Pplbamba

Good video

50:13 Ac8h8s2s review table
you discuss leading club rivers if you were to call and you also mention the fact that you think you might x/r some ac hands on this turn. I think both of those considerations speak to the fact that x/r this turn might be worth considering. It doesn't seem like he can viably three bet a x/r and it also seems that even thought he might not delay Cbet a lot he might do it enough that you have some immediately turn fold equity in addition to the potential river fold equity you will have on CC and possibly the straightening cards in which 88 is relevant. I think there is also a very small chance that you can check blank rivers and have him check back a worse hand. Do you feel that these considerations might be overly optimistic? And if so wouldn't it perhaps be an argument for not calling that hand pre because not only is it a bad hand but in many instances it might be too thin to use its blockers effectively?

Table 3 36:21:

What I often find most surprising about your videos is how close your intuitive assessment actually matches the composition of your range. It appears that your range consists of about 20% hands that are weaker than 99+ meaning that the odds you lay him with a 1/3 pot sized bet are about exactly the odds he would need with an over pair. However, I don't understand why you think this would be a poor candidate for a c/r. Opponent likely has very few boats, even if he checks back the occasional boat on the turn. I can't imagine he has more than 7% boats in his river range and the majority of the time significantly less. He does seem to have at least 15% 9 high straights, however. I don't think you allude to whether or not he ever bets this hand for value. If he does, your hand seems to be a pretty good candidate for a c/r bluff. At the very least you block all the board pairing cards, and this in a spot where you probably don't have more than 5% dry 6's in your range, as opposed to probably at least 15% boats. Do you you expect him to call that 1/3 pot very often with overpairs? Do you think that he won't be betting 9-high straights very often? I suppose that if both of these assumptions holds true that the 1/3 pot sized bet is probably good.

9:04 Table 3 As2sAd5cTs board:
Heuristically seems like it would be rare at these stakes to find opponents who would check quickly on the river holding a full house. It also seems likely that even if he is capable of folding a flush, he probably won't do so when confronted with a small bet. Actually, I don't think you should be too worried about c/r either. If anything, it seems that sitting in his seat on the river with an inordinate number of dry trips relative to checked boat combos, that he might be inclined to over bluff with a c/r facing with a small bet. Therefore, small bet seems the exploitative play. Or do you think some of my assumptions are inaccurate?

Good video

Table 2 37:30 Ah7hAs5s:
I like your analysis of this hand. One thing I think you don't mention, though, that could be of some consequence is if you think opponent is peeling flop with gutters. You mention that he is peeling with 456 specifically and likely all 45 combos generally but given how narrow ranges are already, a4,a5,56 are not inconsequential parts of his range. Do you think he is ever continuing with these by calling?

I suppose if he ever had a flop raising range he could balance some 3x with some of these. It doesn't seem particularly good though. Nevertheless if he were to both call flop with some of these gutters and maybe also turn some JJ-QQ combos on turn into bluffs, for example, those with or without clubs depending on whether he thinks he can make you fold AA or wants to only turn his hands with low equity in bluffs, you may be up to 40% on the turn. But that to me seems optimistic and the sort of assessment you have to make on the turn prior to your river decision. Otherwise it appears against his turn betting range you're at least a 70% dog and should fold.Without some pretty specific reads, that appears the much better option.

Luckily in the heat of the moment he likely made the same oversight :)

5:35 table 1:

Had to do a double take on this one. However I'm pretty sure that you cannot turn a jack into a bluff on this board run out unless you are specifically trying to make him fold a pair in his hand. Any hand with a jack in it is still better than his high card hand. Your KQJ9 would be KJJJ4 whereas his AK hand is AK444 so you have better trips. A jack would only be a bluff if you were trying to make him fold a pair in his hand. I think that makes his call bad.

Thanks for the response.
I think you misinterpret slightly the significance of the line you quote. As opposed to being in reference to capped ranges it is directed at a comment you made in the video about IP being able to bet any four profitably in position after UTG checks diamond turns. The reason I think having more Ad in your flop checking range is significant is because I think UTG has more Ad overall, meaning that depending on how you structure your ranges, you can actually make the diamond turn better overall for UTG. I do not disagree with you that one need always have the nuts in every line in every spot. I think that is a miscommunication.

Still though, I'm curious, based on practicality or experience (just generally, you don't need to give super rigorous explanation) what sorts of hands do you feel UTG should be betting this flop with and why?

P.S. If I am not doing this incorrectly I believe that the toy game solution is that I bet 10000 something very close to 40% of the time 39.999% or something like that- my 20% hands that beat K8 and another 20% of total hands that don't, making K8 indifferent between calling and folding and giving me very close to .4 overall equity and giving you .6.

Good Video

Table 4 14:35:

Seems like a spot where whoever holds Ad in their hand will invariably win an overwhelming percentage of the time when diamond hits turn.

