  We present two collective games with new paradoxical features when they are
combined. Besides reproducing the so--called Parrondo effect, where a winning
game is obtained from the alternation of two fair games, a new effect appears,
i.e., there exists a current inversion when varying the mixing probability
between the games. We present a detailed study by means of a discrete--time
Markov chain analysis, obtaining analytical expressions for the stationary
probabilities for a finite number of players. We also provide some
qualitatively insight into this new current inversion effect.
