Not a solver approved flop x/r

XR middling hands is doubled edged sword, you fold out overcard's but he still has All T9o+ in his range. What you don't want to do in all spots is take a middling hand and isolate it vs hands that beat you/have high equity vs you good draws, good tp+ etc. Also as a human it makes future streets extremely hard to play compared if you have a more polar range. What do you do on Broadway turns, diamond turns etc.

If he's tighter its worse, if he cbets too much then you probably can CR at will. In practice I would XR more air/draws, maybe XR more tp for value but keep the middle of my range around the same.

It seems like the solver does XR T8o w/ a diamond at some freq though.

I think that the reason not to c/r with hands like T8o is that most of the time when Villain is behind (even with hands like 66-99) he will fold. And when he is ahead he will call and not raise. So we are increasing the size of the pot OOP in bad situations. Yes Villain will also call with flush draws and potentially 64/A4/A2 hands (though I think gutters will also be folded a lot) but the turn becomes a big problem. Because we will be behind most of the time, bet sizing on the turn is tricky. And if Villain calls our turn bet same for the river if we don't improve.

My guess is that solvers are trying to balance the semi-bluffs with strong hands so Villains won't know what to do and also to make it profitable whether Villains are mostly calling or mostly folding.

I do see the advantage of getting two overcards to fold and I do remember all of the times where I call the flop bet a higher card comes on the turn or river and I lose because I let Villain get there. But there are also many times where I haven't overpaid when I am behind on the flop.

This is probably better against real life players who bet the flop too much, and don’t defend the check raise appropriately. You will get folds from a lot of hands the solver will continue with.

The other reason you need to be more polar is simply this is a very high SPR. You just don’t want to build the pot here with this hand class.

Yeah, I get that T8 is the wrong hand for this move for those reasons but I was surprised to see that GTOW doesn't even put hands like A3 in its x/r range here. But I think that's a spot for exploitive play. Solver will defend the x/r with a lot of better hands a human opponent will fold. But it does raise an interesting question about whether raising to deny equity is even a thing for the solver.

I think you're right the SPR is probably a major factor.

Another factor: there's a lot of value to be gained by letting him barrel/bluff into you with hands you're way ahead of. Like QJo does have a fair amount of equity, but is it really a bad thing to let him continue bluffing with it when he's way behind?

You need hands to call with when he barrels turn. Otherwise if you raise all your top pair hands on the flop he can double-barrel you with impunity when you call flop.

Also, you can always raise on future streets (mainly when your hand improves to 2-pair+).

I looked at an 80BB solve, and did find a lot of the check raises you talk about, hands like Ad3x do get to check raise some, so we can have bluffs on diamond turns, and cooler his bigger Ax combos when we turn an ace.

I am a little surprised GTOw doesn't mix in a lot of the various hand types like that so as to have good board coverage on turns, and to have a decent bluff combo when the flush card falls.

FWIW, this is a check raise (the Ad3x) I'd always make, as my opponents over cbet and under defend to check raises. I suspect most of your opponents won't defend enough either (as I mentioned above)

The solver as Villain never folds so many of the hands your Villains will fold. It never folds any BDFD, never folds 2 overs to the ten. Most of the folds are coming from hi low hands like K7o no diamond. I take back the part about never folding a back door flush draw, it will fold its weakest BDFDs like Kx7d.

All that is to say this is a great spot for a very diverse and aggressive small check raise size. My solve showed ~20%, but if you jacked that up to 30%, I'd bet you are printing in most fields.

Even at 80bb? Interesting. So the stack depth is clearly a major factor here.

I think you're right that x/raising at a higher frequency is +ev in a spot like this. One major deviation most humans make from the solvers is they fold at a much higher frequency.

I agree that increasing the check raise frequency is a good exploit for the reasons 3for3 mentioned, but T8o isn't a good combo to be raising, IMO.

You generally want to raise with hands that have some potential to make a very strong hand by river.

