@dshin What your are describing is the definition of "undecidable" and I agree with it. I also agree that the article prove that Magic is undecidable.
My points are:
- If a game always have a finite number of possible move then it is decidable
- Magic with Swamp, Rat, unlimited deck size and randomness only produce finite possible moves during a full match
Consequence: Magic with Swamp, Rat, unlimited deck size and randomness is decidable.
So my claim is:
Undecidablility of Magic is not already contained in unlimited deck size and randomness.
We need more than only unlimited deck size and randomness to prove undecidablility and it is done in the article.
@protoaddict MTGO is limited by the memory of player's computers and/or the memory of the MTGO servers.
The claim of the article has nothing to do with the randomness or size of decks.
Take two decks with any number of Swamp and Relentless Rats. You can construct a list of all the possible moves for both players for all the possible starting hands and top-decks. This is a very big (exponential in the size of the deck) but finite and computable list.
The article prove that for any method you could to compute such list there is a stat of the game (using this deck) where the method take an infinite amount of time to finish. The game is called undecidable.
In practice no human player can distinguish between exponential complexity and undecidable complexity. The purpose of the article is only to prove something in game theory.
Narset, Parter of Veils
Each opponent can't draw more than one card each turn.
-2: Look at the top four cards of your library. You may reveal a noncreature, nonland card from among them and put it into your hand. Put the rest on the bottom of your library in a random order.
Look like a really good planewalker for blue mirror matchup.