Definition
An anonymity set is the count of indistinguishable possibilities among which your activity is hidden. In a Bitcoin CoinJoin, if you mix with 50 other participants who all receive the same output denomination, your coin's anonymity set is roughly the number of equal outputs in that transaction, because an observer cannot tell which of those outputs is yours. The larger the set, the more people you are hiding among, and the weaker any deanonymization claim becomes.
How the set grows and shrinks
A single mixing transaction caps the anonymity set at the number of participants. Cascading coins through multiple rounds multiplies the set: three rounds among 32-participant transactions can theoretically blend you among over a thousand histories. The set shrinks when you damage privacy after the fact, most commonly by consolidating mixed coins with change or with other identified UTXOs, which lets an analyst correlate them back together.
Why it is a probabilistic, not absolute, measure
Anonymity set is a useful heuristic but not a guarantee. Timing analysis, amount correlation, address reuse, and post-mix consolidation can all carve down the effective set below its nominal size. Treat the headline number as an upper bound and protect it with disciplined coin control. For sovereign Bitcoiners, a healthy anonymity set is what restores fungibility, ensuring one coin is treated the same as any other.
Related: equal-output CoinJoin and post-mix spending.
In Simple Terms
An anonymity set is the count of indistinguishable possibilities among which your activity is hidden. In a Bitcoin CoinJoin, if you mix with 50 other…