We study the problem of maximizing a stochastic monotone submodular function
with respect to a matroid constraint. We study the adaptivity gap - the ratio
between the values of optimal adaptive and non-adaptive policies - and show
that it is equal to e/(e-1). This result implies that the benefit of adaptivity
is bounded. We also study the myopic policy and show that it is a
1/2-approximation. Furthermore, when the matroid is uniform, approximation
ratio of the myopic policy becomes 1-1/e which is optimum.