Thanks again for running the numbers, Zach, and thanks for explaining your assumptions.  As usual, no logic I can argue with.

Interestingly enough, I'm starting to wonder if his raise is a good play, at least a chunk of the time. 

A983 is a board on which a lot of my 3b range has decent equity, so forcing me to fold (even if my folds are correct) allows him to protect his hand and take down the already big pot.  Not to mention he can force me to put money in bad, like he did :)

I think the most interesting question about spots like this might be how you should play with A974 here vs how you should play with AJT9 or AT97.

The majority of players will be much more likely to raise the latter two hands, but I think that the element of protection and representing an uncapped and somewhat polarized range (forcing your opponent to give you free showdowns when he hits a bigger two pair hand or better, when he otherwise would've bet bet and made you lose the same amount) makes raising with A9-no redraw pretty attractive.

I've gone back and forth on spots like this, so I'm curious to hear what everyone thinks.

The most obvious counter-argument to me is that raising with the strong hands puts in more money with stronger equity vs. your opponents range, and plays well against drawing hands.

PS.  I'll remember to call you Zachary when I'm mad at you

Beyond equity considerations, not raising AJT9 and AT97 would be criminal since you have good board coverage when the board changes and when the board doesn't change. So it prevents your opponent from bluff leading his made hands that might or might not be good when draws complete on river. 

Why would we 3bet a bluffcatcher on 336r? Also on 346r you can c/r bluff smallish JT87 w/ bfd to balance value c/r w/ 57,52. Obviously you have to do it with low frequency because on this board his range is stronger than yours. The solution to reduce his advantage is to 3bet more low rundowns and hands like A456ss,K456ss,J456ds.

re: check-calling your whole continuing range on 643r, do you think think it would be theoretically optimal to have multiple ranges (bet, check-call, check-raise, or perhaps just check-call and check-raise) but too difficult in practice to execute the mixed strategies that would be necessary, or is it just impossible because we have too few strong hands?

DirtyD, I would imagine a complete strategy would use all of the options/be mixed.  I would guess most of the action would be a check though, but that is just a guess.

Hey Brian. I'm extremely excited to see you jumping into the discussion here! I hope our other members appreciate it as much as I do.

That's really interesting that we can profitably shove at 100bb on 336 flops.  Not shocking, but I've never thought about it that way.

I think that the confidence in your range you get from evidence like that is powerful, but I think jumping to a 100% cbet conclusion without looking into more detail is premature.  As I sit here before my morning coffee has kicked in, I'm trying to come up with "proof" of some kind that supports or rejects a 100% cbet strategy here and drawing a blank.  Let me think on it a little more....

Intuition tells me that 100% is way too high, and that we can develop a strategy that plays much better than that.  I have some rough ideas about how to go about it.

Okay...

What if we give you a simplified range of AA, KK, QQ, AKJT, QJT9 at some frequencies that are fair for your true preflop range (leave out 3xxxx or better for now and see if you can add it in later)?  Then we give them an 80% range or so and try to develop the best strategy for them and see how it goes.

For a simplistic simulation, I'd have them raise with their full continuing range and make your decision jam-fold (with a ratio that makes you indifferent) and see how often they get to take down the pot.

That won't tell us a TON, but it will give us a little extra information.

The next step would be devising the best strategy we can for your opponent against a somewhat simplified strategy from you, which involves a 100% cbet (we could simplify both of your ranges or make them both full). I suspect you may be in more trouble than you think against a proper strategy, especially because of the straight draw on the board.

I'm assuming that (biiiig assumption here and could be way off, as I haven't run sims like this) his best strategy involves a small flop raising range and a larger calling range. One which will allow him to win on most straight and 6x turns, as well as continue on turn bricks against a bet at at least a frequency that makes betting twice with air not work well for you.  He likely would then force you to check AA/KK on brick and straight rivers and put you in a situation where you need to bluff-catch against a balanced polarized range.

Anyways, what I suspect is that he'll do pretty well in this spot (but you'll be much better off on 833 flops than 633)... probably well enough that if you know the flop is going to come 633r, 3betting would become -EV with your standard 3betting range.

Whatever that sim would prove unfortunately won't give us a good inclination of a best strategy for you, but it would at least provide extra insight into the situation.

Of course, he doesn't need to make cbetting worse for us than open mucking in order for us to rethink our strategy. 

I suspect that your average player will play poorly against a 100% cbet strategy on these boards, either out of fear or laziness, so I don't think you could be making a big mistake in practice.  Another argument for it is that coming up with cbet, x/f, x/c, and x/r ranges makes it extremely difficult to stay balanced.  I'd still prefer to go that route and give it a shot.

