AbstractFibonacci Solitaire is a combinatorial algorithm which associates with a permutation of [n]={1,…,n} a partition of [n] into couples and singletons. We study the output configuration when the algorithm is applied to a random permutation, with emphasis on the large n‐asymptotics. We show that the set of singletons, properly scaled, resembles a familiar ‘stick‐breaking’ Poisson configuration, whereas the configuration of couples becomes close to uniform. © 2002 John Wiley & Sons, Inc. Random Struct. Alg., 20, 71–88, 2002