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.
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.