This is sort of a question/confirmation of my understanding in regards to where does the EV come from in a given situation...

I)Say hero bet a value-heavy range of only [#7] nut flush combos and no bluffs using a pot sized bet sizing, therefore here is bluffing 0% of the time.
Villain's calling range consists of only top pair combos but villain folding range is 75% villain is folding 75% of the time.

In this spot the EV of villain calling vs. hero's range is -EV due to hero's value heavy range.

II)Say hero bet's a range of [#7] nut flush combos and [#7] bluff combos using a pot sized bet sizing, therefore hero is bluffing 50% of the time.
Villain's calling range still consists of top pair combos and villain is still folding 75% of the time.

In this spot the EV of hero bluffing w/7 bluff combos vs. villain's range is +EV because villain is folding more then 50%.
In this spot the EV of villain calling vs. hero's range is +EV because hero is bluffing more then 33% of the time.

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Even if our bluffs are +EV coz of villain's folding range, villain's EV of calling is still going to increase with his bluff-catchers so does that mean we should stop bluffing a certain amount if villain has really +EV calls with his current range?

So now we have to compare the EV of betting with our bluff combos vs. the EV of checking (x-calling, x-raising, x-folding) with our bluff combos to find the highest EV line. Assume we are OTF or OTT, because if we are OTR then betting w/our bluff combos is obv going to be better in II) example (if he continues to play a fixed strat and never adjusts)?

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The second question i have is say villain is imbalanced towards bluffs say he bets pot and is giving us correct odds to call with all of our bluff-catchers in that all our bluff-catchers will be +EV, but we don't know what the EXACT EV is per bluff-catcher.

Well how do ik/calculate the exact EV for each hand combo, i always thought that if we had a +EV call with all our bluff-catchers our EV would be the same for every single bluff-catcher in our range. Except for the ones with really good blockers, but when i check in CREV or some software it gives different values for each bluff-catcher and idk why those numbers are what they are?

EV of calling is: EV = (Combos of hands we beat)(Bet+Pot) + (Combos of hands we lose to)(-Bet)

^If we get the same answer from this equation with different bluff-catchers i don't get why the EV's per bluff-catcher are different.

There is no other equation that helps me get the numbers from why the numbers are what they are in the software, and from what i understand the bottom of our range will be less EV compared to the top of our range which will yield a higher EV.

you should never be bluffing 50% of the time as villain should just call 100%, so are you jus exploiting him or what?

difference in EV for bluff catchers pry have to do with blocking value hands.

"I)Say hero bet a value-heavy range of only [#7] nut flush combos and no bluffs using a pot sized bet sizing, therefore here is bluffing 0% of the time.
" Wrong why the betting range should have only strongest value.

"II)Say hero bet's a range of [#7] nut flush combos and [#7] bluff combos using a pot sized bet sizing, therefore hero is bluffing 50% of the time.
"

Better unfortunately wrong again. Bluff 33% with potsizebet.

I am betting a range of #7 nut combos and #7 bluff combos, i'm adding the #7 bluff combos because villain is only calling 25% of the time and villain is folding 75% of the time so my bluff's should be +EV as i risk 1/1+1 = 1/2 therefore villain is folding more then 50%.

And i think in general if we never have some bluff's that the average bad reggy type villain can easily adjust and exploitatively fold as well but this is a small consideration.

In this scenario i provided villain is over-folding given the math's, but what i really want to find out as well is in real time in game how many profitable bluff combos can we add to our overall value-heavy range.

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@brokenstars that is what my question and clarification is so yeah villain should always call 100% vs my imbalanced bluff-heavy range in II) but my bluffs will still be +EV because he isn't defending enuf w/that fixed strat unless he increases his calling range.

then just bet 100% IP

his IP strategy vs. our check can change our EV and it may be better to check vs. him depending. (if we are OOP)

Imagine you're playing some form of 1-card poker, with a 2 being the nut low and an ace being the nuts. Let's suppose villain bets his entire range. You decide to call with a nine or better. Isn't it obvious that a 9 won't win as often as a ten, or a jack or Q/K/A, so your EV with a 9 will be lower than your EV with the better bluff-catchers? The higher cards will literally win more often, so they have a higher EV, whereas the bottom of your bluff-catching range will be closer to breakeven.

