  \emph{Cardinality Estimation} (aka \emph{Distinct Elements}) is a classic
problem in sketching with many industrial applications. Although sketching
\emph{algorithms} are fairly simple, analyzing the cardinality
\emph{estimators} is notoriously difficult, and even today the state-of-the-art
sketches such as HyperLogLog and (compressed) \PCSA{} are not covered in
graduate level Big Data courses.
  In this paper we define a class of \emph{generalized remaining area} (\tGRA)
estimators, and observe that HyperLogLog, LogLog, and some estimators for PCSA
are merely instantiations of \tGRA{} for various integral values of $\tau$. We
then analyze the limiting relative variance of \tGRA{} estimators. It turns out
that the standard estimators for HyperLogLog and PCSA can be improved by
choosing a \emph{fractional} value of $\tau$. The resulting estimators come
\emph{very} close to the Cram\'{e}r-Rao lower bounds for HyperLogLog{} and PCSA
derived from their Fisher information. Although the Cram\'{e}r-Rao lower bound
\emph{can} be achieved with the Maximum Likelihood Estimator (MLE), the MLE is
cumbersome to compute and dynamically update. In contrast, \tGRA{} estimators
are trivial to update in constant time.
  Our presentation assumes only basic calculus and probability, not any complex
analysis~\cite{FlajoletM85,DurandF03,FlajoletFGM07}.
