I don't know if you got wind of this, but Chess.com is developing what is supposed to be the first-ever variant of chess that can be played with four players simultaneously, which they call four-player chess. The variant was announced on September 1st 2017 on chess.com here. I first heard of this through IM Danny Rensch with Chess Today, who spends most of his video trying it out for the first time: https://youtu.be/f-cVupxkQpo
The board looks like this:
And prior to entering the game, you are shown this notice, which includes the gist of the rules:
I played only one game, and somehow I finished 1st out of the four players. I technically lost on time while there was one player left in the game, but the penalty for this is 20 points being awarded to my opponent, and because I had more points than my opponent even after they got their 20 points, I won the game. From one of the rules above, it sounds like I could have flat-out resigned and still win the game!
Personally, I did not enjoy the game that much. The board is huge, such that your opponents' long-range pieces (like the bishops) take a while to get used to because (1) they can come from much farther away than we're used to, and (2) they can come from 3 different players! You also don't have a choice of time controls--everyone starts with 4 minutes (with some minor increment), which I find pretty fast when you're not used to this variant.
If you want to try it out, four-player chess is accessible here: https://www.chess.com/4-player-chess
Importantly, the variant is still in beta phase, so my guess is it's bound to change in the upcoming weeks. Among other things, Danny Rensch mentions in his video that there is currently no notation system for this variant, such that developing theory is difficult.
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