yeah i agree probably a big mistake. My reasoning was that his sizing on the turn combined with Villains board advantage made me feel like he would jam all his value/bluffs on the river. do you really see villain giving up river in this spot given the turn size? As you said I would have to fold AJ on the river, so I felt that it maybe i should let it go, seeing as I felt his shoving frequency would be very high OTR. I also would check 100% OTF given ranges, and felt although i am very high in my range with AJ, I also have AQss / AQo/ AKo and sometimes slowplay J10ss on this board for balance - hence I felt that perhaps I was protected enough here with AJ to let this go straight away...

2/ regardless, this was def an exploitative fold, as obviously i should be folding a different part of my range on each street , and AJ fits the category that calls turn folds river

This is wrong:
"we should probably be betting 0% on this flop when checked to (because it is such a strong board for the OOP player)"

If we are betting 0% he should never check a strong hand. So we can start betting then. I'm not saying it doesn't work exploitatively tough, just that at equilibrium we never check range IP

Lezaleas no it's not. because if villain is supposed to have an extremely high betting frequency on a particular board in 3 bet pot, and he checks, we shouldn't be arriving at this node at equilibrium and because his range should still be very strong (all hands should be mixed and it's impossible to identify his checking range as either weak or strong) then we can end up checking back 100% of the time.

this is pretty much because of this exact case. clearly villain is saying that on the flop he checked an extremely strong hand and now he wants to bet pot/jam river. so if we start betting with the stronger parts of our range then we are unable to defend vs this delayed aggression properly and end up massively over-folding on latter streets or having extremely low EV with our turn range when facing a bet.

tomdrinkwater12 yeah but the problem is that people will always say that I have x and y hand to defend so I don't need to call with this hand. but in reality they end up betting x and y hand most of the time when checked to on the flop, and thus end up folding basically their entire range on the turn to a large turn bet. i'm not saying this is the case for you, but you have to be very honest with yourself and decide whether you will actually check back both a straight and 2 pair when checked to on this flop.

sure I agree, villain is most likely to go all in on the river, but that doesn't matter because we need some hands to call/fold. in poker you need a region of hands to call on every street, and a region of hands to fold. so even if we know villain is going all in most of the time on the river we still need to call this hand because 1-we can sometimes improve to either a straight, 2 pair or trips and win. 2-we want to prevent villain from having extremely profitable bets on a particular street. it's not GTO to fold 90% of the time on the turn because villain is likely going to fold on the river. it is, however, GTO to fold 50% of the time on the turn, and 50% of the time on the river to pot sized bets as villain isn't exploiting us any longer.

so yeah, even if you know you are folding a hand 100% of the time on the river to a bet it doesn't mean that you just fold on the turn. even though it seems like you are 'saving' yourself vs a large turn bet, in actuality you are just giving villain the entire pot.

Demondoink , are you folding weaker ace's OTT such as A2ss - A5ss (that i chose not to 4 bet)?
Im guessing that you would call turn and river with AK & AQ, and call turn and randomize calling river at low frequency with AJ -A10ss?
Also, I would say I would def. check back AK/AQ OTF, but would really struggle to check back the straight lol

tomdrinkwater12 I wouldn't be flatting any of the lower suited Ax to this huge 3 bet sizing. my weakest defend would be ATs so I wouldn't have any of those hands in my range. if I did have them, then yeah I guess I would probably fold them, but always defend with AJ/AT and I wouldn't be betting any hands on the flop here when checked to. because when we have a straight we don't mind checking back as it's still very easy to get all of our money in by the river and villain will end up turning his range pretty face up when he checks twice ott. allowing us to turn some hands in to bluffs as well.

so when playing vs this strategy I tend to tread extremely lightly on early streets, particularly on the flop, and play a reactive style ott once his range is a lot more defined.

