The \textsc{equality} problem is usually one's first encounter withcommunication complexity and is one of the most fundamental problems inthe field. Although its deterministic and randomized communicationcomplexity were settled decades ago, we find several new things to sayabout the problem by focusing on two subtle aspects. The first is toconsider the {\em expected} communication cost (at a worst-case input)for a protocol that uses limited interaction---i.e., a bounded number ofrounds of communication---and whose error probability is zero or closeto it. The second is to consider the {\em information cost} of suchprotocols. We obtain asymptotically optimal rounds-versus-cost tradeoffsfor \textsc{equality}: both expected communication cost and informationcost scale as (logloglogn), with r−1 logs, where ris the number of rounds. For the case of zero-error communication cost,we obtain essentially matching bounds, up to a tiny additive constant.