That being said, do you think it is right for UTG to have a betting range on this flop, especially one that includes his Ad hands?

Neither players seems to have an extremely distinct pre flop edge equity wise, although if you were more inclined to three bet your AA hands, as he probably suspects, then your calling range would actually be ahead of his range on the flop in terms of equity. You will also have the sets and two pair more often. It also appears obvious that he wants to have a check calling range. Therefore betting at any non negligible frequency seems like it could seriously tarnish his check calling range as well as potentially expose him to an exploitative raising strategy.

If it is the case that he is hardly betting the flop, and finding a way to frequently call nearly all his Ad hands, of which he will have more overall then you, then I think he may be able to protect himself from a strategy wherein you bet large with any four on the turn and river when a diamond falls. Similarly, not betting seems to go a long way towards better protecting hands like KKT that he might be check-calling, because it gives him a more viable means of c/r turn.

Thanks for your reply.
In reference to your second point I think we can pretty say definitively that the situation in which button bets a wide range and we check raise with a hand beating that range and with a decent amount of fold equity is a better situation for us than betting and getting raised by the button and just getting it in heads up vs his range. For one, this hardly seems like a good spot for him to bluff raise considering he has the small blind behind him and your betting range is likely decently strong.
For instance, if he just jams with this range against your bet, ahh,8t+:hh,kk+:hh,97+,9+:8tj+, you will be nearly a 60 percent dog.
Whereas if he stabs (lets say 325) when checked to with something like this (97+,ahh,qq-aa,8tj+:9+,9+:hh,qhh:8t+,khh:8t+,tj!9+!hh,tj+:hh,tt!hh,ah,9!hh!68+!tt+) he will be betting around 50% of the time and if he only calls your shove with this (97+,8tj+,jj+:hh,khh,ahh,qq+:8t+) after small blind folds, then you make 458 automatically.

I think regardless of the action small blind continuing puts us in a bad spot. If button bets and small blind raises, I think you can fold and not feel too bad about it, whereas if you bet and button calls and small blind raises, it still seems like you have to fold but this time feel worse about it.If you bet and they both call you are in a bad spot and probably don't win as much as you should. If you check and button bets and small blind calls you have a lot of options and I feel will always be able to do better than had you bet and they both called.

That being said, I think that the determining factor is how much equity you allow them to realize when the flop checks through that they wouldn't have been able to otherwise. For instance, even if the turn is an offsuit queen and it checks through and then you lose when they make a straight or a better two pair on the river, that would be a big loss. Calculating that would involve analyzing a very big game tree and it would be interesting if you, Phil, or anyone else tried to come up with a preliminary solution. That being said, as a heuristic, it still just seems better to me put this particular hand in your checking range and your 97 hands with backup in your betting range if for no other reason than to really challenge button's ability to stab profitably with a very wide range.

Good video:

12:23 table 1: both initially and as a result of how this hand played out subsequently, it really feels like a spot where you would like to check and try to get in a jam vs Ike and deal with it if it checks through.
For one, such a jam would certainly be profitable. You can effectively jam even against his relatively small stabs, which means that you should be getting some number of bet folds, even against hands like QQ w/out hearts (which I guess he might make a small stab with at some frequency) that do better against your particular hand than they do against your range. And even against the range he bet calls you are not doing so poorly.
When you bet, I don't think you can hope for two folds much over a third of the time and the hands that they would be folding: non-flush draws and wraps, non pair and straight or flush draws, non overpair and flush draws don't do great against your hand anyway, while you are likely not pushing much equity (a concept that you often mention) against the hands that do.
And the factor that seems most significant to me is that this is a hand that is extremely difficult to play on subsequent streets meaning that you would like to either get it over with on the flop or keep the pot smaller and more manageable which will give you a better chance of being able to show down two pair.
It seems you should be much more inclined to bet 97 in this spot with any sort of straight or flush draw or overcards to go with it.
Please let me know what you think

I think part of the discrepancy lies in the fact I am attributing to opponent what I consider to be a sounder strategy than the one he is apparently playing. I don't like any of the decisions he made in this particular hand.
I have him three betting narrower range pre (10%) against an open and your flat. I don't think his actual hand is a good three bet. As is having him three bet this range pre $3b15o,20% means that he will have about 55% equity on 9h5hts against your range of ($Fi40)!($3b15i)!(aa) and will be folding a third of the time betting the same range I listed in my previous post, making the shove with your particular hand profitable, so you're right in that regard, and I retract my previous contention that it is negative EV. Given his frequencies it very likely is +EV.

Taking its immediate profitability as a given, I still think it is hard to imagine a shove very often at all doing better than a flat, at least in my opinion, although proving it would involve going through all the whole turn and river decision trees. I think that even using your metrics that it would very likely amount to more than 11.

