In this paper, we construct a winning condition $W$ over a finite set of colors such that, first, every finite arena has a strategy with 2 states of general memory which is optimal w.r.t.~$W$, and second, there exists no $k$ such that every finite arena has a strategy with $k$ states of chromatic memory which is optimal w.r.t.~$W$.

翻译：本文构造了一个在有限颜色集上的获胜条件$W$，使得：首先，每个有限竞技场都存在一个具有2个状态的一般记忆策略，该策略关于$W$是最优的；其次，不存在任何$k$使得每个有限竞技场都存在一个具有$k$个状态的染色记忆策略，该策略关于$W$是最优的。