  In the framework of the game-theoretic probability of Shafer and Vovk (2001)
it is of basic importance to construct an explicit strategy weakly forcing the
strong law of large numbers (SLLN) in the bounded forecasting game. We present
a simple finite-memory strategy based on the past average of Reality's moves,
which weakly forces the strong law of large numbers with the convergence rate
of $O(\sqrt{\log n/n})$. Our proof is very simple compared to a corresponding
measure-theoretic result of Azuma (1967) on bounded martingale differences and
this illustrates effectiveness of game-theoretic approach. We also discuss
one-sided protocols and extension of results to linear protocols in general
dimension.
