Certainly a thought provoking article. The first question that comes to my mind is, why do we want to balance a x/r with QQ? Or more specifically why do we want to turn QQ into a bluff on this flop? It seems to me leading QQ and AQ on this flop get called by worse often enough to make both plays maximize EV and balance each other. QQ can get called by enough floats and draws to play for value as we can still catch up if we are behind some top pairs or 2 pairs. Our opponent is fairly capped and we remain uncapped. I don't think we really need a x/r range here. I could be wrong and am open to debate.

I use a combination of 1 & 4 currently against tougher opponents playing my BDFD blocking combos as bets and my non-blocking as calls. It makes the most sense to me because I don't want to be blocking hands that have incentive to barrel and my having blockers means they have less combos of blocking combos so they're incentivised to include more turn semi-bluffs into my range. I can't really tell if I would do better always using 1 for my entire range but obviously we're giving up significant EV for range protection so I really only use this vs tough regs. I've been meaning to toy around with this type of spot in CREV so I'm glad this post reminded me.

As far as protecting our bet/bet/check set lines assuming board remains unchanged I'm not sure we need to include AQ in that range. Assuming villain is calling down all or part of his AQ I feel like it's difficult for him to make our sets worse than indiffirent OTR without betting a significant part of his own range that blocks sets. Again I'd have to run this and I'm putting it a lot of volume these days so it's hard to find the time. How do you feel about this? I mean, unless we're open to exploitation or we somehow have an automatic range leak OTR by not playing AQ this way I don't think we should.

I'm most split about the x/r line. With us having AQ it's pretty hard for villain to feel comfortable bet/calling much as he'll have very few combos of bet/calls that block AQ. What bet/calling range would you assume villain to have besides sets and DP which I assume he would want value from? AK I suppose? KQ that wants to extract from weaker Qx? My other concern here is that we're definitely getting all the value from sets with a bet/bet/bet line as I doubt they'll ever bet/call and end up felted given 16 combos of AQ. What I'm trying to get at, in a muddled way, is that playing AQ this way would be to allow ourselves to bluff QQ with the added benefit of making our QJ combos harder to play against I suppose? I'm not sure this is a goal we need to have.

The posts of yours I've come across are definitely interesting and I feel bad that I can't contribute quite as intelligently for lack of time. My feeling about the spot as most spots is that, exploitive ideas aside as those are villain dependant, we have to ask ourselves what we want to accomplish, always. Essentially here, what we are trying to accomplish would be to be tougher to play against when we check. Correct me if I'm wrong but it's what I get from your musings and it's what the spot makes me wonder about. I think it's a valid question and I actually do think it's probably necessary for us to not be capped at middling SDV when we check flop assuming deep stacks. I think as a general rule, check/calling accomplishes this well. We have a similar problem in villain's shoes. Say villain has AQ, does he want to call an uncapped range always or does he want to raise sometimes to make us forfeit equity with some X part of his own range? If he wants to do the latter, he'll need to split his AQ as well. My feeling is this board hits both ranges so similarly hard that once we or villain take the postflop betting lead, it's reasonable for the other to take a passive line always. Again, sorry I can't contribute much better than musings and "my feeling is" right now.

Except that I'm not rly a fan off x/r-line in this situation I think you got some good thoughts. Personally I like to x/c this board a lot with a hand like AQ for example since it can call down on every run out and makes our check/back-range rly strong. And second of all I like doing the same with QQ and x/r on later streets as a bluff because we'll have good blockers. villain will have hands like KJs / KTs / JTs or w/e which may bet 3 streets if checked to, but it's very hard for villain to call if we x/r river with QQ since we block the majority of his nuts.

There have been good discussions on RIO about similair boards, if we x/c ppl will assume we're capped and do some rly stupid things sometimes. The problem with x/r is that we remove this ideas that we might be capped imo. Vilain will so often have some kind of piece of the board as well like backdoors / draws, seems like a spot where villain is kinda likely to overbluff if given the chances.

So personally I would do a betting range and a x/c range otf. Potentially x/r turn.

I also keep my bluffs for future streets be it as hero or villain in this scenario. Either turn or even river vs some villains. It actually reminds me of something Phil Galfond discussed in one of his NL videos where he was discussing bluff-friendly textures in NL vs PLO and talking about "lockdown" boards such as this one where AQ is the obvious nuts.

In NL I think it's good to bluff more flops in spots where say TPTK would be near the nuts and anything less would be drawing very thin whereas it's pretty reasonable to delay our bluffs on boards such as 3straight, 3flush, rainbow paired boards etc. In my view, NL being a game in which 1) it's hard to catch up when behind with say TP vs better than TP and 2) when we do catch up we don't with that many of our combos (say we bink a flush, but we really don't bink a flush that often when a 2flush board becomes 3flush) it's reasonable to put more pressure on T82dd and less presure on KJTr be it as a bluff or for value. This can change a bit depending on preflop ranges but it tends to be the way I see things.

