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
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.
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 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.
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.
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.
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."
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.
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.)
https://gatherer.wizards.com/pages/card/Discussion.aspx?mult...
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.