  We present a novel reshuffling exchange model and investigate its long time
behavior. In this model, two individuals are picked randomly, and their wealth
$X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading
to a binomial distribution denoted $B \circ (X_i+X_j)$. This dynamics can be
considered as a natural variant of the so-called uniform reshuffling model in
econophysics [2,14]. As the number of individuals goes to infinity, we derive
its mean-field limit, which links the stochastic dynamics to a deterministic
infinite system of ordinary differential equations. The main result of this
work is then to prove (using a coupling argument) that the distribution of
wealth converges to the Poisson distribution in the $2$-Wasserstein metric.
Numerical simulations illustrate the main result and suggest that the
polynomial convergence decay might be further improved.
