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In this paper, we uncover the Bloom paradox: sometimes, it is better to disregard the Bloom filter results, and in fact not to even query it, thus making the Bloom filter useless. We first analyze conditions under which the Bloom paradox occurs, and show that it depends on the a priori probability that a given element belongs to the represented set. We also show that the Bloom paradox applies to Counting Bloom Filters (CBFs), and depends on the product of the hashed counters of each element. Indoi:10.1109/infcom.2012.6195533 dblp:conf/infocom/RottenstreichK12 fatcat:enstjrux6radnfarapnfbebdna