  We derive some results on contrarian and one-sided strategies by Skeptic for
the fair-coin game in the framework of the game-theoretic probability of Shafer
and Vovk \cite{sv}. In particular, concerning the rate of convergence of the
strong law of large numbers (SLLN), we prove that Skeptic can force that the
convergence has to be slower than or equal to $O(n^{-1/2})$. This is achieved
by a very simple contrarian strategy of Skeptic. This type of result, bounding
the rate of convergence from below, contrasts with more standard results of
bounding the rate of SLLN from above by using momentum strategies. We also
derive a corresponding one-sided result.