Thanks for dumbing it down for me, but ur example isn't that clear this is what i'm not quite understanding if villain bets the nuts like an "ace" in ur example and some bluffs @ x frequency like a "2 or a 3" what's the diff between calling with a 9 or a T then they are both equal.

I think it has something to do with frequencies, and we need some way to measure how often we are calling like why would we start calling with a 9 before a T, but if both bluff-catchers are going to be +EV in this spot given imbalances then yeah i doesn't matter that much.

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Anyways the second question i had regarding that topic isn't of a big concern to me like if my decision is going to be +EV that's all i really care about ya know.

But just the numbers don't add up or make sense to me, such as your standard pen and paper single street EV equations in relation to the EV #'s shown in solvers like i can't get the same answers/#'s :l

Calling with the T instead of the 9 will be best vs all potential non optimal strategies.* If any deviation from gto will result in a loss of ev = or > 0, then you can find where your strategy is benefiting from the deviation.

Take Arty's example:

This will benefit your strategy in the form of gained ev even if you don't actively exploit the mistake. The specific hands that gain ev will be your worst bluffcatcher and anything better. Your junk hands will lose ev because you lose the ability to bluff or win showdown, but this loss is more than compensated by the ev gained by your good hands. Always ask yourself, "who benefits?"

*I think.

can you give us some calculations? i dont understand at what point some bluffcatcher becomes more valuable and different. I see no equity in this formula.

Maybe some of those bluffcatchers beat a portion of the opponent's value hands in addition to beating bluffs.

I've never used CREV so I don't know what EV results you're looking at, but real two card poker (i.e. not a very basic toy game) seldom has pure 'polar vs bluffcatcher' scenarios at the equilibrium. The ranges and frequencies get very complicated when both hero and villain are using mixed strategies, such that sometimes your "bluffcatcher" loses to a low frequency "bluff" by a better hand, or the top of your bluff-catching range actually beats some of villain's value-bets.

both of you are wrong and aren't even answering the question he had. You can have a bluff heavy range of 50% or even more in some spots. For example, you raise the hijack and get called by the button flop comes Ad 7s 4d.
In this spot you should be betting close to if not more than 50% of your hands as bluffs; flush draws, gut shots, 89h, JTs, some 4x, Air and value betting hands like most aces and strong combo draws ex. K7d (maybe some 7x hands or 88-KK vs some opponents).
Why is it ok to bluff this flop so often? Cant Villain exploit us by calling all the time for +EV or raising our bluff heavy range? No he can't because this flop doesn't connect with his preflop calling range. The 7 and the 4 are not cards that are in many of his combo hands, he is way more likely to have a hand like QT than 76. BB wont be calling with 56o which also means he has way less draws than us to continue his aggression, only flush draw combos really. Therefore, villain simply does not have the hands to play back at our profitable bluffs.

Also, one thing you should always be looking for is capped ranges because it plays a huge dynamic and can make for some great spots or terrible ones. In the previous situation the capped range of Villain eliminates his AK/AQ combos since he would 3bet those hands most the time. This only leaves 77 and 44 as very strong hands villain could have, a very thin value range.

"Better unfortunately wrong again. Bluff 33% with potsizebet."
serious misinformation, the 33% for pot sized bet thing really only applies to river bets (And in most situations this is not the highest +EV approach it is just a GTO approach). Earlier streets your bluff frequency should be higher because your bluffs have equity.


