Marginal how? Can you provide math to show that they're very close in EV?

With a c/c line, assuming villain bets all offsuit broadway hands with a diamond, all flopped flushes, all sets, some overpairs and underpairs, we are left with a range that looks something like this. Granted this range is rather air-heavy given hero's read of villain betting a good % of the time when checked to. These are the hands from which villain called preflop that have some sort of equity.


Board:

Equity Win Tie
UTG 62.65% 61.73% 0.92% TdTh
UTG+1 37.35% 36.43% 0.92% 22+, AdKd, AdQd, KdQd, AdJd, KdJd, QdJd, AdTd, KdTd, QdTd, JdTd, Ad9d, Kd9d, Qd9d, Jd9d, Td9d, Ad8d, Kd8d, Qd8d, Jd8d, Td8d, 9d8d, Ad7d, Kd7d, Qd7d, Jd7d, Td7d, 9d7d, 8d7d, Ad6d, 8d6d, 7d6d, Ad5d, 8d5d, 7d5d, Ad4d, Ad3d, Ad2d, AdKh, AdKs, AdKc, AhKd, AsKd, AcKd, AdQh, AdQs, AdQc, AhQd, AsQd, AcQd, AdJh, AdJs, AdJc, AhJd, AsJd, AcJd, AdTh, AdTs, AdTc, AhTd, AsTd, AcTd, Ad9h, Ad9s, Ad9c, Ah9d, As9d, Ac9d, Ad8h, Ad8s, Ad8c, Ah8d, As8d, Ac8d, Ad7h, Ad7s, Ad7c, Ah7d, As7d, Ac7d, Ad6h, Ad6s, Ad6c, Ah6d, As6d, Ac6d, Ad5h, Ad5s, Ad5c, Ah5d, As5d, Ac5d, Ad4h, Ad4s, Ad4c, Ah4d, As4d, Ac4d, Ad3h, Ad3s, Ad3c, Ah3d, As3d, Ac3d, Ad2h, Ad2s, Ad2c, Ah2d, As2d, Ac2d, KdQh, KdQs, KdQc, KhQd, KsQd, KcQd, KdJh, KdJs, KdJc, KhJd, KsJd, KcJd, KdTh, KdTs, KdTc, KhTd, KsTd, KcTd, Kd9h, Kd9s, Kd9c, Kh9d, Ks9d, Kc9d, Kd8h, Kd8s, Kd8c, Kh8d, Ks8d, Kc8d, Kd7h, Kd7s, Kd7c, Kh7d, Ks7d, Kc7d, QdJh, QdJs, QdJc, QhJd, QsJd, QcJd, QdTh, QdTs, QdTc, QhTd, QsTd, QcTd, Qd9h, Qd9s, Qd9c, Qh9d, Qs9d, Qc9d, Qd8h, Qd8s, Qd8c, Qh8d, Qs8d, Qc8d, Qd7h, Qd7s, Qd7c, Qh7d, Qs7d, Qc7d, JdTh, JdTs, JdTc, JhTd, JsTd, JcTd, Jd9h, Jd9s, Jd9c, Jh9d, Js9d, Jc9d, Jd8h, Jd8s, Jd8c, Jh8d, Js8d, Jc8d, Jd7h, Jd7s, Jd7c, Jh7d, Js7d, Jc7d, Td9h, Td9s, Td9c, Th9d, Ts9d, Tc9d, Td8h, Td8s, Td8c, Th8d, Ts8d, Tc8d, Td7h, Td7s, Td7c, Th7d, Ts7d, Tc7d, 9d8h, 9d8s, 9d8c, 9h8d, 9s8d, 9c8d, 9d7h, 9d7s, 9d7c, 9h7d, 9s7d, 9c7d, 8d7h, 8d7s, 8d7c, 8h7d, 8s7d, 8c7d

This is 313/1326 hands (23.6%). Given a c/shove we are looking at probably only the following hands continuing (strong TP+flush draw type of hands, flopped straights with a flush draw, JJ+ with a diamond, sets), which comes up to 138/1326 combos (10.41%).



