I see what you're getting at, but it seems like you're jumping ahead of a few things. You say we can't have a balanced value range - do you mean that we can't value bet 1 pair? That's not necessarily a problem, just something we work around. It's possible this is true, and it changes our bet sizing and frequency (and gives villain a reason to donk bet sometimes).

The 2nd point is that we will fold a lot vs xr. What are you implying is going to happen? That villain will first make a lot of top pairs we can't beat, then he will check to us intending to check/raise, and then we'll oblige his strategy by value betting lots of weaker hands? We can choose how thin we will vbet, based on villain's range equity in the pot, and then we choose how often we call when we actually do get xr.

Once we've established how we feel about all those things, and decide if they really hurt our EV, we can think about including more Kx/Ax combos in our turn betting range as a method of improving our EV on K/A rivers.

This is a reference to a basic indifference equation, where we use villain's pot odds to determine how often we are going to have bluffs. This way, villain will be indifferent on his calls with bluff catchers, given the price of my bet.

In this hand, my value hands are strong enough to bet larger, which gives villain worse pot odds with his bluff catchers. If I want him to keep calling me, I'll need to bluff more often (as a percentage of my value hands) with this size.

Keep in mind that this is a ratio, not a total number of hands. In an absolute sense I might have fewer bluff combos than your average turn double barrel situation, because I also have fewer value bet combos.

I haven't done anything with this yet. It's on my radar!

Thanks for the comment Phil :)

I think you're right here, given the detail that kickers don't actually play here. I'd chosen the (simplistic) randomization system from a pattern I noticed in sim results on building things like cbet range, turn probe range, etc. On a blank in the same turn situation, I think I would stick to my approach in general, since the EV of betting will vary more by kicker strength.

The best counterpoint I can make is that when betting for protection, blocking his calling range (specifically K8 in this case, not Q8 or J8) seems like an argument in favour of bet. If we generate a higher % of folds with a hand that isn't strictly value betting, then the EV of betting should be improved from that removal effect.

It's kind of a strange contrast to our typical framework of checking to induce bets when we expect to be good, but I've noticed it come up in a variety of other situations. Ever since I started relying more on piosolver, I'm finding myself breaking away from a lot of traditional logic on value bets and bluffs before the river. I'd have to run a sim on this spot to see if it matters enough to show up at equilibrium, because I'm also guessing a bit with regards to how important protection is for 8x vs. hands < K high, as well as the significance of our K8 removing only 25% of a pretty common hand class.

Hey kevin! can you explain more of what you mean above that you are 'breaking away from traditional logic for vbetting b4 river?

Yeah sure, when I say 'traditional logic' I'm thinking of a strict dichotomy between "value bets" and "bluffs". This was the prevailing method of discussing ranges for a long time, and we assumed that if you weren't either value betting or bluffing you were making a mistake by betting. In modern games we don't really think in such a black and white manner unless we're playing the river, because we better understand the importance of betting for protection, or betting to help range distribution, avoid exploitation, etc.

I think K8 should be a check since you're blocking his calling range as you said. When deciding which other 8s to bet you basically have to weigh the protection value betting the lower 8s like 87 vs the freerolling value of betting the higher 8s like Q8 against opponents 8s like 86. I'm not sure which is more important. You could do the math or pio it. One other minor importance is to consider that he is more like to check back higher cards on the flop than lower ones so if the borderline somehow fell on betting Q8 or J8, both have overcards for freerolling but J8 would be a better bet since it requires more protection.

Keep in mind the pair is 22 on this board so there's no 'freerolling' with any 8x like there would be if it was AA82 instead of A822.

I'm interested in whether 'blocking the calling range' actually does mean we want to check, because it isn't obvious to me. Has anyone done simulation that might suggest this? It seems complicated to isolate.

It's really just a matter of having more equity. When I block diamonds I'm more likely to be good on later streets, and when I'm behind I have additional outs with a bdfd.

It's really just a matter of having more equity.

I think its more than just this. If it was the case you would just cbet all your Ax but in this spot you want to have both betting and checking range well constructed.

What I meant was that among all Ax that I could cbet, the ones with bdfd have more equity (and also block equity). I'd rather bet with those qualities so when choosing Ax to bet, these are preferable. My checking range can still be well constructed as long as I'm not taking this preference so far that all single diamond hands become a cbet. My frequency can't accommodate this much air, though, plus I like to check several 2 card flush draws, so there shouldn't be a big problem for future streets on diamonds.

Yeah, I see.
I wasn`t trying to expand the discussion to whole flop strategy but I see logic behind the strategy of specific flop hand class (weak_TP) linked with your whole flop strategy.
And yeah blocker effects of specific hand class are insignificant relatively to some other hand classes in terms of our flop strategy.