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In this paper, we construct a winning condition $W$ over a finite set ofcolors such that, first, every finite arena has a strategy with 2 states ofgeneral 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 memorywhich is optimal w.r.t.~$W$.

Infinite Separation between General and Chromatic Memory