Clever. My first impression was that surely this saturates the filter too fast as we're setting more bits at once but looks like the maths checks out. It's one of those non-intuitive things that I am glad I learned today.

It works because the original filter has suboptimal settings. An optimal filter of that size and number of items would set 5 bits per item and have about a quarter of the false positive rate. The 2 bits per item in the blocked filter is still suboptimal, but it's also saving them from saturating a bunch of 32-bit blocks, at the cost of a much higher overall false positive rate.

True, I had the same feeling. The article does go off 256K elements in a bloom filter of 2M. After 1M elements, using 2 bits actually increases false positive rate, but at that point the false positive rate is higher than 50% already.