  Both single-player Parrondo games (SPPG) and multi-player Parrondo games
(MPPG) display the Parrondo Effect (PE) wherein two or more individually fair
(or Llosing) games yield a net winning outcome if alternated periodically or
randomly. (There is a more formal, less restrictive definition of the PE.) We
illustrate that, when subject to an elementary optimization rule, the PG
displays degraded rather than enhanced returns. Optimization provides only the
illusion of control, when low-entropy strategies (i.e. which use more
information) under-perform random strategies (with maximal entropy). This
illusion is unfortuntately widespread in many human attempts to manage or
predict complex systems. For the PG, the illusion is especially striking in
that the optimization rule reverses an already paradoxical-seeming positive
gain - the Parrondo effect proper - and turns it negative. While this
phenomenon has been previously demonstrated using somewhat artificial
conditions in the MPPG (L. Dinios and J.M.R. Parrondo. Europhysics Letters 63,
319 (2003); J.M.R. Parrondo et al. Advances in Condensed Matter and Statistical
Mechanics, eds. E. Korutcheva and R. Cuerno, Nova Science Publishers, 2003), we
demonstrate it in the natural setting of a history-dependent SPPG.
