Is there any practical strategy that approaches this complexity at all? I have never played. But I assume this claim is just that you can technically create some stateful stuff if you’re explicitly not trying to win
Turing machines? Not really. Infinite loops[0]? All the time. The designers generally try to avoid those being legal in "Standard" unless it's extremely unlikely to happen (only the most recent few years of cards are legal in tournament play. In casual play anything can be legal if your group is okay with it).
A common trope is to have a card that allows you to create mana, and then a way to infinitely bring that card back from the discard pile, allowing for infinite mana. Then you play a card that says something like "spend X mana to deal X damage" and you deal a trillion damage.
[0] the above commenter is correct that a true infinite loop is not allowed. But you're allowed to create a scenario where an infinite loop happens according to a repeating choice you can make (essentially a while loop) and repeat as much as you want within the match timer while still allowing time for your damage card. The general etiquette is just to say "I can do this a billion times and so I deal a billion damage".
I've actually been at a local (mostly informal) tournament where someone with an Elf deck managed to pump their life into the thousands (you start with 20 or 40 depending on the ruleset), and his opponent with a Goblin deck got an infinite combo for infinite damage. But the Elf player refused to accept "I can do this infinity times" and made him actually try to perform his card combo over a thousand times before the round timer ran out. Goblin deck did not win.
> I've actually been at a local (mostly informal) tournament where someone with an Elf deck managed to pump their life into the thousands (you start with 20 or 40 depending on the ruleset), and his opponent with a Goblin deck got an infinite combo for infinite damage. But the Elf player refused to accept "I can do this infinity times" and made him actually try to perform his card combo over a thousand times before the round timer ran out. Goblin deck did not win.
So the Goblin-deck owner allowed the Elf-deck owner to do a "I give myself 1000 life" with a combo but the Elf-deck owner wouldn't let the Goblin-deck owner do the same with damage? That's kind of a jerk move if so.
If the Elf can give themselves infinite life in response to the infinite damage, then they have essentially won, because however much damage the Goblin would deal, they can just go "OK, but before that damage applies I give myself enough life to survive". The Goblin deck can never reach a game state where they win.
If the combos are sequential and the Elf has to commit to a certain number of life before the Goblin commits to a certain number of damage, then the Goblin would win.
There are some other possible intricacies (can they give themselves 1 life infinite times? or infinite life once?) From the mechanics of how the game usually goes, I would assume the first case applies here.
The way match/tournament rules work, when you have an infinite loop you can pick any number of iterations, but it has to be a number, not "infinity". Which means that the interaction of two infinite combos comes down to which one occurs with priority over which other.
If the elf deck can gain "infinite life" at instant speed, then they'd win over a goblin deck that can deal infinite damage at sorcery speed, because whatever number the goblin player picks, the elf deck can pick that number squared, for instance.
If both players can combo at instant speed then it's an impasse and they have to jockey for who can put their opponent in a position where they're tapped out, etc.
> If the combos are sequential and the Elf has to commit to a certain number of life before the Goblin commits to a certain number of damage, then the Goblin would win.
I agree that in formal tournaments this would happen, but the comment I was responding to was about a "casual tournament." I was assuming the 1000 life was with a sorcery (e.g. infinite mana combo + stream of life). In casual play, shortcuts are only when both sides agree, so it would be a jerk move to not agree to one that benefits your opponent after your opponent has agreed to one that benefited you.
An interesting result of how MtG handles infinite loops plus how it handles priority is that in a scenario where two players attempt to go infinite whoever gets to name their number last wins. And that most infinite loops are non-reloadable, in that when you stop repeating them, you can't restart them for free. I have seen a game that was lost because one player had an infinite life combo, named "a hundred trillion" and wrote their life total down on a piece of paper, and later in the game an opponent who had apparently mis-heard "a hundred billion" and didn't think to check only elected to repeat their infinite combo a trillion times.
So the moral of this story is, uh, always name Graham's number. Or don't because I'm not sure what a Judge is to do if two people name numbers so large that the Judge can't work out which one is bigger on a pocket calculator.
(I think that in a Comp REL game, in your scenario, the Goblin player should have won unless the combo was non-deterministic.)
I'm not terribly familiar with tournament rules, but AFAIK in paper games you can always shortcut truly infinite actions by picking a number and the opponent has to accept it, it is not just etiquette.
This is only true if the series of actions you take in the combo are fully deterministic. If the combo includes non-deterministic steps (usually anything related to deck shuffling) you can't use shortcuts and have to actually perform the steps.
It's a bit of a can of worms (but you're right, I should have said "deck/discard pile manipulation").
