With your examples, you might want to define what you mean by "complex" and "deep."
Go, for example, really only has a few rules. (Place a stone, remove stones that are completely enclosed. Repeat until both sides agree the game is over.) This makes it with virtually no complexity, if defining complexity as knowledge of rules. Depth of play, though, is another matter.
Chess is much more complex. Each of the 6 pieces has its own unique movement, with pawns having unique movement between capturing and non-capturing moves (and even more with the en-passant ability), with some pieces moving in pairs (castling). This makes learning the rules much harder, and therefore more complex. Based on when computers were able to defeat humans (and how it was accomplished) chess is not as deep as go, though.
As far as games on this site, check out the "for core gamers" section in the game list (
https://en.boardgamearena.com/#!gamelist)
For general games, watch the flame wars on BoardGameGeek