Moreover, it seems correct to put this particular opponent to as many decisions as possible. Given the fact that he auto-bet this hand with this sizing and then had to consider whether or not to go with it means he will be likely be making bad decisions across multiple streets increasing your capacity to exploit his strategy.

I think the strategy you're attributing to opponent is a bad one, although because it was you rather than me playing against him, I'll take your word for it. In my sim (PokerJuice) I had opponent betting this range ahh,9t+,qq+:hh,t+:8jq+,9+:qj+,kj!t+!hh,kq!t+!hh,qq!hh!78+,9!t+!qj+!hh,jj!hh!78+,ah*!hh!kk+ which is 46% and stacking off with this range 9t+,qq+:hh,t+:8jq+,9+:qj+ which is 37% which leaves hero at -15. I also had him 3 betting a narrower range.I would think that your sim is optimistic and mine is cynical and that the actual result would lie somewhere in the middle. At the very least, I would think that calling would realize a lot more equity than shoving against the part of opponent's range that is going with it and whether it induces folds against hands that have a ton of equity against yours is up for debate.

Good video:

Table 2 21:30

I actually think flatting 8dKhJsQc would have in this instance been a lot better than shoving, particularly given what opponent showed down. This is probably about the weakest hand you're going to see opponent go with and you are still a 60-40 dog. Moreover, I think it is important to note that this is a texture where opponent will likely have very few bet folds. Unless opponent is very weak, he will likely not be bet folding very many combos of KK+ at all leaving things like dry KJ and KQ gutters and dry QQ,JJ, and Ah which based on preliminary numbers would certainly constitute less than 30% of his overall flop betting range. This actually makes shove very slightly negative EV. Conversely, calling allows you to use Kh which may frequently become important, most obviously on this actual runout, but also in situations wherein you would like to continue calling but don't feel comfortable bluffing without blockers on the river.

What is your impression of opponent flop Cbet? Mine is that it is bad. He was lucky in this instance because you raised with basically the weakest hand you are going with but in many situations, such as if you had called, it will end up hurting him. So I think that in addition to being the best vacuum play, flop call with this hand and shove with a stronger range will end up being the best strategic play as well.

Good video:

27:15 table 1 Ac8c- I think calling all flop range and then c/r turns and rivers is a viable strategy. And I agree that based on that strategy you want to have a c/r range on the turn with nut flushes, and perhaps the second couple of second nut flushes you mentioned, but I don't think you need to do it at the frequency at you mentioned. After you are check raising you are playing a two street game so it is not necessary to have a 2:1 value to bluff ration but rather closer to a 3:2 or 1:1 value ratio so long as you bet river at an appropriate frequency (and opponent should be simply calling 100% given that you are c/r with nut flushes and blockers). Given that it seems reasonable to occasionally call with the nut flush to protect your weaker hands on rivers, although the majority of nut flushes should still fall into the c/r range. Would you agree?

Good video
20:08: You reference checking as a means to protect your river checking range. However, given opponent's lack of hands worse than two pair (about 16% according to my analysis) as well as possible inclination to check back flushes (especially T-high or worse which constitutes about 9% of his 14% flush range) I would think that this is a spot where you should be leading your nut flushes much more frequently than you check them. It seems doubtful that you will be able to get a successful c/r in against those 9% of flushes whereas they would very often call a lead. You also really want to target the 70% of his two pair range (according to my analysis) and I don't think you have much to worry about the 16% of his range that is worse than two pair (13% that is worse than an ace) because you will have other flushes to protect yourself with anyway.

Good video.

14:32 Table 4 KhKsThTd:

My first impression was also to bet the turn. And initially I wasn't entirely convinced that checking back might be good. However, after running some preliminary numbers I think that you might be relatively spot on in your analysis.

I had him continuing close to 59% on the flop with around an 8% value CR, so he should be making it to the turn with around 50% of his pre flop range.

With that in mind it appears that around 11% of the time on this turn card he should have j6+ and have you basically drawing dead.
An additional 18% of the time he will have j+,qq+:(hh,cc) (his turn calling range presumably) against which you have 85% equity. (66 without clubs or a wrap is about 4-5% of his turn range)
And qq+,hh,cc,AKQ (not counting j6+) is 65% of his total flop calling range against which you have 95% equity total.

So betting gets him to fold the vast majority of his range on the turn, against a large portion of which (qq+,hh,cc,AKQ) you might potentially get a river bet out of.

Another consideration is that he might very well stack you over two streets with his 11% j6+ if you bet the turn (and potentially the river), when he might not otherwise.

Finally, if he does call the turn with J+ and you bet the river, you give him the opportunity to either fold or c/r bluff rather than call with some of these hands, for instance on flush rivers, when he does not know how thin or not you may be value betting. And assuming he does it in a somewhat balanced manner it really disincentives you from betting over the course of two streets.

