficient entropy. Otherwise, the probability of duplicates
could be significantly higher, since the statistical dispersion might
be lower. Where unique identifiers are required for distributed
applications, so that UUIDs do not clash even when data from many
devices is merged, the randomness of the seeds and generators used on
every device must be reliable for the life of the application. Where
this is not feasible, RFC4122 recommends using a namespace variant
instead.

Source: The Random UUID probability of duplicates section of the Wikipedia article on Universally unique identifiers (link leads to a revision from December 2016 before editing reworked the section).

Also see the current section on the same subject on the same Universally unique identifier article, Collisions.

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