The mathematics of Magic: the Gathering (1999)

I know this proof but I'm not happy with it. It goes out of its way to setup a Turing machine (though not a very obvious one) using M:tG cards- however, that doesn't prove that the M:tG _game_ is Turing-complete. It proves that the specific cards chosen can be used to create a Turing machine under a subset of the game's rules, which is not quite the same thing.

For a more complete proof one needs to take into account the fact that the text printed on existing cards is a derivation from some grammar - the grammar of the M:tG "ability text" (there is no official name for the game's language). In other words, the ability text on existing cards is no the whole ability text language. The complete language is a superset of the strings on existing cards. To prove the game as Turing complete, one needs to prove this language is Turing complete- not a subset of its strings.

To give an analogy, think of the game's rules as the JVM, the ability text grammar as the syntax of the Java language and the actually printed cards as some arbitrarily chosen set of Java programs. You can perhaps put together a Turing machine by stitching together those Java programs, but that will not tell you anything about the Turing completeness of the language itself. Instead, the straightforward proof is to use the Java syntax to write a Turing machine and run it on the JVM.

There is, of course a slight problem with taking this approach for M:tG; that the game's rules are very well defined (there's the Comprehensive Rules that go a long way towards resolving any ambiguity) but there is no full specification for the ability text language itself. So the M:tG machine is not well defined.

Then again, it's easy to derive at least a subset of the rules of ability text. For instance, if you see a card that says "Destroy target Elf creature", and you know that "Elf" is a "creature" type, you can substitute "Elf" for any creature type and generate any number of very probably correct ability text sentences- "Destroy target Goblin creature", "Destroy target Cat creature", "Destroy target Pirate creature" etc [1].

In this way it may be possible to generate the appropriate ability text expressions to construct a Turing machine- and prove that the M:tG game is Turing-complete.

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[1] Actually the ability to generate arbitrarily many well-formed expressions in a language is a hallmark of Turing-completeness. If we can't assume that the ability text on existing, printed cards is not the whole language, then Turing completeness becomes much harder to argue for.

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That's more an issue with the design of your deck than with the game, or the design issue is that one may not know how to build a deck to avoid such issues.

MTG isn't built for a consistent (late) game natural Mana curve and being able to do what you suggest would fundamentally change the game. For worse imo.

For example with no Mana acceralation/mananipulation the optimal number distribution to have to maximize Mana spent through turn 5 is 29 lands and only 3 five drops.

After which you will quickly have more Mana than you need.

Very few decks run 30 lands.

You can't design a deck that satisfies the condition of natural ly dropping a land each turn and spending the most Mana.

The more consistently you want to say, have 5 lands on turn 5, the more lands you need, which means less space for other cards in your deck.

Similarly the more you want to be able to spend that 5 Mana past turn 5 the more higher cost cards you need, which means fewer cards of other cost. Which means your more likely to be Mana flooded early since your deck won't have the space to consistently play smaller stuff. Try to and will come at the cost of making it more difficult to curve at higher N.

The optimal turn 5 deck curve has no 1 drops. You can't have it both ways.

As for your suggestion, it would only be better for beginners who don't know how to build around a curve, as the cards are not designed for such rules and would break the game in other ways.

For Hearthstone players who do like the mana problem there is shaman class with overload. Some warlock cards also destroy mana crystals, while druid plays around a lot with gaining these.

Hearthstone has too much RNG for my taste though, and I don't like the business model related to the RNG of packs.

Slay The Spire, which has a more fair business model IMO (even though the price is cheap at 16 EUR), allows you to have more strategy and play around the RNG via liberal deck building and a rogue-like game. It has a relatively stable mana/energy resource system which can be modified by game mechanics. But it is a PvE game with ladder system increasing difficulty.