Hopefully that helped shed some light to the original question you were asking which was very broad and would take a lot of depth to fully answer. Actually calculating the EV of a spot you have to take all things into consideration. Most people use somewhat simple formulas for EV, but the more info you use to analyze a spot the closer you can get to the EV. Then to figure out optimal strategy for a range that has the highest EV you have to determine the EV of every single hand for all lines of play and possiblities. I know this sounds overbearing and extreme. Is number crunching EV to such an extreme even worth it or will being close enough to the EV get me almost just as far? Yes I think it is, there's still huge edges to be found and the best players in the world are far from GTO.

Here's a more specific answer to the situation you posted, we make this spot on the river to simplify it. You gave villain a calling range of 25%, lets say KTo+ on Kxxxx. How do we most profitably exploit and bluff this villain at the highest EV? Lets say with 7 value combos and 7 bluff combos his frequency will stay at 25% and then for every combo added to the bluffs villains calling frequency will go up 1% once we get to 17 combos villain will call at 35%. We can compare the EV of both very easily

EV1 = 7 (2pot)25% + 7(pot)75% - 7(pot)25%
EV2 = 7 (2pot)35% + 17(pot)65% - 17(pot)35%

Its hard to quantify how villain will adjust to us bluffing more, and if you make a big adjustment to exploit your opponent then you leave yourself very vulnerable so watch out for villain readjusting to you. I won't go into which combos you should pick because this post is long enough as is.

Evoxgsr I am looking for someone to share research with, let me know if you are interested in forming a study group I sent you a PM

you're right I made the false assumption we were on rivers.

why? The OP said the guy had rigid strategy

to compare we must divide the first result by 14 and the second by 24. No?

"why? The OP said the guy had rigid strategy"

The reason being is I am looking at this situation in a long-term approach, in the example I gave I said villains current playstyle has him calling with KT+ but folding hands like K9 since K9 falls just below the theoretical 25% calling range villain has.

Once we make the adjustment to bluff this high fold frequency at an exploitable rate we leave ourselves vulnerable by giving our opponent a very high EV call. But that's ok because we know this player is exploiting themselves with this high fold frequency already. So that leaves us with two options, we can play GTO which in its purest form means that our opponents value between Fold/Call/Raise is all the same, therefore with our GTO strat it doesn't matter what our opponent chooses to do since all options equal the same EV = "X" meaning our EV = -"X" (the inverse of villains EV). A winning approach but not the best option.

So that leaves us with playing an exploitative style, once we have gathered info and found Villains leak (folds too much) we can adjust accordingly to raise our range EV(always consider your entire range and how your strategy affects it). Since we are no longer in GTO fold/call/raise do not have the same EV for villian, now its EVfold= Z, EVcall= Y, EVraise= R. We know that fold is going to be this players preferred option, so we want to make the EV of fold as low as possible by bluffing. As we bluff more that "Z" value goes down while the "Y" and "R" values go up, which as I said before leaves ourselves exploitable but that is the whole point of exploitative style. Compare this to a simple rock paper scissors example, my friend Bruce always throws rock 80% of the time once I figured this out I adjusted my range to be full of paper combos but I still throw rock and scissors sometimes so that Bruce doesn't figure me out as a paper machine and starts adjusting his leak.

We want to keep villain in the dark. The less he knows about what we are doing, the more mistakes he is going to make. Once we make an adjustment like this we open up a hole in our game for the purpose of punishing the hole we found in villains game. A dicey situation because once he finds out the jig is up. So when we are adapting this exploitative style we want to use finesse to reach our grand goal of Max EV. That's why you shouldn't be betting 100% versus this guy because you will inevitably destroy this great situation.

The only logical way to theorize what the EV of adding more bluff combos will be and where max EV lies is to look at the spot for the long term. Now once you choose to make the adjustment of going from 7 bluff combos to 17 villain will not know. So your 17 bluff combos will have their highest value for a short period versus villains highest fold frequency. After time this fold frequency will go down for a few reasons. Villain will develop a read on you and will start to notice your higher aggression. From betting 14 combos you now have 24, so lets say in this spot your entire range consists of 100 combos. This means your betting frequency went up from 14% to 24%, something that villains HUD might pick up on. Also villain will be calling your bet 25% of the time and going to showdown, so 1/4 times he will see your now weaker holdings which will make him more likely to call wider than 25% in the future.
This is why you have to widen villains calling range, I used a generic ratio of 1 combo = 1% increase.


