I’m not aware of 10x10 chess ever being attempted, let alone codified. Here’s my suggestion: add another set of bishops (or knights, or one of each) in between rooks and king/queen. Castling works the same, king goes around rook.
Former world chess champion Capablanca suggested a 10x8 board with two additional pieces in the 1920s, but there have been many variants proposed earlier and later [0]. Grand Chess [1] is the most known 10x10 variant, also with 2 additional pieces and a different start position, castling not allowed. See wikipedia for links to programs implementing these rules.
Interesting. Note that both of those types involve introducing new pieces. I would argue that this changes the fundamental nature of the game in a way that increasing board size alone doesn’t. The reason is that I (as a human chess master) would need to retrain myself to learn the new piece movements.
What I really want is a 10x10 or even 8x10 board using the original set of pieces. This would be sufficient to prove that human chess masters can adapt in a way that machine-learning based algorithms cannot.
Wouldn't adding more of the existing pieces in the back row change the game a bit too? Which piece(s) would you suggest having more of to accomodate the extra fields?
It would change the game but not enough to reduce the performance gap between an expert and a novice. See my grandparent comment for a specific suggestion on which pieces to use.
Generalized NxN chess is a thing I've seen talked about in complexity theory. I'm not sure if anyone has actually made a proper set of rules for it though. It looks like they often just don't care about such trivialities as starting positions (and probably castling). E.g. http://www.ms.mff.cuni.cz/~truno7am/slozitostHer/chessExptim...