Ad3 is a much better check raise candidate. You have the key Ad blocker to bluff when a diamond hits, and you build a pot so that when the runner runner flush hits you can potentially stack your opponent. The villain will also float a lot of Ax so you can cooler Ax when an ace hits.

You also benefit more from the protection effects you mentioned in your first post. For example it's a win if 87 folds with 6 outs. Also you are more likely to get better hands to fold by river (like 5x and PPs smaller than Ts).

You typically want to raise a polarized range. T8o (at this stack depth) is too strong to bluff with and not strong enough to raise for value.

All that being said, we've got to remember how wide the ranges are in button vs bb formation. Ad3 is actually fairly high up in our range, which is likely why the solver calls with it. It's a strong enough hand to call with in this formation, and there are plenty of other hands to choose from as bluffs.

I would prefer to c/r with Ad4 or Ad2 here than Ad3.

With Ad3 we do get some PP's lower than T to fold sometimes which is good. But because we may block Ax hands from getting ahead of us if an A hits I prefer to just call with Ad3. Or any A3 really. On the turn we often get to see if we are ahead based on sizing of 2nd barrel.

With Ad4/Ad2 we are semi bluffing with a gutter and BDFD which makes getting folds excellent and gives us an easy fold to a raise (or a raise on the turn if we continue after not improving).

Yeah I personally wouldn't bluff with Ad3 in this spot, but I don't think it's a bad play. The hands you mentioned are good candidates too. When there are lots of potential bluffs I prefer to use hands with less showdown value. 64, 76, even hands interacting with the ten to give backdoor possibilities are all good candidates. I think having the proper frequencies is more important than the exact combos we choose. It is nice to have some Adx to bluff with when the flush completes as we'll have a lot of flushes in those spots.

Personally I prefer to bluff with small pairs + backdoors like Ad3 when it's too weak to call with, and the opponent's range is strong enough that blocking sets and two pairs becomes more relevant. So I'm more likely to bluff with a hand like that in a tighter formation than button vs BB.

Small pairs are also nice to double barrel with in position, then check back river. In those spots you can fold out better and still win against missed draws when you check back river. OOP like this spot if we check river we'll often get bluffed out by the missed draws.

Regardless of solvers, you usually x/r with a big hand, a semibluff, or a bluff. With a middle strength hand like this, it is usually best to call down.

What about if we're IP (let's say CO vs BTN), does the same reasoning apply?

Or would raising the flop make sense to slow down villain and incite him to check the turn?

My solver agrees, using the gutter+BDNFD much more often than the Ad3x combo.

If, like me, you believe that we can exploit by check raising more than a solver, both of these combos are good candidates.

It also likes check raising A5 a lot. I guess this is sort of a weird mergy kind of check raise, in that it can also get value from worse 5x.

Moving up the AdX ladder, it does check raise Ad6, and Ad7 some of the time as well.

One big heuristic to take from this spot is that the Ace of the Flush draw suit is a VERY powerful card, and it should automatically get you at least thinking about taking aggressive lines.

BTW, Ad8/9/J don't get check raised. I think that is a combination of losing the back door straight draw, and gaining showdown equity vs Villains weaker Ax

I am not like you, yet...

I probably don't c/r enough. I wouldn't c/r with A5 either. Even Ad5. It didn't occur to me to c/r with BDFD & BDSD with an overcard (like Ad6|Ad7) which I would normally just fold to a cbet.

But I will think about it. Here I would mostly c/r with flush draws that have one or more overcards to the flop. And that balances with my 2 pair and set combos. But if I was going to extend my bluff combos it would be with straight draws (with no overcards) and flush draws with no overcards (which apparently solvers like more than with overcards).

A highly justifiable raise against BTN opener/smallish cbet

• 99, 88, 77, 66,
  
• A5,
  
• why not even T7, T6,
  
• Ace high esp. with a backdoor,
  
• diamond draws, wheels...
  

