So interesting hand where I guess a lot of it is the maths behind it.
So my initial plan was to checkraise/shove on the flop thinking I'd have decent equity even against an Ace (I could be wrong?)
But then a pot sized bet and a call...so obviously I am behind. But
1) Can I call profitably?
2) Could I shove profitably even though I'm near certain of being called?
BTN is a 52/4 over 100 hands with an aggro factor of 1.4
SB is a 20/8 with similar aggro
My reasoning behind the simple fold is the honest answer of that I really didn't know if I had the odds to call/shove, in my quick look in my head I figure I was relatively close but I decided to err on the side of caution.
First off I agree with the decision to fold in spots where you're totally lost. I do the same and just make sure I mark the hand and review later to figure out why I was lost / make sure I'm not lost in future.
I don't personally take the check-jam line there with the flush draw, but not for any good reason - I just tend to bet. Definitely think it's an interesting way to play it - you get a decent amount of dead money in the pot for you to check-jam over.
Agree that you're pretty unlikely to get them to both fold if you check-jam (although I wouldn't say it's impossible). Pretty unlikely the SB is folding given how short-stacked he is.
It's feasible that you'd get it in versus a lower FD from the BTN and the SB with some kind of weak top-pair hand, but that's kinda the best-case scenario.
So the maths...
On the flop you have 8.55 left behind (effective stacks as the BTN started with 90bb, SB with less). So that's what you'd be risking if you check-jammed.
The pot is 1.9+1.81+1.81 = 5.52 which is the reward.
So risk / (risk+reward) = 8.55 / (8.55+5.52) = around 60%
It's kinda more complicated than that because if the BTN folds then you're actually only risking 3.31 (your effective stack with the SB). The reward remainds the same so now you have...
risk / (risk+reward) = 3.31 / (3.31+5.52) = around 37%
37% is definitely achievable (you just need SB to have a few combos of worse flush draws, which is pretty reasonable to assume given he over-called preflop).
However the 37% only applies if the BTN folds, and we obviously can't assume that. In fact it's pretty likely that the BTN isn't folding (he's a fish, he's presumably got lots of AX hands in his range that he's not folding, he potted it). So really we're looking more at the scenario where we need 60% equity... which is pretty friggin' tough to see us having.
It would be a different story if the board was a low two-tone board and we had the nut flush draw with two overcards - then we could feasibly get it in versus lots of worse flush draws, pairs that we have two overcards to etc etc. This is a pretty gross board to have the nut flush draw on.
So with the % we need to win in mind, I actually don't like the check-raise line at all....
I think I'd like it on the other kind of board I mentioned (where it's way easier to get it in versus worse hands) but this board is kinda gross. Fish flop top pair a lot on AX boards and aren't really ever going to be folding. A lot of the profit you'll make from check-jam lines with draws are from the times that the villains folds and that just isn't going to happen much here.
I think I'd actually just bet-fold the flop.
However, once you've checked, check-calling is an option...
We need to risk 1.81 to win 5.52.
1.81 / (1.81+5.52) = 25%
Given we're probably only going to see one card and we have to hit our flush to continue, we've got like 18% equity at best. So it's not even a call.
Definitely make sure that all makes sense to you because I might have made a mistake... intuitively that's definitely not what I expected. I thought bet-fold > check-jam > check-call > check-fold would have been the order of best lines but I think it's actually bet-fold > check-fold > check-call / check-jam
Also worth noting that if he'd bet 1/2 pot we'd still need around 20% equity so wouldn't even really be a call then.