EDIT2: In the limit, if the number of hash functions equals the number of bits, then we can see that inserting one element would set all bits in the case where we use separate tables, but only 50% of bits if they use one big shared table.
So the false positive rate is higher if they use separate tables.
Someone 3 hours ago [-]
Assuming independent hash functions, giving each hash function it’s own bit table is equivalent to having one bit table with a number of bits equal to that of the sum of the numbers of bits in each hash function.
It would be more effective in avoiding false positives, but require more (typically a lot more) space.
https://prog21.dadgum.com/29.html
EDIT: Although, https://chatgpt.com/share/6a67336b-8600-83ed-9671-fab769b485... - it is in fact ever so slightly less effective if you have a separate table for each hash function
EDIT2: In the limit, if the number of hash functions equals the number of bits, then we can see that inserting one element would set all bits in the case where we use separate tables, but only 50% of bits if they use one big shared table.
So the false positive rate is higher if they use separate tables.
It would be more effective in avoiding false positives, but require more (typically a lot more) space.