Actually I was playing "Chess on an infinite plane" for a while and even held the title (and might still do) of World Champion, seeing as we were the only people in the world playing that variant that we were aware of!

That's obviously infinitely complex in terms of theoretical potential.

But I want the biggest finite thing in the universe. Some variants of chess on finite boards will exceed Go, but chat GDP isn't giving numbers because there are too many variants. Just adding a new piece adds many orders of magnitude of complexity.