  In this work we improve on a result from~\cite{GryKosZma15}. In particular,
we investigate the situation where a word is constructed jointly by two players
who alternately append letters to the end of an existing word. One of the
players (Ann) tries to avoid (non-trivial) repetitions, while the other one
(Ben) tries to enforce them. We show a construction that is closer to the lower
bound showed in~\cite{GryKozMic13} using entropy compression, and building on
the probabilistic arguments based on a version of the Lov\'asz Local Lemma
from~\cite{Peg11}. We provide an explicit strategy for Ann to avoid
(non-trivial) repetitions over a $7$-letter alphabet.
