I really hate free-for-all Magic, but some of my favorite "gaming" experiences of all time have involved free-for-all formats.
Ownage
This pubescantly named game was a 5-player, real life arena combat game won by the last man standing. Basically, you have 5 people on this small park playground arena, each person holding a tennis ball and with 10 other tennis balls scattered about on the ground. One player (the previous round's winner) starts at the center of the structure, most vulnerable to attack. The other four start on the ground, in the sand, at the four corners of the arena.
To eliminate a player, you hit them with a tennis ball. Players may legally block using the part of their arms from their elbow to their fingertips. If you catch (with one hand) an opposing throw, that player is knocked out.
Players may not hold more than one tennis ball at a time.
As a "last man standing" format, the prevailing strategy could, in theory, be to hide and avoid conflict until the end of the round. We collectively played under the cringey mantra "play to own, not to win". Rounds were quick, usually about a minute. And exhausting. Nobody kept count of the number of times each player won.
Winning happened as a biproduct. What we remembered were the amazing plays. The evasive maneuvers, creative kills. Some of the plays still remain in my memory. Here we made it work by eschewing (as players) power-max for fun-max. The game might be really dumb it played "competitively".
Phantom
I don't remember many of Phantom's rules any more. It was a 3-player pool game (pool as in billiards) we invented that used 9 balls, and some semi-complex rules for player elimination. From what I remember, upon sinking a ball, you got to choose whether you played with balls 1-3, 4-6, or 7-9 as your own. You had to shoot at opposing balls in order, e.g. you couldn't shoot at ball 5 until ball 4 had been sunk. So at the beginning you are shooting at balls 1, 4, and 7. But you could sink balls off of deflection. e.g. shoot hitting the 4, which knocks the 9 into a pocket.
If you scratched each opponent got a ball back. There were other rules I can't recall.
The mechanics of the game made it very challenging to actually "team up" on anyone. And there was never any disincentive to play your best. Shooting well and winning were very naturally correlated. Here, the rules we put in place didn't violate the underlying mechanics of pool.
Munchkin
Some of my worst gaming experiences are from this game. Some of my best as well.
Munchkin, as designed, is a terrible game that incentivizes players to hold on to their interaction until somebody is about to win, and there being some dumb Russian Roullette thing where everybody gets to Level 9 and then somebody walks it in because everyone else ran out of interaction. It's also atrocious with any more than 4 players.
In college I had a good 4-player Munchkin group. We used a number of house rules and a custom-curated stack of piles that were chosen to provide fun gameplay. This was, in a way, my first "cube"-like experience.
And we were aggressive as hell. We got started early with complex, creative and competing deals. We had deals that were "legally binding", and others that were more open to interpretation. Munchkin "working" required a perfect crucible of player count, player attitude, house rules and a custom pile to provide fun. It was a very fragile system.
Every other time I've played Munchkin has been a waste of time. It's not an inherently good game. This is how I imagine EDH to be. I'm sure there are specific conditions under which free-for-all EDH can be fun and rewarding, but it takes a lot of engineering and is all to easy to get wrong.