  The CHSH no-signalling game studies Bell nonlocality by showcasing a gap
between the win rates of classical strategies, quantum-entangled strategies,
and no-signalling strategies. Similarly, the CHSH* single-system game explores
the advantage of irreversible processes by showcasing a gap between the win
rates of classical reversible strategies, quantum reversible strategies, and
irreversible strategies. The irreversible process of erasure rules supreme for
the CHSH* single-system game, but this ``erasure advantage'' does not
necessarily extend to every single-system game: We introduce the 32-Game, in
which reversibility is irrelevant and only the distinction between classical
and quantum operations matters. We showcase our new insight by modifying the
CHSH* game to make it erasure-immune, while conserving its quantum advantage.
We conclude by the reverse procedure: We tune the 32-Game to make it
erasure-vulnerable, and erase its quantum advantage in the process. The
take-home message is that, when the size of the single-system is too small for
Alice to encode her whole input, quantum advantage and erasure advantage can
happen independently.
