Hashes do reduce it, by an amount determined by the hash size and algorithm. This has nothing to do with client vs server. SHA1 of STRING will always have the

Hashes do reduce it, by an amount determined by the hash size and algorithm. This has nothing to do with client vs server. SHA1 of STRING will always have the same entropy wherever it is computed; it must, for the hashing to work. EDIT: I suspect you are confusing PRNGs or KDFs with hashing. Entropy is relevant with the former, not the latter.