  Consider a permutation $\sigma\in S_n$ as a deck of cards numbered from 1 to
$n$ and laid out in a row, where $\sigma_j$ denotes the number of the card that
is in the $j$-th position from the left.\rm\ We study some probabilistic and
combinatorial aspects of the shuffle on $S_n$ defined by removing and then
randomly reinserting each of the $n$ cards once, with the removal and
reinsertion being performed according to the original left to right order of
the cards. The novelty here in this nonstandard shuffle is that every card is
removed and reinserted exactly once. The bias that remains turns out to be
quite strong and possesses some surprising features.