So all told, it makes a lot of sense, at least in a vacuum, to check back this hand for it helps protect you from the part of his range that beats you, or can potentially bluff you, and also exposes the part of his range that is basically dead against your hand to situations in which it might lose another bet.

7:20 AAJ6 vs sb:
sb three bet range against your UTG range likely pretty tight so
$3b8o minus AA since he did not get it in
flop is 50-50 equity-wise
SQEQ: 32:09

he has flushes 30% of the time, he has two pair or better (which i presume usually constitutes KK combos almost exclusively) an additional 10% of the time, and then K+ an additional 17%

his 40% 63+ and hh range has 93% equity against your hand

with just his 17% k+ (without 63+ or hh) he has 34% equity against your range (so you do gain a very slight amount of EV with your exact hand by having him fold rather than call a shove with this part of his range)

against the 43% of his range that is not K+ he has 21% equity

if you shove and he calls 63+ and hh and folds everything else you make $46

if you bet $30 and presume he balances by just calling his entire continuing range of
63+,hh,K+ then you make $62 immediately but have very tough turn and river decisions IMO- and you also have to deal with contingency of him possibly c/r balanced with some flushes and perhaps the occasional blocker against your bet or choosing to bluff this blocker on subsequent streets
Against his calling range, you only have requisite equity to get it in on 18 different turn cards (presuming he isn’t overfolding), constituting the bottom end of the deck 6 and below and Ax. A lot of cards are pretty close.

if you check and manage to win just your share of the pot on subsequent streets you make $71

so it seems to me that you should be able to do better than shoving by betting small or checking back but that depends on your ability to be able to balance this hand with the rest of your range that would take these actions and play decently well against what should be a relatively polarized range on his part and also a subset of hands (K+) more capable of realizing their equity. Against an opponent who plays more straight-forwardly and may even fold some K+ to a very small bet, betting small seems best, especially if that opponent would shove sometimes and almost never as a bluff- would make your turn and river decisions much easier. Against someone extremely tough and capable of balancing and realizing equity and putting you in really thought situations, checking back might be slightly better. But I don’t know how much these flop numbers might change your assessment of the situation.

Alright so bottom right last hand QcJs9h8d
I gave button 60%,$FI50-$4b5,60%-55%
I gave you $FI30-$3b15o
And I gave BB $3b15o
Obviously these are not at all precise but let me know if the you think they might work for the purpose of analysis.

So on the flop it appears you actually have slightly less T+ than they do, they both have about 20% and you have 18%

BB has 37% (T+,kk+:dd,qj+:dd,add) and button 30%
your hand is getting crushed against these ranges, it has 15% against both of them and 32% if only button continues

button has:
T+,jj+:dd,qj+:dd,add,jj!dd!qj+
33% of the time
So assuming pretty tight continuing and very tight bluffing ranges, even just on the part of the button, it looks like you are going to have a very tough time leading this hand given that optimistically you can expect them to continue at least a combined 58% of the time
.37+.33-(.37)(.33) ip against your hand which does very poorly against their hands

I think the interesting aspect of this hand is that BB bet his hand on the flop. This is a very weak hand relative to the texture against two callers and if he is betting all these hands at a high frequency, the range I think he will be capable of defending will be pretty weak overall.

If he is betting ( kk+,t+,qj8,add), this constitutes 60% of his total range and has 60% against your actual hand so I suppose a call is not very bad. However, if you find that he is consistently C-betting this range( kk+,t+,qj8,add) in this spot (kk+, add, and basically the hand you were contemplating leading) and calling off with this range: kk+:dd,t+,qj8+:dd your shove will be very profitable as he will be folding half the time. Of course factors like him sometimes checking rather than c-betting aa-kk:dd speaks even more in favor of a shove.
On the other hand given what a large part of his range KK constitutes, this is actually not all that good of a turn card for you at all. Even though you made your straight, you are actually still an equity dog to his range with 45%. Granted, given that he will not be calling with all these hands it is still profitable, but not nearly as much so as jamming the flop.

It would matter in a more general sense if it were 41% but significantly less so for the type of analysis I am conducting. As an extreme although plausible hypothetical,because I don't have time to do a more practical one, let's say you have the option to C-bet or check back the flop and when you do C-bet he will check raise 15% of the time and you will have to fold 50% equity. But he will also fold 50% of the time to your bet with a range that has 50% equity vs your hand.In this case, you would have to believe very strongly, and probably unrealistically, in your ability to take equity away from your opponent on subsequent streets to justify checking back the flop. Our particular hand definitely lies somewhere in the middle so is much more of a gray area because he is folding 35% equity 45% of the time. What my equation does show is that even if it is the case that he check raises you off your 41% equity 15% of the time, it is still a better scenario than the case in which he check raises you less frequently but calls you with a very wide continuing range that has good equity against your hand. And because this is a profitable bet and fits into a balanced strategy the onus would be up to the person inclined to check back to demonstrate that with his check back strategy he can achieve more equity on subsequent streets by checking back, than the equity he can achieve immediately by betting- which makes the equation I use for the immediate equity that can be gained with a bet, a valuable one.

