We study the relation between the discrete--time version of the flashing ratchet known as Parrondo\'s games and a compression technique used very recently with thermal ratchets for evaluating the transfer of information -- negentropy -- between the Brownian particle and the source of fluctuations. We present some results concerning different versions of Parrondo\'s games showing, for each case, a good qualitative agreement between the gain and the inverse of the entropy.