  This short note investigates convergence of adaptive MCMC algorithms, i.e.\
algorithms which modify the Markov chain update probabilities on the fly. We
focus on the Containment condition introduced in \cite{roberts2007coupling}. We
show that if the Containment condition is \emph{not} satisfied, then the
algorithm will perform very poorly. Specifically, with positive probability,
the adaptive algorithm will be asymptotically less efficient then \emph{any}
nonadaptive ergodic MCMC algorithm. We call such algorithms \texttt{AdapFail},
and conclude that they should not be used.