Just reran it to check. Sometimes, when I am running many sims, Poker Juice will shoot out slightly distorted numbers. It appears that number is wrong. Your hand only have 33% against his c/r range.

However, I don't actually think it would matter even if it were 41%. Obviously, it appears worse the more equity your hand has vs his range. But as shown in my first post, even against a low c/r percentage and a wide continuing range you stand to lose immediate equity by betting (that's the -2 number from my first long post). And in that case your hand has only 28% equity vs his check raise range. So comparing it to this output demonstrates that you would still rather bet your hand in this instance, despite the fact that he check raises more frequently and you would be folding significantly more equity when he check raises. Again, it is counterintuitive but I am using the exact same equation so it is comparing apples to apples.

Hey Alex, looks like we now agree on most stuff.
That's actually probably an important part of the equation to explain.

Ok. So again when you bet, you can subdivide his range into three parts. One includes the hands that he will c/f. Another includes the hands that he will c/r. And the third is hands that he will check call. As stated previously, his check call range has an equity advantage vs. your hand. So when you bet the flop he gains equity with his check call range on the flop that he would otherwise not gain if you checked back. So when you are calculating the equity of a C-bet you stand to gain immediate equity against the part of his range that c/f the flop.However, he stands to gain immediate equity against you when he c/r and makes you fold your hand. He also gains equity when he calls you with a range of hands that have better equity than your hand.

When he folds:
The pot size is 225 and his c/f range has 35% equity vs your hand and he will fold around 45-46% of the time so this is equity you stand to gain: (225)(.35)(.46)

When he calls:
After he calls the pot size will now be 225+167+167 and he will have 58% equity. To get to that point, though, he needed to call your bet of 167. Also he only gains equity with this part of his range because the pot size is larger so you needed to discount the amount of equity he would already have in the pot anyway if you instead had checked back so (225)(.58). And overall, he check calls 37% of the time vs your bet. So here is the equation for the equity he gains with his check call range when you bet the flop.
((225+167+167)(.58)-167-(225)(.58))(.37)

When he c/r and you fold:
After you bet the pot size will be 225+167. You will have 41% equity vs his c/r range and he will be c/r 14% of the time.So the equation for the immediate equity you stand to lose is:
(225)(167)(.41)(.14)

So the overall equation for the equity you stand to gain immediately looks like this:

(225)(.35)(.46)-((225+167+167)(.58)-167-(225)(.58))(.37)-(225)(167)(.41)(.14)

Hey Alex, thanks for responding, I understand that it must take you a lot of time to reply, particularly given the language barrier. My Spanish is pretty good but no doubt no better than your English, particularly discussing something with so many uncommon words.

Ok so in the course of thinking about what we have discussed I realize that we've changed topics and that may be driving some of the confusion. I think there are still a few things left to clarify.

The first point, with which you agreed in your last post, is that a C-bet is good on this flop with this hand. So we maintain a consensus on that point. Just to make sure, do you think that this is a decent C-betting range?

j6+,ass:3+,ass:25+,ss:45+,aa-qq:ss,j+:25+:ss,j+:457+,j3+:25+,63+:ss,qq-aa:45+,qq-aa,j:ahh!(57,54),6!45+!3,57!ss,99-TT,77!ss,55!ss,57!6+!ss!4,47!6+!ss!5,qtk:hh,jtq:hh

It's about 55% and includes the hand we have been looking at. It also includes a fair number of SS and straight draw check backs, although most j and better hands with nothing else are being bet, because all bets, based on his defending frequency, are immediately profitable, and these would be the hands that we most like to just win on the flop. It also includes enough value hands (conveniently listed first and mostly in order of how well they can be defended against a check raise) that I think he would have a hard time attacking us very light.

I realize now that the argument has shifted. The reason I chose to use these equations in the first place is because in your video you make the argument that you would be more inclined to C-bet against a lower c/r frequency and against an opponent less likely to attack you light. When I initially heard it, it made sense. But testing the assumption against an opponent most inclined to not let you C-bet profitably with any four cards (that is he has a high c/r frequency and a wide calling frequency), I established that based on the nature of your hand and the nature of his potential c/r range, that you actually did better by C-betting when he was more inclined to c/r light and defend wide than when he was less inclined to do so. My calculations in my first post are in favor of C-betting against someone who will attack your bet more aggressively. In the course of conducting this analysis I realized that the reason for this is that if he is going to widen his c/r range, the most likely candidates to do so with will be his really dry Jx hands against which your hand does poorly anyway. In which case C-betting your hand is good not only as a range play but also in a vacuum.

