We introduce Parrondo's paradox that involves games of chance. We
consider two fair gambling games, A and B, both of which can be made to have a
losing expectation by changing a biasing parameter $\epsilon$. When the two
games are played in any alternating order, a winning expectation is produced,
even though A and B are now losing games when played individually. This
strikingly counterintuitive result is a consequence of
discretetime Markov chains and we develop a heuristic explanation of
the phenomenon in terms of a Brownian ratchet model. As well as having possible
applications in electronic signal processing, we suggest important applications
in a wide range of physical processes, biological models, genetic models and
sociological models. Its impact on stock market models is also an interesting
open question.