Board:

Equity Win Tie
UTG 44.83% 43.63% 1.20% TdTh
UTG+1 55.17% 53.96% 1.20% 99-77, AdAh, AdAs, AdAc, KdKh, KdKs, KdKc, QdQh, QdQs, QdQc, JdJh, JdJs, JdJc, AdKd, AdQd, KdQd, AdJd, KdJd, QdJd, AdTd, KdTd, QdTd, JdTd, Ad9d, Kd9d, Qd9d, Jd9d, Td9d, Ad8d, Kd8d, Qd8d, Jd8d, Td8d, 9d8d, Ad7d, Kd7d, Qd7d, Jd7d, Td7d, 9d7d, 8d7d, Ad6d, 8d6d, 7d6d, Ad5d, 7d5d, Ad4d, Ad3d, Ad2d, AdKh, AdKs, AdKc, AhKd, AsKd, AcKd, AdQh, AdQs, AdQc, AhQd, AsQd, AcQd, AdTh, AdTs, AdTc, AhTd, AsTd, AcTd, Ad9h, Ad9s, Ad9c, Ah9d, As9d, Ac9d, KdQh, KdQs, KdQc, KhQd, KsQd, KcQd, KdTh, KdTs, KdTc, KhTd, KsTd, KcTd, Kd9h, Kd9s, Kd9c, Kh9d, Ks9d, Kc9d, QdTh, QdTs, QdTc, QhTd, QsTd, QcTd, Qd9h, Qd9s, Qd9c, Qh9d, Qs9d, Qc9d, JdTh, JdTs, JdTc, JhTd, JsTd, JcTd, Jd9h, Jd9s, Jd9c, Jh9d, Js9d, Jc9d, Td9h, Td9s, Td9c, Th9d, Ts9d, Tc9d

C/C you have $100 to win $235 with 62.65% equity
C/R you push an extra $345 to win $335 with 55.9% fold equity, and 44.83% equity when called.

EV of C/C = 0.625 * 235 - 0.3735 * 100 = 109.525
EV of C/R = 0.559 * 335 + 0.4483(0.441) * 635 - 0.5517(0.441) * 345 = 228.866

You were right in saying that up to this street EV was probably not marginal and thanks for calling me out on this. This was probably the reason I was favoring a raise in this spot before I did the calculations. But if you allow for the fact that villain is continuing with a far weaker range and will barrel weaker hands on the turn, this could in fact bring the 2 closer together.

Are we looking to bet/gii or b/f? What would be our sizing?

bet/ get it in on the flop

i dont like gettin blown off out hand if it checks through

also if hes playing position well he may raise the flop or float- which we want with this hand as its super strong

c/r really will only get action from hands that have us in bad shape most of the time

cbeting is more balanced and can get multiple streets of vakue vs a lot of hands

First of all, appreciate the effort.

I agree with most of your range assessment - not much would change even if I expand that ~300 other hands and reduce ~130 down.

Here is my only problem, in which you're comparing apple to orange. EV of C/C accounts for ONLY flop play, ignoring both turn and river.

Whereas EV of C/R accounts for every street because hand is going to showdown.

Work is not done yet. Perhaps do a few scenarios with certain turn and river card and discuss how to proceed on turn/river.

I think that's where the complication lies in a c/c line here. There aren't a lot of cards that are great for our hand, we can never really be confident v-betting any straight or flush that we would have had equity getting it in on the flop, and often with a 4-card straight/flush on the board we are not getting it in against worse. Will think about a couple of turn/river scenarios but given the EV of a c/shove here and the ability to realize equity from possible straight/flush outs against a weaker range, it looks like a clearer decision.

Love the line, it sucks if we bet and get raised because we are facing a range that is probably flipping with us if not crushing us.

But if w check and shove, we now get extra $$$ the times when we crush villians hand, even though its unlikely he'll call unless he is crushing us.


So it makes us the most $$$ when we are ahead, if were crushed were stacking off regardless. Ask yourself this, if you bet and got raised that would be a very ****ty spot.

Not to mention TT on this board needs protection, so you cannot check call with these remaining stack sizes.