I've never heard anyone say, "I think we should be more likely to bet this hand against a higher c/r frequency even though we will have to fold to the check raise."
Which is why to me this conclusion should be an important building block in constructing your overall range. Obviously you want to have a more global perspective on your frequencies, but you also want to know how each individual component works. Knowing that your hand actually works better against a high c/r frequency may mean in the future that you use that stat differently than the standard way must of us are accustomed to.This will depend on your actual hand, the board, and the composition of your opponent's potential check-raising range.

I think the argument shifted in your second post because you did not accept the composition of my theoretical range in the first post. So all I was trying to establish in my second post was that even against his actual range, that the equation I was using in the first post still holds. Granted this is a micro perspective. Showing that C-betting your hand works as part of your overall range is another matter. But again, if you think that the C-betting range I have listed above works against the range he is playing, this should not be a problem.

As for my equation. I think that the equation I was using is different than establishing whether a bet is profitable or not and works better in the context of the first post.Obviously a bet remains profitable as does likely a check back, but in the context of the first post I think the equation helps establish that you actually gain more against an aggressive check raiser than you do against a less aggressive check raise. I think you are right in asserting that my equation is not as good for the second post. And I think some of the conclusions I made in the second post are overly broad and that I state them too strongly. The equation does not definitely establish that betting gains more EV than checking, but I think it shows more than you think. First of all, to reiterate, the equation is different than an equation to establish whether or not the bet is immediately profitable. As you recognize, you could do that much more simply .75/1.75= .42. This time, as will usually happen, the two equations correlate, but this will not always be the case. For instance, in the first post, in both instances he is continuing with about 62% of his range but one equation gives a negative output and the other a positive output. What the equation does show is that you gain more immediate EV against his range than he gains against yours by you betting. So you are not actually too worried about him calling so frequently with such a strong hand relative to yours that you are actually costing yourself by betting in a way that you would not cost yourself by checking. And I think my analysis points more generally to the fact that you have less to lose against his 15% c/r range that folds you off on the flop and 37% of hands against which you are an equity underdog and calls the flop then you have to gain against the 45% of his range that will just c/f the flop. My equation says he folds equity immediately. Your hand does not have good back draws and by checking back you are capping your range. When you bet will be be able able to fold him off a lot of his equity immediately and your range will remain uncapped which gives you more room to navigate against his 37% calling range.

But you are right in asserting I did not prove that you definitely make more money across three streets by betting rather than checking.And I think you are also correct that most of your analysis should be directed at establishing whether or not the bet fits well into an overall value/bluff, board coverage C-betting strategy. But it is also useful to establish what your bet is accomplishing against different parts of his range so that when decisions are close or when you are deciding more generally what types of hands to include in your overall C-betting strategy against his range, you know which hands work best. For instance, in the future if you still feel that as part of your overall strategy with your range this hand would be a borderline C-bet and you want to play a mixed strategy with it, after conducting this analysis you may actually be more inclined to bet it when he has a high c/r stat and more likely to check it back when he has a lower c/r stat even though on first glance this reasoning seems somewhat counter-intuitive.

Good video.

Table 1 12-14 minutes jh9h:
I want to get your general impression of his strategy. He seems to be checking an inordinate number of flops after 3 betting and choosing to do so on this board seems to me indicative of the fact that he is overdoing it. Am I correct to think that he can cbet profitably his entire range on this board (842)r for his standard half pot-sizing? And if so, how much more do you think he might be able to possibly make by employing this c/c strategy that seems much more difficult to balance? Also do you think he is actually balancing it?

The second part of my question deals with the first. What sort of metrics do you use here to prevent yourself from over-stabbing. Do you feel he is ever c/f this flop with any frequency at all? Is he never c/r? What is the balance you try to achieve between making sure you have the backdoor flushes straights as well as the j, t, j, q cards in your range against not betting too frequently with all your backdoor flush + backdoor straight + overcard hands on the flop? I do not think you can necessarily even call all these hands profitably against a balanced half pot cbet on his part if he is playing a balanced and relatively polarized turn and river betting strategy. So my conjecture is that you achieve something by checking a large majority of these hands back (that you wouldn't if he bet) since his hands are likely better and he is almost never folding (and you have very few combos-maybe 11- of very strong hands). Do you agree with this?

Open ended questions but I would really like to know what you think.

Also, as i mentioned before I think this hand can easily be bet as part of a, balanced and difficult to exploit betting strategy on your part but showing that would require many more calculations.

I realize that the way I analyzed the hand was somewhat strange, but I believe viable, although certainly difficult to articulate; I probably could have done a better job If you think there is something off about the assumptions, please let me know.

Alex thanks for your response. In the interest of not spending a ton more time on this problem, I am going to try to explain more generally what I am trying to do and then address your specific concerns.I will highlight my assumptions to make them more obvious.