Once we get up to 150bb and 200bb, I'm sure we'll see our opponent doing better and better, which is why I always argue for an expanded 3betting range with more board coverage as stacks get deeper.

Hey again, Brian.

As far as your thoughts on 643, they sound exactly like my thoughts on it.

It feels like we just need to check always, yet I run into the same problems of wanting to be able to continue somehow with gutters or strong double backdoor draws.  

I would imagine a complete strategy would use all of the options/be mixed.  I would guess most of the action would be a check though, but that is just a guess.

I completely agree with this and I feel pretty strongly that we're right.

I suppose we need to cbet and check-raise at such a low bluff frequency that we can include some JT87 type hands without being exploited.

Or maybe we need to be check-calling most of our continuing range and going for turn check raises when we can apply more pressure with our polarized range?  This seems like it makes sense.  I shy away from x/c here with AA and with AKJ6ds and JT87 because opponents just seem to bet the turn all the time and force me to fold.

If we can slowplay flop enough, we can include a few floats such that we can x/r often enough turns to discourage them from always firing (which also allows us to float and bluff rivers and to get to showdown sometimes with AA type hands).  The main reason I'm thinking a strategy made up predominantly of flop x/c's may work out best is that the flop favors them SO heavily that we may as well put as little money in on the flop as possible so that we can see turns which swing the equity one way or another... Not that we become big favorites on many turns, but we get much closer when we turn Ax/Kx, and we become much weaker on straightening turns and can just get out cheaply.

"I always argue for an expanded 3betting range with more board coverage as stacks get deeper."

I have played around with my three betting frequencies to try to incorporate more board coverage, and we can to some degree, but I find to have a truly balanced range we need to weaken our three betting range so much that we gain nothing vs a strong opponent.  Sure vs weak ones we can over c-bet and they will fold to much, but vs tough opponents we can never have as many hands on a 346r board vs a AKTr board as if we do we aren't pushing any equity preflop and making our three bets less profitable or unprofitable.  It kinda feels like a damned if you do damned if you don't scenario.  What I think may be the case in this scenario is that on certain boards our opponent shows a profit and there is nothing we can do if he plays well.  I suspect that may be the case on the 346r boards, he can c-bet 100% and we don't have enough hands to check call or check raise to counter his c-bet even though we may have 55%-60% hot cold equity vs his range.  What does occur though is we show a profit on the AKTr board when the preflop action is raise call and we c-bet 100%.  There is very little our opponent can do on those board textures since our range is much stronger than his.

oboltys88, I don't view AAxx on a 336r board as a bluff catcher.  I think of it as how many hands do I have to call or reraise with so my opponent can't bluff raise me.  Then I take the best hands in my range and go with them and fold the weaker parts of my range.  

As for adding more rundowns, I have tried but not found a reasonable way to include enough hands that cover all boards.  I 3-bet almost 100% of my AA combos and probably at most 20% of my 66 combos preflop.  Coming up with a preflop strategy where I have the same amount of sets on AKT and 346 boards doesn't work since we end up three betting 66J7ss and other weak hands that we aren't pushing any equity preflop making our three bets unprofitable since he can 4-bet and call in position.  Sure you can add a few hands in to give some coverage, but your range is still incredibly weak on the 346r board.

Brian, I think we can reduce his advantage a little bit on 346r but we will never make profit on this board v a good opponent. I would personally c/r 2.5x w/ my sets or better for value and some % of gutters and pairs+2 bdfd as a bluff if he cbets 1/2 pot. Id be folding to a jam with my bluffs and stacking off with value hands. I would be jamming sets or better on almost any turn and jamming my semibluffs when i pick-up a flushdraw on the turn. I think this kinda strategy works a little better than check-calling flop because this board a little more dynamic than 336r in a sense that roughly 66% of the time there will be flushdraw on the turn possible and ur gonna have it around 38% of the time so ur gonna be able to jam ur pr+fd and have around 28% equity v his stacking off range and fold equity. If u check call u take a risk of him checking back turn when u pick-up a flushdraw and not being able to jam to win dead money in the pot and him playing most rivers better than you (value betting and bluffing).

Brian, As far as 336r flop you have 18% v his stacking off range w/ dry AA and you fold out all his bluffs by jamming. By calling you lose roughly the same amount when bluff catching 3 streets and win more when he bluffs. Since this board is more static than 346r you don't run a risk of him picking up much equity with his air hands and outplaying you later in the hand. So imo bet/call >> bet/jam.

Awesome post, Ben.  Thank you.  That's what I was trying to say (without the exact #s), but I should really leave that kinda thing to you :)

Nesterz,

Thank you very much for putting in the work on this problem.

Could you explain a bit more about the numbers you used to reach your conclusion?

