  Several authors have implied that the original inspiration for Parrondo's
games was a physical system called a ``flashing Brownian ratchet''. The
relationship seems to be intuitively clear but, surprisingly, has not yet been
established with rigor. In this paper, we apply standard finite-difference
methods of numerical analysis to the Fokker-Planck equation. We derive a set of
finite difference equations and show that they have the same form as Parrondo's
games. Parrondo's games, are in effect, a particular way of sampling a
Fokker-Planck equation. Physical Brownian ratchets have been constructed and
have worked. It is hoped that the finite element method presented here will be
useful in the simulation and design of flashing Brownian ratchets.