I. Overall argument
1. My main point was that perhaps we should be more inclined to bet against an aggressive check raiser with our specific hand, even though we would be forced to fold it.
2. My secondary, although more implicit conclusion, was that with this specific hand, KQT6, we should probably C-bet regardless.

II. Your concern number 1
I agree with you that opponent is not likely calling 99+ and folding some of his weakest Jx and probably some of his 6+gs. Believe it or not I did not include those hands in my initial calculations. The reason I chose to include them here is that I was trying to make it as potentially unprofitable as possible for you to bet your specific hand KQT6. The fact that he is leading 5% (which will certainly include some of his stronger hands that might detract from his value c/r range) and only continuing with 50% speaks even more in favor of my argument that you should cbet.

III. Your concern 2
I do not understand why you think this. All my calculations reference the bet size you actually made: 167. Nowhere do I include you making a pot sized cbet as far as I know.

III. Your concern 3
Referenced above

IV. Your concern 4
I do not try to do this. Here is the one fundamental assumption I make explicitly:
"Your hand plays at least as well on turn vs the subset of hands that he calls the flop with against your bet as it would against the same subset of hands if you checked back the flop because you leave your range uncapped by betting"

In other words, all I am assuming explicitly is that you do at least as well against the range he will call your cbet with as you would do against the exact same range if you checked back the flop.

Here is my implicit assumption (and this is taking into account the new set of ranges I am giving him that are more consistent with the numbers of 5%,50%,45% -lead, defend, and c/f you give me in your post):
When you check back you are not able to make more money with your specific hand against the part of his range that would c/r you off in on the flop as opposed to the amount of money he is able to achieve when you check back with the part of his range that you did not cbet him off on the flop. Because the part of his range that you did not cbet him off on the flop constitutes 46% of his range and has 35% equity against your hand and he is check raising you off of 41% equity 14% of the time, I think you can say clearly that regardless of your turn strategy you will never do better with these portions of your range by not Cbetting the flop.

V.
What I will now try to do is rewrite my formula using the actual as opposed to theoretical range you give villain, plus a high c/r frequency, and try to see if that confirms my argument that a Cbet will gain EV against his range.

Here is his new overall continuing range including all of his c/r, c/c and hands that don’t lead.

His new c/r range:
j!ss!25+!3!6,ass:6+,ass:74+,j6+:ss,ss:457,j3+:45+,66+,j6+:25+,45!3+!2!7!ss,as:75+!j+,ahh!j+!45+:(57,74),ahh!j+:(78,qt),qtk:hh!ss!j+,6:(74)!ss!3!j!qq-aa!5,6:(75)!ss!3!j!qq-aa!4 (includes the 6x and gutshot combos you mentioned)

minus

j!ss!25+:[T-][T-][T-]!3!6 which he is now c/f and j3:ss which is is now leading
=15.47% c/r of his preflop range (59% against your range)

His new calling range
j+,ss,245+,3+:45+ again minus his c/r range, leading range, and j!ss!25+:[T-][T-][T-]!3!6

which constitutes another 37.35% and has 58% equity vs your hand

Now the portion of his range that is c/f which is about 46% of his total pre flop range (which corresponds closely to what you said based on the fact that he is leading 5% and defending 50%):

*!((j3:ss,j!ss!25+!3!6,ass:6+,ass:74+,j6+:ss,ss:457,j3+:45+,66+,j6+:25+,45!3+!2!7!ss,as:75+!j+,ahh!j+!45+:(57,74),ahh!j+:(78,qt),qtk:hh!ss!j+,6:(74)!ss!3!j!qq-aa!5,6:(75)!ss!3!j!qq-aa!4,j+,ss,245+,3+:45)!(j!ss!25+:[T-][T-][T-]!3!6))

and this 46.37% of hands have 35% equity against your actual hand
so when you check back these hands will remain in his range whereas when you bet he will fold flop

So now I believe that the difference between betting and checking can be distilled to two decision trees- one involves you checking back against the 95% of his preflop calling range that does not lead and the other involves you c-betting, getting him to fold his folding range, getting him to call his calling range, and him folding out your hand with a c/r
So the equation for how much equity you get him to fold when you bet vs how much equity he gains vs you when you bet is (keep in mind this equation takes into account that you are betting 167 into 225 (for my equations I did not include rake but it is negligible)

(How often he check folds)(Equity his c/f has against your hand)(pot size)- ((Pot size after you bet and he calls)(his equity)-bet-his portion of 225 had you checked))(frequency at which this occurs)- (his c/r frequency)(your bet plus initial pot)(the amount of equity your hand has vs his c/r range)

(.46)(.35)(225)-((167+167+225)(.58)-167-(.58)(225))(.37)-(.14)(.41)(167+225)
36-10-22=4

So using numbers that correspond much more closely to the hands and numbers you have me, this bet will be more profitable than checking back as long as you meet the conditions I reference in IV which I think you undoubtedly will. And in this case, this will also extend over to the cases in which opponent is using a lower check raise frequency because he is folding an even larger percentage of preflop range.