Yeah. You generally want a check-raising range to be polar - where your value hands are fine getting it in or continuing if you're three-bet, and your bluffs are fine folding. Hands like a flush draw with an overcard have too much equity to fall into the latter group. It's why hands like bad gutshots and double backdoors are commonly chosen by the solver - they're easy to give up against a 3-betting range, but if you're called, you can turn a disguised monster hand or extra equity you can keep barreling with, and give up if you don't improve (and particularly if the card is bad for your range vs. the raiser's range).

Very interesting discussion.

Since you all seem to prefer x/calling with A3, that suggests you also don't buy into the "x/r to deny equity" philosophy. So I'll ask a f/u theory question:

Under what conditions, if any, would you opt for a x/r with A3 in a spot like this?

Only with shallower effective stacks, say 40bb? What about if villain has a CB frequency over 80%?

two spots to train on to get an idea just how much EV is attributable to aggression for protection reasons:

• the deep stack overjam spots like the ones that have been posted here recently
  

• short stack flop and turn spots (think SPR ~1) where you'll see jams for protection-needy combos and a small sizing for pure milking purposes with strongest combos (especially when theres convergence between strongest combos and heaviest blocker disincentive)
  

I found where the solver likes to get its 3x from (The solver always wants good board coverage, so, if you don't have sufficient 3x, Villain can exploit you when a 3 turns).

It's not the A3, it's the 63 and 43 combos that can turn straight draws, and even stuff like 83hh which can turn a heart draw.

The main thinking here is that when we check raise 3x and get called, we aren't in great shape, we mostly have 30-40% equity in solver land, so those hands have to give up on blank turns. When you have the back doors, you get to have more barrel cards.

A3 can pick up a straight draw, but a lot of that time the draw is to a chop, so it isn't nearly as valuable as when 63 turns a 4 which gives us pair plus open ended.

I find this stuff fascinating, even if I am past the point in my life where I can assimilate all of this into a complete strategy over the table. I 'know' some of the concepts for finding these check raises, but I'll never be like the 20 somethings that can make this part of a complete strategy that they can play IRL.

OK, more geek time.

We check raise and get called.

Our equity when called (with all of our check raises) is 46.4.

What are our best turn cards? What are our worst turns?

Diamonds are all good, more than 50%

6s and 4s are also good, as they give us lots of straights, pair plus draws and 2P

Our worst cards are any of the board pairs.

Why is that? Even though the solver tries to use some of its pairs as check raises, it just doesn't do it enough. It also cuts down on our value combos, and makes it more likely that we had a semi bluff than 2P or a set.

I think we all know that intuitively, when the board pairs that a range consisting of value and semi bluffs now becomes more weighted towards the bluffs.

This is why we DO need some of these oddball one pair hands in our semi bluff range. Villain will rightly think our range is weakened when we actually have a very strong hand. That is the scenario where you make the most money, of course.

There can be a threshold with a very short stack where a hand like A3 bottom pair becomes strong enough to raise/get it in. This is probably something like 10 bbs deep though. At some point just having a pair is "enough." In similar spots the solver will C/R small (allowing for non all-in bluffs as well), then call it off if opponent jams. I assume this line is mainly taken to deny equity to random over cards.

One heuristic I like to use in a given spot is to think about how I will respond in the case of a re-raise. Typically I like to C/R with combos where I have a clear continue or clear fold. I tend to avoid check raising with combos if I'm not quite sure how to respond in case of a reraise. I think Ad3 at a deeper stack depth would qualify as a hand where you kind of hate all options when reraised. It's usually these medium-strength hands that you don't want to check raise with. This isn't always a perfect way to think about things from the perspective of a solver but practically it makes a big difference.

As an exploit though, against an opponent who responds predictablly, Ad3 seems like it could be a fine check raise.

That makes sense, a hand like 63 is a much more intuitive x/r for me. But it's a good reminder of an important principle for bluffing before the river that we've known since long before solvers: you don't want to bluff with naked hands that have no chance to improve. The solver outputs here are demonstrating that principle by choosing x/raises with hands that can improve and x/calling with the hands that are in bad shape when called.