  This paper studies the equilibrium behavior in contests with stochastic
progress. Participants have access to a safe action that makes progress
deterministically, but they can also take risky moves that stochastically
influence their progress towards the goal and thus their relative position. In
the unique well-behaved Markov perfect equilibrium of this dynamic contest, the
follower drops out if the leader establishes a substantial lead, but resorts to
"Hail Marys" beforehand: no matter how low the return of the risky move is, the
follower undertakes in an attempt to catch up. Moreover, if the risky move has
a medium return (between high and low), the leader will also adopt it when the
follower is close to dropping out - an interesting preemptive motive. We also
examine the impact of such equilibrium behavior on the optimal prize
allocation.