((Pot size after you bet and he calls)(his equity)-bet-his portion of 225 had you checked))(frequency at which this occurs)

Apparently brackets function as some sore of hyperlink in red so the parts of the equation in red should look like this ((559)(.64)-167-144))(.51) and ((559)(.57)-167-128))(46)

Hey Alex, Thanks for your response, what you said makes sense intuitively. While I was awaiting your reply I ran some numbers using PokerJuice and what I find really interesting is that I think the results may be counterintuitive depending on the range that you assign to opponent. That is, you may do better c-betting when he c/r 15% than when he c/r 10%. Also based on my assumptions and analysis, c-betting will do better than checking back only when he has a 15% three bet and not when he has a 10% 3 bet.
I have villain flatting pre with 85%-$3b15o against your hand KdQcTd6h
Here are my assumptions for villain value c/r (hands he can get in with):
ass:6+,ass:74+,ss:457,j3+:ss,j3+:45+,66+,j6+:25+=7.35% of his pre flop range so close to what you said

adding in these hands as c/r bluff brings his total c/r to 10%:
45!3+!2!7!ss,as:75+!j+:*!ss,ahh!j+!45+:(57,74),ahh!j+:(78,qt),qtk:hh!ss!j (some dry gutters to the nuts, most dry As, some ahh without much else, some backdoor straight and flush draws)

Also adding in his super dry Jx will bring it to 15%
j!ss!25+:[T-][T-]!3!6

I have him calling this subset of these hands that are not in his c/r range:
6+:25+,99+,ss,245+,3+:45+ (6 plus with gunshot and better, 99 and better, ss, wraps, and 3 with open ender or better)

Overall this is a pretty wide flop range that has him defending close to 61% of his range at a slight overall range disadvantage (48-52% range vs range on flop) making it difficult for your weakest hands (like the hand you have) to cbet profitably.
The difference between the 10% number and the 15% number is that he moves his weakest and most dry Jx into the c/r range in the 15% instance

So my next set of calculations I make the following assumptions:
1) Your hand plays at least as well on turn vs the subset of hands that he calls the flop with against your bet as it would against the same subset of hands if you checked back the flop because you leave your range uncapped by betting
2) Given 1, you can calculate profitability of flop bet based on the equity you are able to deny him vs the equity he is able to achieve or deny you

Also it is important to note that his calling range has better equity than your hand so for the purposes of this calculation I am just having him achieve that equity, although you should be able to do better in position than allow him to achieve 100% of it

These calculations are from poker juice based on the ranges I mention above.
So: (How often he check folds)(Equity his c/f has against your hand)(pot size)-(pot size after you bet and he calls)(his equity in that pot)-your bet-his portion of the pot if you had checked-(his c/r frequency)(your bet plus initial pot)(the amount of equity your hand has vs his c/r range)

vs his 10% c/r:
(.39)(.38)(225)-559(.64)-167-144-(.10)(.28)(392)
33-24-11=-2

vs his 15% c/r
(.39)(.38)(225)-559(.57)-167-128-(.31)(.15)(392)
33-11-18=+4

Conclusion: Even if opponent is able to achieve 100% of his flop check call equity, you do better betting against his 15% c/r range than checking. Against 10% you do worse based on this calculation, but again this is assuming he achieves all of his check call equity, so this might also very well be a bet. For this to be otherwise, you would have to have different assumptions about the composition of his flop check raise range. In this instance because you achieve a lot of equity against his c/f range and because you are not really concerned about folding if he is c/r a lot of his dry Jx, a bet actually works well.
Also, I don't want to go down this rabbit hole, but I think it would be really hard for him to c/r more than this without being exploitable. And adding hands that he would otherwise be folding and do not block Jx could be really difficult to play, especially since I already gave him what I think is a reasonable amount of gutters, dry open enders, dry As, and what would amount to his stronger backdoor draws, all of which can't call vs shove on your part.

first hand qckd6htd table 2 flop 3s6sJh:

Can you explain what your rational is when you say that you would not be inclined to cbet this hand when you anticipate he will be c/r 15% on this board whereas you would be when he would c/r 10% or less. It seems perfectly reasonable that you would have a threshold for how often villain must check raise before you start checking back but I am wondering what you are basing it on. Is it just a rule of thumb based on experience? Is it what you notice other players are doing? Is it based on some sort of equity calculations? I think it's pretty cool that you have a distinct number you are looking at and I'm just looking for a general impression of how you come up with this.

actually in those spots where you have at least 27% on the turn it looks like you more often you have on average 55% against his range so 100(.4)-(.6)(88)= -12 so slightly less negative but still losing