Here it is. Player 2 (red decision) calls, when he value raises (q%) and fold, when he bluff raises (1-q). I assumed, that he raised 3x times player 1 cbet size. So, I counted EV for player's 1 green decision, when he pushes and has 15% equity, when called, and then made him indifferent between folding and pushing. I got q=17.5%. Then, using this number, I counted overall players 's 1 EV for stack to pot=4, bet =0.66 and recieved EV=0.55*pot

Phil is 3betting many combos of KK and hands like AKQT, KQJT, KQJ9 etc yes so he doesnt hit the flop that often really hard but keep in mind villain has a near 100% opening range and was cbetting wide so much of his range will be very weak and just give up.

Phil is still going to have value hands though. He wont be 3betting raggedy KK nor most QQ combos PF. He can also have KQJTr, KQ54 with K-high FD, AhTh85. All hands that are either value or willing to continue vs a flop 3bet.

Accordingly Phil is going to need some combos to bluff with. He can opt to cr blocker hands like naked TP like he did vs FakeorReal in prior videos. Those will usually have higher FE. But naked medium FDs are also good candidates because they have a lot more equity and playability yet are just a little to weak to xc so his FE doesn't need to be extremely high to make it better than xf. 

I was curious about this as well.  I would check call with this hand on the flop.

What Zach said :)

Yeah I'm not entirely confident that I'm right, but I don't see much profitability in check-calling with this hand.  If I did, I'd go with a weaker drawing hand though... we can't only use blockers (and not hit many board changing turns) and we can't shy away from having a x/r range just because we don't have many monsters in our range because they don't either.

If he wants to cbet 90% on this board with his 90% opening range, maybe my best strategy involves raising a lot more of my weak KQ hands than I do now, and maybe even some more decently strong pair+draw hands.  Thoughts?

From a totally experience based preservative I have found check raising dry top two on these board textures not to be as profitable as check calling.  For one it greatly weakens our check call range, making our opponents able to value bet much more thinly by the river with hands like K8 and Q8.  Even vs someone c-betting a high amount they can make lots of calls in position and turns don't play exceptionally well for us out of position.  There are so many turns we have to check fold or bet and pray they fold, missing out on value from weaker hands or putting in money poorly vs his stronger ones.  

Here is my attempt at backing it up with math.  Lets assume our opponent can never raise us, but only call and fold.  Obviously a huge assumption, and I have to make other big ones but most that I will make work in our favor.  We hold KQ22 with no suits and the flop is the same in the video, with a runout of 3s on turn and 4d on river.  On the flop we check raised to $900, villain has to call 58% of the time assuming we have no equity.  In practice this would have to be wider.  If we assume he c-bets 100% and plays 90% of hands in the small blind he has 189443 combos of hands and has to call with 109877 combos or roughly a range of 90%:(*h*h,KK,QQ,88,KQ,Q8,K8,AJT,JT9,AA,K,QAT,QJT,AJ,AT)

Turn is the 3s and we will pot turn, so he has to call with 50% of this range with no equity.  On the turn his combos drop to 103777 since there is another dead card.  So he has to call a turn bet with a range of 90%:(Ah*h,Kh*h,Jh*h,KK,QQ,88,KQ,Q8,K8,AJT).

On a 4d river (I gave us the best runout we could hope for with our hand) he has 46288 hands as there is another dead card and assuming we bet pot he has to call with 50% of hands again, 23144 combos or a range of roughly 90%:(KK,QQ,88,KQ,K8).  Vs this range we have 48% equity so our river value shove is losing money in this instance and at best break even.

The point I am trying to make with this rough math is that even with a 100% c-bet freq (Which I don't think he has, even on this board) he is still an equity favorite on the river on one of our best runouts and only has to call with one worse combo of hands than ours.  Dropping his flop c-bet frequency to 80%-85% gets compounded by the river making our shove even worse than now.  In this example we just looked at one of the best runouts for our hand, if we assume runouts where we can't value bet turns or rivers (any heart, A, J, T or nine) I think it further strengthens my assertion that check calling is best at 100bb.  As we get deeper and he can start raising rivers with his KK combos and some bluffs it makes our line even worse.

I ran some numbers and discussed this hand a bit. Imo having Axxx in villains shoes and a big club is a better candidate to call down than a flush given Phil is polarized on turn and that hand does the best job of blocking his value range. 

That all said, this is a spot where even if Phil employs a fairly wide 4b range he estimated he has AA 50% of the time. Accordingly, I think villains range is so dominated by Phils that he won't have a profitable calldown with almost any bluff catchers especially because when Phil doesn't have AAxx he will have other hands that with SD that won't opt to bluff.