In the video I was thinking of Phil was saying how when transitioning to PLO, NLHE players tend to not bluff enough on T67 boards and bluff too much on say K73 which is an issue given how easy it is in PLO for AK94 to catch up vs KQ87. Don't mean to derail the thread but I find thinking about this even just in NL interesting. The KJTr board is peculiar in the sense that villain can definitely draw to improve with most of his decent range (sets in particular), but sets aside if we represent that we have the nuts he is drawing to split with little to no freerolls which is an awful proposition. It's also peculiar in the sense that while AQ has a solid lock on the hand there are 12 possible nasty turn cards, 3 of which make us split quite often and 9 of which make us question our hand strength more than a bit. I'm not sure how willing this should make us to fastplay once our opponent takes the lead and my instinct says "not all that much" but it definitely has merit. I think I'd still mostly prefer using the QQ/AQ raise mix on the turn once we x/c flop than using it directly OTF.

I really like waiting til later streets to x/r QQ. Lots of really really good thoughts here!

If we never bbx AQ vs nemesis nemesis is going to jam every AQ and a bunch of bluffs and possibly win the entire pot every time we check river after betting twice. Obviously this might not be a problem vs a human villain but that is why we would sometimes want to bbx AQ against a nemesis. We don't need to ever bxx it because our turn give up is just air which isn't continuing to bluff IMO.

If you guys think people never bbx AQ here we should be always jamming river on them when we are villain and they check :).

I think the point about not bluffing flop on a board like this is really interesting, doubly so because we can't get three big streets of value with any hand. Maybe we should be checking flop always and construct our polarized ranges to start betting on the turn. This also makes it much easier to balance them because there is only one card left to change the board texture.

The reason I was suggesting flop x/r with QQ is I'm pretty sure that's mathematically the fastest way to narrow villain's range to only AQ. I definitely think I could be wrong about that now that I'm thinking about it more though.

Given he has 16 combos of AQ and the rest of his range will have board blockers + duplicate cards in almost any hand we hold I see villain presented with two issues.

1) I don't think he'll have enough bluffs that don't have strong SDV. Our perceived range being pretty puch capped to KT or so villain may want to bluff KQ but on average that's less than 8 combos (given likelihood we hold Kx or Qx). Villain may want to bluff with JT if he assumes we are folding better two pairs and never trapping but again that's going to be at most 2 combos. He could take these hands and have enough bluffs to value AQ to a PSB but then we run into issue

2) Villain's EV with his bluffs compared to EV if he checks. Say villain bluffs something as strong as JT. Assuming we are playing 1-A or at least trying to follow pot odds (so calling between 33% equity and 50% of our range) and villain bets river for a PSB. We show up with never AQ but 5 combos of sets. If we aren't betting F+T with something like AK or KQ he is looking to make us fold KJ/KT. Pot odds would dictate we never fold a set and 1-A would have us call some of our KJ combos.

I don't really see a way that we are getting owned by villain assuming GT approach (we know his strategy). Maybe exploitively villain could own some given field that overfolds rivers here but he has too many bluff candidates to ensure he can just auto-bet all his bluffs. I see villain using KQ as a bluff miles more profitable than a check and same goes for AK but if he's using those hands he's already far beyond the balance necessary for a PSB with 16 combos of AQ (which shouldn't be blocking our bluff catchers). So vs a program or a human I don't see a way that we can't just call 1-A if we feel the need to. What am I missing?

BTW, I don't think there is an issue with b/b/x AQ here, we can have that kind of mix easily. I'd definitely do it exploitively vs some opponents, or if stacks allowed for a sensible x/shove for instance. I'm just wondering about the balancing necessity of it.

Sure that's sensible. Hadn't understood that you meant owning us in range EV. I think we'd need to run this spot to get some idea of how to manage three lines for AQ (namely x/c line, b/b/b line and b/b/x line). We'd have to consider if we want to be checking sets on the turn as well. I mean, at this point it's pretty clear which merits every line has given which other hands get played that way, so we'd have to run something making some assumptions. For instance it'd be reasonable to assume villain is raising turn with maybe 25% of his AQ and say QQ 15%? We could decide that we check turn with our bottom sets. Then we could give villain a river bluffing range that makes sense and we can see what the EVs look like at least for Hero. It should be interesting to see if AQ loses significant value in one branch, assuming we've balanced villain correctly.

Sure that's sensible. Hadn't understood that you meant owning us in range EV. I think we'd need to run this spot to get some idea of how to manage three lines for AQ (namely x/c line, b/b/b line and b/b/x line). We'd have to consider if we want to be checking sets on the turn as well. I mean, at this point it's pretty clear which merits every line has given which other hands get played that way, so we'd have to run something making some assumptions. For instance it'd be reasonable to assume villain is raising turn with maybe 25% of his AQ and say QQ 15%? We could decide that we check turn with our bottom sets. Then we could give villain a river bluffing range that makes sense and we can see what the EVs look like at least for Hero. It should be interesting to see if AQ loses significant value in one branch, assuming we've balanced villain correctly.

PS : we also need to be weary that if we never hold AQ on the river, villain can value bet top set. As a matter of fact, If we're calling with more than 50% combos that lose to top set, that's enough for him. So he starts getting value from more hands than AQ. Chances are this would occur to a perceptive villain, or just one who assumes we're never checking the nuts with PSB left on the river. If we have room to x/r, villain may be less hot about vbetting a set.