The problem of document replacement in Web caches has received much attention in the literature research, and it has been shown that the eviction rule "replace the least recently used document" performs poorly in Web caches. Instead, it has been shown that using a combination of several criteria, such as the recentness and frequency of use, the size, and the cost of fetching a document, leads to a sizeable improvement in hit rate and latency reduction. However, in order to implement these novel schemes, one needs to maintain complicated data structures. We propose randomized algorithms for approximating any existing Web-cache replacement scheme and thereby avoid the need for any data structures. At document-replacement times, the randomized algorithm samples N documents from the cache and replaces the least useful document from the sample, where usefulness is determined according to the criteria mentioned above. The next M