Let πn be a uniformly chosen random permutation on [n]. Using an analysis of the probability that two overlapping consecutive k-permutations are order isomorphic, we show that the expected number of distinct consecutive patterns of all lengths k ∈ {1, 2,…, n} in πn is
{{{n^2}} \over 2}\left( {1 - o\left( 1 \right)} \right)
as n → ∞. This exhibits the fact that random permutations pack consecutive patterns near-perfectly.