  We consider pattern containment and avoidance with a very tight definition
that was used first by Riordan more than 60 years ago. Using this definition,
we prove the monotone pattern is easier to avoid than almost any other pattern
of the same length.
  We also show that with this definition, almost all patterns of length $k$ are
avoided by the same number of permutations of length $n$. The corresponding
statements are not known to be true for more relaxed definitions of pattern
containment. This is the first time we know of that expectations are used to
compare numbers of permutations avoiding certain patterns.