Yes, if we have strong read that he traps at high frequency on this board, then his betting range becomes weak. Its likely in this scenerio that he either was trapping or had hands like 109ss or 98ss or 99-77 and decided he had no showdown value, whilst having such a range advantage that he decided to barrel off turn and river with no equity. Regardless, I exploitively folded turn as I knew he would shove river at high frequency and felt i had better hands to call - call with. Its very hard to decide to go with hand when you dont have a very specific read of villains tendancy's and so I let it go without more reliable info. As for his line, he should be c-betting range small on this board, and i agree his line is very non-standard.

PIO will say the SB should bet all his range on this board due to such a heavy range advantage, so it makes it hard for the software to evaluate what I should do in position when checked to as it doesn't account for this. What I imagine however is that my betting frequency OTF, pio will say IP will have close to 0% betting frequency due to strength of villains range as the 3-bettor even with the check

5

I explained this in another response here, I think, but it's impossible that we ever have 0% bet fq at eq IP. As you said, his range is so strong here that he should cbet range. PIO can't say that you should never bet unless you node-lock him into some strat where he checks and we are not talking about eq then, in which case you may node-lock a range so strong that we never bet then. It's certainly likely that he's checking such a strong range. I just wanted to clarify that it never happens at eq.

Edit.: it's also impossible for IP to have a low betting frequency either, we should bet at least 45% when checked to, no matter how strong the initial OOP range was. You can check this in your solver

You're right that IP should never have a 0% bet freq at equilibrium, although there are certainly some boards where this frequency drops below 45%. Two examples off the top of my head would be ace high boards and monotone boards. The flop actually goes xx pretty often, with most reasonable ranges and high-ish SPR.

I’m a little out of touch with online atm as well, playing mostly live, but what would the bottom of your Ax’s region be? Because y’all have some depth, I’m thinking you may be defending a fair amount of Ax’s, including ATs, A9s maybe A2-5s, right?

If this is the case, he could just be attacking that region pretty hard. Plus all the 2nd and 3rd pairs in our range like QJ, KJ. I think against a straightforward player maybe we actually could just fold this, but against a strong reg who’s aware this seems like a pretty good bluff catcher

yes my range of ace x is as you said... this is high in my range, but i would check my AK, AQ in this spot as PIO says i should be basically never betting this flop giving Villains range advantage. if i bet my strongest hands on the flop, my checking range is always weak and can be exploited. I need to be able to call 2 streets on turn and river, and if he checks again i can start to value bet. I believe weaker ace x's are protected by checking range so I can fold the weaker ones straight away, but AJ may be too strong to fold.
The dynamics with regs online on these boards in which they have such a nut advantage is that they bet frequently and beggining polarizing early in the hand... indeed they should probably be tripling off bluffs such as 10 -77 and 109ss, q10ss at a somewhat high frequency. This hand just really confused me due his flop check and turn overbet, when PIO wants him to c-bet range on this board
Also, no problem with you Cbetting your strong value hands on the flop in an exploitative sense in live poker; with online 500nl you just cant get away with being unbalanced in such spots as you have large hand histories and such regs will pick up that you are only betting value hands on such boards.

I feel like 77-99 aren't getting 3bet very often with such a big size. Granted it's a SB 3bet, but I think if villain were playing a 3b or fold strategy he would pick a smaller size, maybe something like 4.5x. I don't actually play 500z but this is just something I've observed from watching people like Sauce.

From the sims I've run on these triple broadway boards, Pio tends to bet AK/AQ almost always, and check sets some of the time since they are less vulnerable to getting 2-outered. So I think a big part of his turn overbet range would be sets. But obviously that's gonna change with preflop ranges, and if you add/remove JTs from either player's range I imagine the solution would look totally different.

Edit: oops just noticed it's 500nl not 500z

yeah it would be sketchy to take these hand with no blocking/equity bluffs such as 99-77 after checking flop - these fit much more with a triple barrel.. still torn on whether this line was weak or strong tbh. I think there are the traps you mentioned earlier, and perhaps some 10 10, J J and 109ss as bluffs