  We introduce and realize demons that follow a customary gambling strategy to
stop a nonequilibrium process at stochastic times. We derive second-law-like
inequalities for the average work done in the presence of gambling, and
universal stopping-time fluctuation relations for classical and quantum
non-stationary stochastic processes. We test experimentally our results in a
single-electron box, where an electrostatic potential drives the dynamics of
individual electrons tunneling into a metallic island. We also discuss the role
of coherence in gambling demons measuring quantum jump trajectories.
