A random number of things really "clicked" lately, and I'm really just seeking confirmation and discussion on these things. I'll try to put this the best I can, but a lot of it still seems fairly abstract to me in ways that are hard to describe, but here we go.

I posted a hand in the FR forum where I 3-bet a 37/10's raise from the SB with AQs (villain was three seats off of the button). The rest of the hand isn't so important, but in the discussion I noted that the wider our 3-betting range, the more value our big pairs [and AK] hold since people will pay them more money per hand on average.

A few weeks/months ago I remember reading an interview or some other post on ISF's blog (I think) where someone was talking about "blending" value-betting ranges and bluffs post-flop. The idea was like sometimes when you're value-betting you're not even sure if you're ahead of his range or not so you're not sure if you're really value-betting or bluffing. I sort of understood whatever example was given, but I didn't understand the concept. Then the AQs thread above happened and I woke up in the middle of the night two nights ago thinking about the following:

When we widen our range in any spot, our range is strengthened in terms of EV because the best hands we hold will yield more value as our opponents adjust. This applies to our big pairs gaining value when we 3-bet preflop more, and this applies to situations where we don't know if we're ahead or not but we bet when it's close anyway.

I'm pretty sure that this is an instance of second-level thinking. We do something based on what we think our opponent thinks we have. Since the only other general thing I really understood about second-level thinking had to do with ISF's theorem, I went back and read over that like six times and now I'm just like holy crap because it seemed so much clearer this time.

So consider any situation where our apparent range is ahead of our opponent's range. ISF's theorem tells us we should bluff and semibluff more often, but it seems very closely related to what's going on when we 3-bet a wider range than before or when we "blend" our value-betting and bluffing ranges. I'm just not exactly sure how yet.

I'm trying to transcend these individual applications and figure out what concept is at work, and I'm having a hard time. The Shania explains quite a bit of it in a more general sense, but I feel like there's something in between that I'm missing. Like if these applications are on one level, and like four levels up there is the Shania, I'm missing everything on the three levels between and like half of the three levels before.