Your strategy should start from GTO -> Exploitative once possible.

"to compare we must divide the first result by 14 and the second by 24. No?"

No, doing this will not give you the answer you are looking for. Diving by the # of combos will just give you the average EV per combo. The way I had set up that equation was for range EV, as I wrote above you always want EVs of ranges not just hands.

EV1 = 7 (2pot)25% + 7(pot)75% - 7(pot)25% = value+bluffs = 3.5 + 3.5
EV2 = 7 (2pot)35% + 17(pot)65% - 17(pot)35% = 4.9 + 5.1

In this example you went from betting 14 hand combos to 24. This means that instead of only 14 combos to win with you now have 24. The bluff combos individually will have their EV go down, but the range EV will go up because you are winning more pots. Adding those bluffs combos not only makes you more money from bluffing but also increased your profits from value bets. Once your opponent starts adjusting to calling more you can throw in more value combos as a readjustment to get closer to max EV again.
Here's how these adjustments would play out;
EV1 = 7 (2pot)25% + 17(pot)75% - 17(pot)25% = 3.5 + 8.5 = 12
*Hero's first adjustment
EV2 =7 (2pot)35% + 17(pot)65% - 17(pot)35% = 4.9 + 5.1 = 10
*Villain adjusted by folding less
EV3 = 9 (2pot)35% + 17(pot)65% - 17(pot)35% = 6.3 + 5.1 = 11.4
*Hero readjusts to the wider calling range by value betting more combos that were too thin to valuebet vs a 25% calling range.

There is a simple method that you can use to keep track and confirm Villains calling range frequency that will allow you to quantify what his call% is in real time. A HUD will also give you this number but once villain adjusts it will take hundreds maybe thousands of hands for the HUD to pick up on villains new call frequency. I won't give away the method for the common interest of poker(fish stay fish), I'm sure most of you thinking players can figure it out there's a clue in this write up that will direct you .

It's not smart to bluff made hands, unless I am seriously missing something.

Okay i understand my initial post was sort of a ramble/unclear, but this is what i was really trying to ask in regards to my 1st question.

I think i was a bit wordy in my initial post, but i'll re-state what i was trying to ask, here is a visual/pic to better explain what i'm asking and talking about.



So yeah our range is 12 bluffs and 13 value, villain has a profitable call with all his TP combos given pot odds/bluffing frequency.

However we also have a profitable bluff with all our bluff combos because 40/120, villain has to be folding more then 33% which he is.

I'm guessing all the EV's with villain's TP combos and our bluff combos even out and this isn't the most profitable strat for hero?

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Well now i also have a 3rd question in regards to EV and folding out villain's equity...

So i understand that if we fold out villain's pot equity like say we are preflop, OTF, or OTT and assume we have a hand that is vulnerable/needs protection or a hand that is behind equity wise + won't get to realize it's equity then getting villain to fold out some PE/the best hand sometimes will be +EV.

Is there a way we can determine how profitable folding out villain's PE/equity is, like how do we know if we bet for protection it's going to be profitable or if we go AI and try to fold out villain's PE is that going to be profitable do we consider stuff like this in a vacuum?

I'm a firm believer that betting exclusively for protection in heads up pots is bad poker with rare exception:

a) you're almost positive you have the best hand.
b) your opponent has a ridiculously high folding frequency.

Occasionally, both will be true and you can bet fold like an exploitive champ. Other times, only (a) will be true and you can bet to induce a bluff raise like an exploitive champ. If only (b) is true, then that would mean that there's a good chance of folding out better hands and you can value bluff like an exploitive champ, which both gets value from draws and causes better made hands to fold.