So overall i like the check shove because it squeezes us a little xtra $ when he decides to bet a fd/sd/pair/etc. Finally, it protects our check back range as the preflop raiser.


The check shove can be thought of as:
-value
-protection

Yes a bet accomplishes the same, but it misses value from certain hands, AND it doesnt get all the $$$ in now when we are ahead.

All those hands that we could have gotten bets out of, will likely bet this flop for us when checked too anyways. So lets say were even $$$ there

True the shove is unlikely to be called by worse, but its just as likely that if we bet and get called, a bad card will come off and we may get pushed off our hand.
Or if we bet and get raised, it puts us in a tough spot.

The check shove really isnt risking all that much, its $445 to win $235, so we need to be ahead of villians bet flop range about 65% of the time or more for this play to show immediate profit.

That doesnt factor in our very good equity, when we are called.

Read everything ITT.

+1 to what HappyLuckBox said, i would also add in a quote when you shove like "bees in the trap, bees in the trap!"

What about all those time we bet and he calls?

So how is this line better?

It's true every time someone raises us when we're OOP, so are you implying to always check so we can't get raised?

Ok, but it would help if you actually provided evidences to support that.

It doesn't make sense to group his entire range into one, and you have yet shown any comparison between CRAI and any other line.

What's a check back range?

Very fuzzy thinking. My recommendation is to dig deeper and evaluate with evidences.

Most back and forth statements I have ever read in a single post.

So which is it? Are we unlikely ahead when villain calls our CRAI or do we have very good equity?

I would cbet and jam lots of turns , if button looks to be cutting out betting chips I could see myself c / evaluating , and probably jamming often here alternatively

1) all those times when we bet and get called, yes we are getting value. My argument is all those times we check and he bets, we get value from the same chunk of his range that would have called a bet regardless, plus air.

2) I feel the check shove line is superior because we likely still get the same value as if we had cbet the flop, (see 1) but now we dont open ourselves up to getting raised off our hand. Secondly, we've manipulated SPR so that it is now favorable to gii with TT in this spot. Yes its unlikely he'll call unless he has a strong hand, but from villians perspective, the SPR is low enough "i has investd already $100!" That his calling range will weaken as a result. Also when SPR lowers, we no longer have to be correct as often for the check shove to show profit, as we are not risking as much.

3) No i am only implying that in this specific situation, its better to check shove then to bet/call? Or bet/bet. If the board was say K 5 2 and we had AK, we can very comfotably cbet this board knowing that it is very unlikely that villian will raise because there just arent enough hand combos that beat us. Even if he raises we still likely have the best hand. So a bet line is clearly superior.
On a board of 789ddd which clearly smashes a calling range, we have to realize that there are a multitude of hand combos that will very likeky raise when facing a bet. But does that mean we can just fold TTd in this spot? Unlikely, so lets get some extra value from the weaker parts of his range by checking and the shoving, once SPR becomes very favorable. And if it checks through our hand is still very playable.

4) TT needs protection on this board once SPR falls if villian bets when checked to, because we cannot just simply call. Once we call, we are committed to this hand, and it plays ultimately better as a shove. 9, Q, K, A, even the T, are all potentially bad cards. Diamonds are also not a great, albiet not a terrible card either. The problem is if we call, and a diamond or any of the above cards turns, what do we do?

5)
Bet line
+value from draws/pairs
- when called and a bad turn peels, we are put in a tough spot
- when raised (very likely on this texture) we are put in a tough spot, likely against a range that is flipping with us or beating us

Check/shove line
+ value from draws/pairs + air
+ manipulate SPR so that we can profitably shove TTd, against a range that contains a ton of weaker hands.
+ no need to protect our hand, as its not a disaster if it goes check check and a card comes off.
+ protects our checking range, by adding in a very strong hand with good equity against most of villians range.

6) I meant check range.

7) I think i clarified as much as i possibly could above

Im not sure how you think its back and forth? My math simply says that a check shove breaks even if villian folds 65% of the time, and calls 35% of the time AND wins 100% of the time when he calls that 35% of the time. Yet we know that even when he calls with a hand that beats us right now, it doesnt necessarily mean it will beat us come turn and river, because we have great equity vs hands that currently beat us. So he is never truely winning 100% of the time.

