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Never heard of it till just now, though I had heard of (but not played or even watched) three player chess. There are a few games I can think of, and have played, that support a free for all 3+ player mode, like magic the gathering. While the history of 3SF is interesting - the Situ connection and also the wiki says an anarchist group was maybe the first known to play it - I don't see what the anarchist ideas would be exactly. Maybe that would come from playing it.

There's definitely a big diplomacy (to use a statist word ofc) component to many multiplayer board and card games that I've played, like in two player mode i tend to think in terms of pure advantage and annihilation, but in multi you have to think very differently, about survival and personalities and emotions, etc.