Magic: the Gathering is Turing Complete

We always knew Magic: the Gathering was a complex game. But now it's proven: you could assemble a computer out of Magic cards.

Magic Turing Machine v4: Teysa / Chancellor of the Spires

Overview - The Cards - How It Works - Difficulties - Future Directions - About

What does "Turing complete" mean?

There's an idea called "Turing completeness", which is used to indicate that a system has a particular degree of complexity. Any Turing-complete system is theoretically able to emulate any other. One way to show that a system is Turing complete is to make a "Turing machine" in it. (I'm grateful to Joe Fitzsimmons for the idea to approach the question this way.) This isn't the most common way of demonstrating Turing completeness, but it is one of the more understandable. In the discussion on this site I assemble a Universal Turing Machine from Magic: the Gathering cards.

But doesn't Magic involve the players making lots of choices?

Normally, yes, it does. But occasionally in normal gameplay you get a sequence of three or four events in a row that are forced to happen by the cards and the rules of the game. The machine below just extends this idea to millions of forced choices in a row.

The idea of my Magic Turing machine is that the players do nothing at all, except when the game offers them a choice.

Once the in-game "machine" has started, processing continues without requiring any choices from the players, with one category of exceptions: Some of the cards in the machine say "You may [do X]. If you do, [Y happens]." In these cases, the machine arranges that the players will be able to do X, in precisely one way. It just requires the players to always choose to take the game up on any options they're offered.

How does it work?

I'm glad you asked! On this website you can see the full list of all cards required in the machine, and an explanation of how it works in detail. You can also find out more about the person who created this monstrosity. Have fun!