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A $$$3$$$-sided battle, I wonder what the optimal strategy for such a game would be
The optimal strategy is not playing.
It would be technically about the same as a regular chess battle but with three players, because each cell has up to four cells adjacent to it just like regular chess
Naming rules of the squares must be complicated.
also how does moving straight or knight moves work here?
For those wondering how this is played check a Uoutube channel called TripleS games