The Tsetlin library is a well-studied Markov chain on the symmetric group
Snβ. It has stationary distribution Ο(Ο) the Luce model, a
nonuniform distribution on Snβ, which appears in psychology, horse race
betting, and tournament poker. Simple enumerative questions, such as ``what is
the distribution of the top k cards?'' or ``what is the distribution of the
bottom k cards?'' are long open. We settle these questions and draw attention
to a host of parallel questions on the extension to the chambers of a
hyperplane arrangement.Comment: 23 pages, 1 figur