  We present a modification of the so-called Parrondo's paradox where one is
allowed to choose in each turn the game that a large number of individuals
play. It turns out that, by choosing the game which gives the highest average
earnings at each step, one ends up with systematic loses, whereas a periodic or
random sequence of choices yields a steadily increase of the capital. An
explanation of this behavior is given by noting that the short-range
maximization of the returns is "killing the goose that laid the golden eggs". A
continuous model displaying similar features is analyzed using dynamic
programming techniques from control theory.
