  Magic: the Gathering is a popular and famously complicated card game about
magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen
(2016) and Churchill, Biderman, and Herrick (2019) have investigated the
computational complexity of playing Magic optimally. In this paper we show that
the ``mate-in-$n$'' problem for Magic is $\Delta^0_n$-hard and that optimal
play in two-player Magic is non-arithmetic in general. These results apply to
how real Magic is played, can be achieved using standard-size tournament legal
decks, and do not rely on stochasticity or hidden information. Our paper builds
upon the construction that Churchill, Biderman, and Herrick (2019) used to show
that this problem was at least as hard as the halting problem.
