Has a single HyperLogLog the same accuracy than merging several ones?

Question

If I create a HyperLogLog per day to count unique visitors, and then the 1st of January I merge the last 365 ones will I get the same value than if I keep a single HyperLogLog for the whole 365 days?

I guess not. But how different would those values be?

Answer 1

Short answer: Yes, both solutions have the same accuracy.

The basis of the HyperLogLog algorithm is the observation that the cardinality of a multiset of uniformly distributed random numbers can be estimated by calculating the maximum number of leading zeros in the binary representation of each number in the set . If the maximum number of leading zeros observed is n, an estimate for the number of distinct elements in the set is 2**n.

Referred from wiki

No matter it's a single hyperloglog or 365 hyperloglogs, the numbers of leading zeros are the same. So they have the same accuracy, and that's why hyperloglog can be merged.