@inkfathombiomage That’s like asking, why doesn’t an integer that is theoretically even and odd count? No such thing can exist.

The current MODO will either output an incorrect value on some inputs, or infinite loop on some inputs. Any theoretical modified version of MODO will have the same property.

That’s true, I was thinking more if they fixed the bugs in MODO. It would still enter into an infinite loop if someone played animate dead with worldgorger as the only creature in their graveyard, but only because the gamestate entered a loop. Is this the only place it would run into problems? Was that even addressed by the article?

last edited by InkfathomBiomage

I think MTGO is protected from infinite loops by the fact that it keeps prompting players when they get priority, and there is a game clock. If you turned off the priority checks and game clock then absolutely you could soft-lock the game within the Rules of Magic alone. I mean, legitimately, not just because MTGO is poorly programmed.

This is, incidentally, why the shortcut rules don't work and certain decks with infinite combos are more difficult or impossible to run on MTGO.

To be clear, just because the game enters an infinite-loop within the rules of Magic doesn't mean that a software program implementing those rules must also enter an infinite-loop. A program like MTGO can, in principle, perform logical deduction on the game state to determine that the game rules yield an infinite-loop, and then output the correct game result (the rules of Magic specify that infinite-loops result in draws). The paper shows that a program like MTGO cannot do this deduction perfectly. Any such attempt will be "buggy" - not due to incompetence of the programmers, but due to the laws of mathematics. But it is certainly plausible that, if well programmed, such a program can do it well-enough to cover all "real-world" situations.

This is the same reason a computer compiler can't tell you if your program is going to fall into an infinite loop perfectly.

I feel obliged to point out that there have been significant attempts at creating MtG Turing machines before: https://www.toothycat.net/~hologram/Turing/

The main difference in this preprint is that the Turing machine runs fully automatically, and continued operation does not depend on any player choices including agreeing to play all "may" abilities.

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