
Magic: The Gathering Is Turing Complete - Sniffnoy
https://arxiv.org/abs/1904.09828
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Sniffnoy
A note on this submission: This paper differs from previous "Magic is Turing-
complete" links you may have seen here in that this construction embeds a
universal Turing machine that runs _without_ requiring the players to make
particular choices.

Note that the previous "Magic is Turing-complete" links you may have seen here
were presumably pointing to the earlier constructions by Alex Churchill,
which, as mentioned, required the players to make particular choices. Well, in
this paper, Churchill (along with Biderman and Herrick) have finally gotten
rid of the holes in the construction; once the machine starts running, the
players have no more choices at all and cannot stop its operation.

So, now Magic is _actually_ proven to be Turing-complete, unlike Churchill's
earlier constructions, which just showed it to be, uh, sort-of Turing-
complete.

FWIW, the key innovation in this paper (compared to the earlier constructions)
is the use of Wild Evocation, together with Wheel of Sun and Moon, to force
Alice (player 1) to cast her cards in a specified sequence for the rest of the
game. (Well, one of two specified sequences, as Coalition Victory is sometimes
skipped due to Mesmeric Orb and Xathrid Necromancer, but that's details.)

