Stack Sizes Hypothetical

ok, you have 56s on the button and open for 4x and are called by the BB. Flop comes down AK2r. Villain checks to us. Do we cbet if villain started with:

100 BBs (8 BB pot, 96 BB effective stacks)?
200 BBs (8 BB pot, 196 BB effective stacks)?
20 BBs (8 BB pot, 16 BB effective stacks)?

Assume villain is unknown.

Why or why not? Just sort of threw in the 200 for additional investigation but I have a specific point I'm trying to make with the first and last one.

I'd say the short stacked situation is the best to continuation bet. You're a lot less likely to get bluff raised (because you've already committed) or called by an inside straight draw. If you're deeper, you can more likely get a pair of kings or a pocket pair to fold, but it usually takes more than the one bullet.

I'm inclined to c-bet a lot in any case. The BB should have a large range in this spot, because you made a raise from prime stealing position, he was closing out the action heads up, and he got a discount in the BB. Against a wide range, that's a very uncoordinated flop.

The one downside is that it kind of looks like he's defending his blind. If that's true and he's anything but short stacked, he's going to bluff check-raise a lot of the time. So it depends on the player. If he's aggressive, I would rarely c-bet this unless he's short stacked.

Edit: If you might c-bet again on the turn versus a call, then I like c-betting the flop against a deep stack better.

I'd probably cbet them all. I think i might know where you are going here, in that our hand has 0 equity, so we are risking the same amount of money with our cbet to win the same amount of money in the pot, even tho typically one would just give up in the 3rd case because villain is so short and will stack off light (tho in some sense this is a good spot vs a ss, since villain will play fit or fold and this flop folds out alot of hands. The disadvantage being that our image takes a hit when we fold once villain shoves over the top of us.

That said, i would NEVER open 56s on the button with a 20bb stack in the bb. And a 20bb bb would be unlikely to flat any hand preflop anyways.

ok one step further, vs. ss what if they flat call, another blank on turn? What if they raise all-in? Same question for the other 2 but I think it's pretty obvious we fold to the other 2 if they raise, and C/F to the 100 BB stack, and maybe consider double or triple barreling the deep stack with big bets because he's not comfortable facing heat this deep with just TP (although C/F turn may be better against deep stack anyway with no reads). Basically yeah I'm referring to what adjustments we make against short stacks. Should we cbet normal? Just C/F flop against shortstack because we don't have the threat of a deeper stack for FE? What happens to our bet sizing when cbetting against this short stack?

Actually I made a mistake, although this could be a good discussion as well, it would probably be more interesting if we give ourselves 55 or so here. This way at least we beat bluffs. With 56 we can never fold to a shove because we're behing most bluffs, but with 55 we can consider calling just because we have a hand that beats bluffs.