It doesn't appear to be heavily dependent on the distribution. It mostly depends on how large your buffer is compared to the number of unique items in the list

It doesn't appear to be heavily dependent on the distribution. It mostly depends on how large your buffer is compared to the number of unique items in the list. If the buffer is the same size or larger, it would be exact. If it's half the size needed to hold all the unique items, you drop O(1 bit) of precision; at one quarter, O(2 bits), etc.