Hash-table lookup is described as O(1), yet the worst case is O(n). Why is the constant-time figure still the honest way to describe it?

A. Because O(1) is the expected cost under a hash that spreads keys evenly.

The O(1) is an expected cost: with a decent hash and a bounded load factor each bucket holds a small constant number of entries. The worst case is improbable by accident and reachable on purpose, an attacker who knows the hash function can construct colliding keys and turn every lookup linear. The defence is per-process randomised hashing, which most runtimes now do.