My theory on openings

In poker the two playstyles are called exploitative play and game theory optimal play. I’ve never heard anyone use that terminology in chess but certainly it’s two different things just trying to find the best move vs finding the move to win, where you factor in things like your opponent and the remaining time.

I honestly say its a spectrum. I have come up with a custom categorization system for openings, with multiple aspects rated 1-5, not just 2 types.

What you would call innovative, I would call sneaky, like the grob, or a sideline. Math is OPPOSITE of results at the amateur level where objectively unsound gambits tend to perform stronger than boring wishy washy GM lines.
Everybody's thought processes are different either way. Tactical and positional players tend to hate or look down on their opposites.
I don't know if I'd like to colour my meaning of the words mathematical and innovative like that, but the categories make some sense.
It's a bit more like a spectrum from sound yet difficult to less sound but with fun chances if the opponent isn't careful. It also changes as you go up in rating, the king's gambit being a notorious example, where it's great at lower levels but more and more busted (but still dangerous in certain lines) as you get up in the elite levels.

I think placing anything into only two categories is often the sign of a poorly designed framework. That said, there are the best moves and then every other option that ranges from just below optimal to incredibly bad. Every position changes and must be evaluated constantly as the game goes on, time is an underestimated factor, but at the end of the day, your opponents are human (at least mostly human) and are capable of error and so are you. What could be the worst move could play out as winning and what could be the best move a computer would make could be useless if you don't understand the principles behind it. Practicality and utility vs accuracy are important considerations. If you can't find a forced mate in 12 but you can simplify to a winning endgame you know but it will take an extra 3 moves, which one is better for you to play? If my opponent is up 17 points, I just usually sac everything, push all my pawns and hope for the best. Are those the best moves I'm making against a computer? No. But against a human, stalemate or losing on time are always possibilities for them. So in a sense, those are the best moves depending on the situation. Everything is relative.

What you would call innovative, I would call sneaky, like the grob, or a sideline. Math is OPPOSITE of results at the amateur level where objectively unsound gambits tend to perform stronger than boring wishy washy GM lines.
Everybody's thought processes are different either way. Tactical and positional players tend to hate or look down on their opposites.
So you consider what I played over the board last night "Sneaky"? I think it's simply a style. Players like Michael Basman played this way. This game was actually full of tactics and insanity:

Hi!
I seem to agree in some way with what you said. I developed an opening repertoire as white that includes the classical 1.d4 as well as the hypermodern -and somewhat offbeat - 1.b3. But 1.b3 is still recognized as a playable opening (if interested check ou my post on my experience with it: https://www.chess.com/blog/maafernan/opening-repertoire-the-nimzowitsch-larsen-attack)
I wouldn´t go further than that, for instance, I wouldn´t play the weird ones 1. g4, 1.a3, 1.Nh3 and the like just to fool my opponent.
Good luck!

indeed. A totally treat ta see one of TF's recent games! Nice. An even RARER treat ta see B-Boy writing less than a Novel in a freakin forum 😃

A strong player applies "math" even when encountering "wild" openings and, more often than not, refutes them.