Cutthroat is a 3-player magic variant a friend taught to me that automatically extends to more-than-three variants, though it gets less fun if you have more than two opponents.
Basics
The basic rule is mostly simple: when you attack, you are attacking both opponents. They may "combo-block" however they want (technically declaring assignments in turn order if it comes down to it) and any damage that goes through is dealt to both of them. So, if I attack with three 1/1s, and my opponents each block one of them, then both players would take one damage.
That's it. Targetted effects can still go in any direction (Disintegrate doesn't hit them both). All players are considered each others' opponents for any other reason.
Details
Double-Damage?
Okay, so that's not all there is to it. Ophidian-effects (Ninja of the Deep Hours, etc) and lifelink should only trigger once.
Unresolved question: Do prevention-effects stop the damage for one player?
Who can attack?
If a creature cannot attack one of the two players (e.g. Teferi's Moat) then that creature cannot attack anyone.
Who can block?
If one defending player cannot block a creature (e.g. landwalk) the other defender's creatures are still allowed to block that creature.
I'm sure there are other issues that would need to be ironed out.
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