All that said, however, these are rare exceptions. In the vast majority of cases, you don't know that you have the best hand, nor does your opponent have a ludicrous folding frequency. Vs most opponents, if you can narrow down your hand value to "decent but vulnerable hand" then that would indicate that you either have a weak value hand or a strong bluffcatcher. Do you really wanna go to town with it though? I don't think so without the specific reads given above because checking and or calling and seeing another street, and potentially making it to showdown with a decent hand, is worth a fraction of the pot. Only when the rare exceptions above add up to a larger fraction of the pot than you would realize by making it to showdown would betting exclusively for protection be correct.

Ok, i see your point. We just take dead hands from checking area (with zero value) and put it in betting area. So it looks like we must bet all dead hands if the villain has "25% call strategy".
The only thing i would add "value bet - villain folds worse hand" situation another 7(pot)75% for full EV picture. No?

As to 13/12 on the turn it looks rather ok, because (according to MoP) on the turn you must have some of you bluffs as valuebets (for example) : (13+6) to 6. In order to have 13/6 on the river.

*BUMP*

I *think* i can answer this... also i messed up we need villain to fold 50% of his range 40/81 not 33% which he still folds 50.1% ^^.

Since i deleted this file i can't really go back and see what the GTO EV's but im assuming we would compare hero's EV and hero's GTO EV?

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OTT i think it's totally fine to be bluffing here as long as we have a +EV turn bet (villain is folding 50%>), most of our extra bluff combos OTT would probably be give ups depending on the run out + how villain will deviate.

Ex:
OTT we have 12 bluff/25 = Hero is bluffing 50%

River = 2

Assume we bet pot size here again (don't know how many combos coz i deleted file lol), Assume villain's range OTR #3 combos of flushes #12 combos of TP's #5 combos of Combo draws we need him to fold 10/20.

But say he doesn't fold 50% now what happens to all our extra bluff combos we obviously can't bet them so now (EV of checking vs. EV of betting OTR) we will be checking more bluff combos then usual in this spot because villain is going to be over-calling here (calling 15/20). Instead of checking back #6 combos of bluffs we will be checking back none i think lol if villain has a fixed strat of calling 15/20?

So when we x back #12 combos of bluff's obv give ups, villain's EV OTT will be:
12/25 (+81) + 13/25 (-40) = +$18 vs. 6/25 (+81) + 19/25 (-40) = -$11

Also how much should we really care about villain's EV... is it only if he super +EV decisions vs. our range, villain having +18bb here is that bad for us how can i tell?

UGH, so i'm sort of stuck here like how do we know if it's +EV to be betting 12 bluff's here OTT what do i have to compare or look @...

Just some pen & paper maths + logic

Depends on how much dead money is in there and whether or not previous decisions were the best decisions.

In a strategy ev vs strategy ev sense, I think the ev will fluctuate a bit based on range asymmetry, but I don't know how much. Likely not so much as to make the opposing strategy have a negative expectation, but I don't think it'll be 50/50 chopping up the dead money. Position, nutty combos, and strong semibluffs will be the prime ev sources. The more marginal hands will be closer to breakeven and thus they'll have much less effect on pot distribution in a long term sense.

Yeah i think i was just trying to say is villain exploiting us here by calling given the EV is +$18.

If hero is doing the exploiting we don't necessarily care if villain has +EV calls right?, but as long as they aren't super +EV as mentioned above...
in addition what aspects do i compare/look @ to know okay villain is starting to exploit us/has super +EV calls we need to adjust our strategy etc...

I think i may be over-thinking some things atm right now using a range vs. range type approach, but im mainly just wondering how important/useful it is to think about villain's EV sort of like the indifference/MDF + balanced ratio toy games...

Too be clearer i'm talking about the EV of calling for villain in spots and knowing when specifically villain is exploiting us by calling/has super +EV calls

I keep on asking this and idk why i can't answer such a simple question lol... what do i look at and compare to know "okay when villain has x EV for calling he is exploiting us but when villain has y EV for calling he isn't"

You would have to be in possession of the entire equilibrium strategy pair to answer this.