I was just about to write a comment about the merits of 4-beting vs. shoving. I was thinking this:

Scenario 1: folded to me in the cutoff with AK. I make it 4xBB, villain makes it 12xBB, blinds fold. I make it 48xBB. Now villain can shove, I'm pot committed against QQ+/AK, so I call, or villain can fold, or villain can call (I.e his range is very well defined as QQ/AK. If I have a read he could also have JJ, maybe AQ).

Scenario 2: Same as 1, except instead of making it 48xBB I just shove. Villain can call, or villain can fold.

Does scenario 1 give me less fold equity than 2? Yeah, about 2% less I think. Does villain get his money in with a bluff in scenario 2? No, never. This basically means 4-betting is way better than shoving, right? But what if he just calls my 4 bet, I auto-shove just about any flop I miss, and maybe check (with the intention of shoving the turn) when I hit to let him bluff-shove me with the underpair? If the flop is KQ2r, I'm in a WA/WB/chopping spot, so check/call shove this, with the intention of shoving a blank turn so that he might just call me with JJ?

Any holes in my thinking here? What about the 4-bet amount?