  In this paper the extended model of Minority game (MG), incorporating
variable number of agents and therefore called Grand Canonical, is used for
prediction. We proved that the best MG-based predictor is constituted by a
tremendously degenerated system, when only one agent is involved. The
prediction is the most efficient if the agent is equipped with all strategies
from the Full Strategy Space. Each of these filters is evaluated and, in each
step, the best one is chosen. Despite the casual simplicity of the method its
usefulness is invaluable in many cases including real problems. The significant
power of the method lies in its ability to fast adaptation if \lambda-GCMG
modification is used. The success rate of prediction is sensitive to the
properly set memory length. We considered the feasibility of prediction for the
Minority and Majority games. These two games are driven by different dynamics
when self-generated time series are considered. Both dynamics tend to be the
same when a feedback effect is removed and an exogenous signal is applied.