If anything neutrogena, you arent making a very good case as to the merits of betting vs check shoving. I would argue this is the nut check shove board given stack sizes
Now if stacks were deeper, i might opt for c/call or bet/call or bet/fold depending on tendencies and raise size.

As a default when stacks are deep i think check/call is best

Hm, I don't know if I would have been checking to him. We know he bets a good % of flops, so why force ourselves into a decision like this. I don't mind the shove though. I think I would have thrown out pot size and shove the turn?

If hes betting a good % of flops when checked to, this is more of a reason to check not bet.

Ok, so we are hoping that when we check, he bets (which is routine), and we can shove on him. Just like OP did, correct?

My only concern would be if OP thought of this prior to the check regarding the shove.

Im sure that was his thought process

Result?

Jamming > taking one card off and get it in or reeval turn > folding.

Very read oriented, but even though you have not used read as support, I'll go ahead and do it for you.

Against average LLSNL players who are passive, check/call and betting flop are very different, because most players would simply check behind with hands that would call a flop bet.

We really don't want to give a free street given vulnerability of our hand and position, and therefore a bet against average passive player is superior than check.

However, if villain is rather aggressive, as in this case indicated in the OP, a check may actually induce a wider range to put more money in the pot than a bet would.

Bold is not true because:

1. We can't win the hand by checking, but we can by betting. Simple comparison of cbet/villain fold to check/villain check behind would show you that the two do not have same EV.

2. Villain's flop raising range is a lot wider than his range of calling our CRAI. Your own read in previous post said that you don't believe this flop texture is favorable to our perceived range.

3. This one actually ties into your following quote:

How do you argue on one hand that we are committed to the pot after villain bets $100 using SPR as commitment threshold, and on the other, make a comment that we could be raised off our hand if we bet?

If you believe we're committed in this spot, how we play against his GII range really doesn't matter. Question becomes how do we maximize value against rest of his range.

I would urge you to reevaluate above thought process. Whether to check or bet (and how much to bet) involves many more factors than whether we are likely holding a winning hand.

In your example of AK on K52, against a non-calling station, I would actually consider checking the flop to induce villain to bluff or bluff catch for the same reason that you're betting.

Depends on which type of villain is doing the raising, size of the raise, and previous HHs that could provide further insight.

Stack-to-Pot Ratio is a concept BEFORE there is action on the flop. SPR allows you to plan pre-flop sizing and post-flop commitment level, which leads to various adjustments such as pot control and overbets.

How are you protecting TT if you're checking the flop? What would you do if villain checks behind and turn is one of the ugly cards you mentioned?

+1 to most of what neutrogena said
given reads i like crai here. this board texture provides really dynamic equity distributions which will generally favor the player in position on later streets, and a lot of his range will either put money into the pot when it shouldnt have (maybe something like 44), or he will be forced to fold a lot of his range that has great equity against our particular hand (KxQd, etc.) which is a very good result for us (that he b/fs these hands). if he adds those hands to his b/c its fine, and were going to have reasonable equity against his normal b/c range of 2p+ (plus we have blockers to straights) despite the amount of flushes he shows up here with.

I think its a much more interesting question of what we should do against a presumably competent unknown player who we dont have reads on, and how we should split our entire range in this spot. I intuitively think it will involve a lot of checking, but I'm not sure about that at all-this will also depend on how wide our range in this spot is obviously.

Im confused, so you agree with neutrogena, yet still feel crai in this spot is best? You also feel checking against superior opponents is best? You realize he believes betting is best, whilst i am making an argument for crai with these stack sizes. I am also a proponent of checking and likely check calling against deeper villians.

As per your response neutrogena, we usually agree on most points, but here i can see you will not be easily swayed, and ive already posted all of my thoughts regarding this subject. So i wont debate it any further.

Sway? I don't care about the result...

I was asking you for more information into your thought process, not trying to convince you of anything.