With the flop play, what you said makes sense. However, If I remove all underpairs from my range, the equilibrium now starts to raise about 12%. This suggests that there is another reason it didn't raise initially, since the points you made still apply.

Makes sense, I suppose there is a threshold in which raising becomes a thing again merely because IP range gets strong enough, so my thoughts aren't the full picture.

Yes, I ran the turn spot at alot of different sprs and does bet bigger at larger sprs. But always less than geometric.

My range for flatting vs utg is 6% mix of all pairs 22-qq, all suited
connectors 45s-kqs+, suited bw, suited ax, and some off suit kq,
aj-ak. I feel like I have to continue my suited connectors, pairs,
ATs+ at some frequency. Is that kind of range really too defined to
defend vs squeeze? Doesn't it become even more defined if I start pure
folding hands like T9s and 66?

that's an extremely wide range imo. the rake at these stakes is very high and you are pretty susceptible to squeezes if you start flatting hands like low pp's as well as off suit broadways. I would be surprised if many of these hands were winning due to both the rake and the fact that the utg range is very tight, and like I said you are also gonna get squeezed a certain % of the time. are you using a solver for this range or just winging it?

it's true to a certain extent about your range being defined if you start folding hands such as T9s/66, but you shouldn't continue hands which are -EV simply for the sake of board coverage.

Re post flop play. Today I ran the sim again, must've changed the
composition of the ranges around a little because It gave me an ev of
60%. And it started raising flop about 10% of the time, and failing to
do so, would cede about 0.7% of the pot. But it chooses the JJ and QQ
(and bw gut shots) in my range instead of the sets, 2 pair, which goes
with what you were saying about protecting our call range.

was this by node locking an OOP cbet or optimally with the 10% raising frequency? it's still pretty low, however. given the fact that our range is already very tight anyways. in 3bp's we tend to prefer raising hands that require more protection/benefit from folds as opposed to the nutted portions of our range (such as sets/2 pairs) due to the fact that the spr is already extremely low and we can easily get the money in by the river anyways. we also don't require protection, and want to keep in villains over cards so he can spike a random top pair and stack off, or bluff off vs our perceived 'capped' range. most players have this backwards though, and raise sets and call with weak OP's/top pairs.

Also I kind of disagree with what you said about his cbet size.
Against a 2/3 sizing, it's not as simple as folding all our underpairs
and AQs. In fact when I node locked all those folds in, it costs us
over 5% of the pot. The big sizing forces ip to play a mixed strategy
with those hands which is harder to execute than the pure call vs the
small size. I don't really see either defense strategy being easier
than the other one, so I feel like we should just choose the sizing
that is used at equilibrium, which is the big sizing.

it depends how both ranges are constructed pre. if your range consists of sets/hands that are going to fold then it makes no sense to use a large sizing. for example you can see this as an example on a board such as 543 btn vs bb. where bb has many more straights and 2 pairs, yet has a bunch of random air over cards that are gonna fold to any sizing, so we end up checking back at high frequencies or using a small sizing. which doesn't seem too intuitive on such a drawy board where 'protection' and value seem to favour a larger IP sizing.

if your range contains more top/second pairs and open enders/gut shots then yeah I can understand the use of the larger sizing. your pre-flop range is probably more merged/weak on this board than most players due to the fact that both your flatting range vs the open, as well as calling range vs the squeeze are wider. which would lead to the use of a larger sizing. if your range was tighter and lets say JJ-88, as well as some suited broadways AQs/AJs then imo OOP would favour the smaller sizing. I could be wrong though I haven't ran any sims on this exact board/scenario.

Demondoink

Was interesting to read your point on people getting it backwards in 3BP's to flop raise the strong portions of their range and flat top pair/overpairs that benefit from protection. Definitely something I do, but also may be in part due to the games I am playing in. This makes sense against aggressive opponents

ryanspicer cheers man. yeah for sure, and it ends up making your flop raising range extremely strong, and conversely your calling range extremely capped.

the reason that you raise on the flop to begin with is:
1-because it is higher EV to do so
2-so that you can leverage the nut portions of your range in order to get max value

however, when you are shallow stacked both of the points are not true any longer. when you raise top 2 pairs or a flop set you end up blocking many of the opponents continues, as well as not letting him 'catch up' with hands that are effectively drawing dead. such as AK/AQ on T9x when you have either 2 pair or a set. you are also not worried about getting sucked out on cos the spr is so low so even when he does the result will not be as costly to negate slow playing as the higher EV option.

when you are deep stacked, these 2 factors hold true, however.
you need to start building a pot with both value/bluffs in order to try and get all of your chips in the middle by the end of the hand and apply a ton of pressure to the bluff catching portions of his range. we also require much more protection with a hand such as top 2 pair because villains range is much wider (it is not a condensed 3/4 bet range) and we want to reduce the spr for future streets.

so yeah. it's not very intuitive but in 3bet pots it's kinda the reverse of 2bet pots. you will also see in PIO sims that it almost always slow plays sets as the pfc but raises hands such as top pair top kicker. this changes to an extent when we are OOP as the caller, however. or when we are 200 bb's deep.

Demondoink when you are constructing a flop raising range with top pair type hands IP, are you using a 2.5x sizing, or anything less than 3x due to the low SPR? Appears to me you can use a smaller sizing.

Also, you're doing this to A) deny equity and Question, B) to check back some turns/fold some rivers rather than calling twice and being put in a tough spot on river with a capped range?

ryanspicer it doesn't happen very often tbh, but yeah i'd be using a small sizing probably somewhere between min and 2.5x. anything larger is kinda un-necessary imo and too large.

yeah because if you never have a flop raising range on any boards then you let the other player bet at a much higher frequency as they still generate your air folds and also get to realise more equity with their marginal hands that aren't scared of getting blown off their equity vs a raise.

yeah you could take that line, exploitatively. if you think that you get AK to fold and they pure continue AA/KK as calls then you can raise and get those AK folds and then just x back and folds. you can mess around with node locking in PIO it reacts the same way if they have a strategy of, for example, bet/folding AK always on Txx and continuing all OP's. we just raise for protection with a bunch of marginal pairs and then give up when called/jammed on, effectively.

find this very interesting "Yet it seems like the bigger oop bets, and thus the small the spr, the more often we raise instead of calling. For example, if oop is forced to bet pot or check, ip now raises 25%.", no idea why this would be the case, any further thoughts on this?

Asdfghjkl1 because we are pretty much playing a one street game and not nuts vs air. so we just get it in with more marginal hands and take their equity as opposed to using them as call downs in a polarized call down situation.