.. A 'bigger' board, with More 'pieces, is Not the only option, for increased complexity.
.. There's also, {at least, hypothetically}, instituting, the 'Shogi'/ Japanese chess, rule, of the 'parachute' drop; Where, on any given turn, after, a 'captured' piece{s}, is available ; That same value, 'piece', {though, of a similar 'color', to the player, making the move} ; Can be made, on the board ; On any 'empty' square.
Aside, from that ; I also like, "Seirawan-chess", {or 'S-chess'}.. as seen, on "YouTube", {several videos}.. that, you may be, familiar with.
Of course ; There already exists, the concept of, 'asymetrical' games ; In which, I like, the time-control, 'handicap' method, {including, 'Armegeddon' games}, with a 'draw' going to 'black's 'win' advantage ; More so, than any, 'piece' handicap ; Which seems deficient, to my Own 'tastes'.
This is more a philosophical than pragmatic topic; apologies if this isn't the right forum....
It seems plausible, if not likely, that we're approaching a horizon in chess AI: a point where the game is simply too "shallow" to differentiate between two AIs of sufficient skill levels. For instance, in the year 2025, the top chess engine (something like AlphaZero self-trained for 5 straight years) competes against a severely handicapped version of itself: it plays as white with 100x the computing resources, and gets 1 hour per move vs 1 minute per move... and yet, after 100 games, finishes with a 0-0-100 (no wins, no losses, 100 draws). This would not *prove* that chess is a drawn game (perhaps there is a mate-in-10,000 series of moves yet to be discovered), but it would certainly make a good case that conventional chess was no longer a meaningful discriminator of chess-playing skill levels.
My question is: is there a variation of chess, using a finite-sized board and conventional chess movement rules, that would be "effectively infinitely deep" in complexity. Where no matter how good a given engine was, any significantly-improved engine would be able to defeat it. A keyword here is "effectively" - by this, I mean, "infinitely deep with respect to the finite amount of time+matter+energy of the known universe". I'd say the variant was "effectively infinitely deep" if the following hypothetical held:
If the best self-teaching AI were self-trained for 10 billion years using 100% of the matter+energy of the universe, and then held a 100 game tournament wherein the AI played white with the computational resources of 90% of the matter+energy in the universe vs black with 10%... white would win the tournament decisively.
The natural response here is to say, "use a bigger board with more pieces". However, the complexity of the game grows exponentially with the addition of more and more pieces. So my real question is, "how big a board; how many pieces would be needed before the complexity of the game approached what I described above as 'effectively infinitely deep'?" Would two chess boards, side by side, with one king replaced by a queen (so each side has double the pieces, but 3 queens and 1 king), be such a variant? Would that be overkill?
If a simplest-such variant could be agreed upon, would it not make sense to switch TCEC-style tournaments to use this variant in the near future?