Shortcuts are supposed to be used to speed up and smooth play, there should be no information exchange, and so as another person pointed out this is about being able to describe all intermediate game states. If shuffling means you will reveal (seemingly) irrelevant but arbitrary information about your deck (e.g. cards that are no longer in it because they were discarded), you can't describe the intermediate game state beforehand (it is random) and the other player can't make an informed decision about whether or not they'd interrupt. And if you could infer from their refusal that there is a situation they might interrupt, you'd have extracted information you shouldn't have had access to. Hence in tournaments it is not allowed.
The deck shuffling is relevant due to other factors. There is a card in the combo deck that reshuffles the discard pile into the deck when it's put to discard, and the deck revolves around (as a shortcutted, freely undertaken combo) dealing one damage every time a certain creature goes to the discard pile. As you re-shuffle every time the 'engine' piece is hit, you can't predict how many times you need to activate the discard combo, so it cannot be shortcutted. Shortcutting in magic requires stating exactly as many iterations as will occur and the clear end state.
Slow play is the phrase explaining why indeterminate combos don't get shortcutted. "An indeterminate-loop combo may take anywhere from fifteen minutes to fifteen hundred years to actually succeed, and we really do not need to be waiting around to see which it's going to be."
It's not that easy. There are strategies but they depend on the game format (standard, legacy, modern, etc) and on a deep understanding of the game meta. You cannot devise a strategy that works under any conditions. Lookup the rules + understand that new abilities and cards are introduced all the time.
I'm not sure what level of complexity you're looking for, but there are some pretty complex combos that have been viable over the years, even in formats that don't use some of the older "broken" cards. One popular strategy for a while in the "Modern" format, which doesn't allow cards for the first 10 years or so of the game, used a mechanic called "Storm" where a spell would be copied for every spell you previously cast in the same turn. A card called Grapeshot had this ability and did 1 damage, so the deck played creatures that made your spells cost less mana and spells that gave you extra mana or draw cards, and the goal was to cast 19 spells and then grapeshot your opponent for their entire starting life total of 20, often as early as on their fourth turn. It was consistent enough that it was a staple in the format for at least a few years (although I haven't kept up with the meta as much for a few years now). Another higher variance but potentially even faster combo used a creature called Griselbrand, which let you pay 7 life to draw 7 cards, a bunch of mana "rituals" like storm, and used a card called Nourishing Shoal to let you exile certain cards from your hand to gain life. The win condition was typically to draw at least 7 lands and cast a creature that let you discard a land to do 3 damage, and it could potentially do this on the very first turn, although eventually one of the cards that was necessary for it to function got banned in modern, although by then Griselbrand decks weren't really ever played due to there being far more consistent options with better ability to deal with an opponent trying to thwart their game plan. If you include Legacy (which allows cards from any point in the history of the game but still with a custom ban list) or Vintage (where all cards are allowed but some are "restricted" to only one copy instead of the typical 4 per deck), there are even more powerful combos you can take advantage of.
Combo decks have always and likely will always be a part of the meta for most formats, although to varying degrees depending on how many cards the format has available and how effective it happens to be in the current meta. It's considered one of the three main deck archetypes along with "control" decks that attempt to shut down what the opponent is trying to do and slowly build an advantage over time and "aggro" which use a more straightforward approach of just attacking the opponent with creatures or spells (or both). Not everything cleanly fits into one of those strategies of course, and even a deck that has a win condition that fits into one archetype might dip into the other as a backup plan (e.g. a combo deck with control elements that help it buy time if it can't get off the combo as quickly as it would prefer, or a control deck with some efficient creatures that it can use for a surprise attack if the circumstance makes sense), but even in a setting like playing a few games at a card shop on a Friday night, seeing a combo deck with the level of complexity described above isn't really uncommon at all.
That said, I've read that a lot of the hardest cards to program tend to be the ones that subvert the basic expectations of the game. One infamous example that comes to mind is a creature that after being cast added an extra turn after yours where you controlled your opponent, after which they took their regular turn and the turn order resumed its previous alternation. Programming that would require adding in the ability to show one player's hidden game state to the other, let them make any sort of decisions using their cards that the player would normally do (short of literally conceding the game) and inserting an extra turn in the order with that weird control mechanism...all just for one card out of tens of thousands! Obviously most cards are not that complex, and Arena specifically doesn't attempt to support literally every card in existence and instead supports cards going back to its initial stable release along with explicitly chosen cards added to special Arena-only sets in order to introduce them, but when its an explicit rule that the text on the card overrides the normal rules of the game when they disagree, it very quickly gets to the point where you need to consider that there will likely be an edge cast for almost any possible state transition.
