I wanted to go back and address some of these comments individually because I don't agree with some of the things you are saying. I am not trolling just expressing my ideas on this subject to have them critiqued by others and to help others learn.
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Originally Posted by Donovan
1) If we are betting a polarized range we should usually exhaust all of our bluffs without SDV before we start bringing hands with SDV into our bluffing range
Minor quibble but a polarized range is defined as betting strong value hands and air so by definition we would be doing this if we bet polarized.
Also if we arrive in a spot where we exhaust our pure bluffs and have to bet hands that have significant showdown value it's likely we would select a bet size that would not make sense for a polarized range or would want to bet a large amount any way.
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Originally Posted by Donovan
3) seems like, if we are in a spot where we have some kind of range advantage and we are betting hands with show down value and <b>checking hands that have no SDV and no equity then we are doing something wrong</b>
The bolded part does not make sense. You certainly want to check hands that have low equity and no showdown value. Just look at 7h6h from Arty's snowie example. It hardly ever gets bet and mostly gets check folded.
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Originally Posted by Donovan
even though it could be counterintuitive that we would check some hands that have some SDV even though we will check and fold them but bet some hands that are strictly weaker as bluffs.. this def does come up.
I don't think anyone was arguing against this. I wasn't arguing against it. I was arguing that in this contrived example 76s is too weak to use as a bluff but that doesn't mean all hands that aren't pairs or immediately draws are too weak to bluff. Take ATs for example. According to my equity It's only a 70/30 dog vs even a pretty conservative range of only made hands. It only has back doors going for it but it would be a much better betting candidate here because of blocker effects (76s had 24% equity for what it's worth).
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Originally Posted by Donovan
It's because some of the hands we want to check and will have to fold to a bet will be a lot more valuable when the street checks back and maybe we don't want to be bluffing too often in a given spot.
Your argument seems to be focused a lot on showdown equity. This is not always an appropriate substitute for EV.
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Originally Posted by Donovan
EG:
CO opens and we 3 bet, he 4 bets small and we flat with JJ (Feel free to tweak the stack sizes, bet sizes, villain propensities, pay out structure/ICM however you need to get this to be an OK line pre-flop)
Flop: A88r
check
check
Turn: Qr
It prob makes all the sense in the world to bluff hands worse than JJ maybe if we have TT or 99 or some hand we were bluffing with but called getting a huge price with a playable hand (KTs? KJ?)
but with exactly Jacks it can make sense to check even if we will fold to a bet.
That is probably the perfect example where having a polarized betting range won't be ideal and we will select bet sizes more appropriate for our range vs our opponents range.
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Originally Posted by Donovan
If we are "turning JJ into a weaker hand" by betting it then we can have about the same EV of bluffing with some weak hand or betting with this JJ hand. But maybe the weaker hand doesn't have enough value or equity to make us any money even when the turn checks thru.
So here is where I get lost. I don't know why you are comparing the EV of 2 different hands as if it means something. You should take the most +EV line with any hand and if the EV of 2 options is equal with that hand you can choose either option 100% or choose both options with certain frequencies.
If JJ makes more money checking you should check it. It doesn't matter what the EV of your other hand is. You take the most profitable line with that hand too. Your range is just a consequence of the fact that different hands have the same betting line to maximize their EV. This is how poker solvers work.
Quote:
Originally Posted by Donovan
Anyone disagree with that in terms that, preferably without using the idea of "protecting hands"? Not that I am saying that getting your opponent to surrender their equity when you have a hand that is prob best right up until you bet and are called is ALWAYS bad. It isn't. But I don't want to have a long discussion about why I think protecting hands is not a good way to think and that there are better, more efficient ways to think about betting strategy.
I would say we disagree on what protecting your equity means. What you describe above (i.e. making an opponent fold his equity share) is what I would call bluffing though I will agree the term is antiquated and there are plenty of situations where we have the best hand now and would prefer a fold.
What I was describing is betting to prevent villain from correctly bluffing you thereby robbing you of some of your equity. There are even situations where you can bet and not expect to be called by worse and your still better off betting than allowing villain to force you into a 0 EV call.
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Originally Posted by Donovan
Basically, (blocker affects aside) your hand only matters if there is a show down and you don't win extra money for having the best hand when your opponent folds and so we ought to at least try to avoid sucking the value out of our hands by using them as bluffs when we have better bluff candidates and would like to have a range of hands that will check and fold.
I think I agree with what you're saying here but I am certainly confused by the way things are worded. Again it's as simple as take the most EV line with your hand and don't worry so much about constructing the perfect range of hands off the table.
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Originally Posted by Donovan
*btw, what I mean about having too much overlap is that we get better board coverage, all else equal, by having hands in our range that hit different boards.
So, for instance, if we are playing a tight range from UTG at a live low stakes cash game and a good player sits down and starts making things hard on our UTG range by flatting us in position very deep and; Never giving us action when we c-bet AK8r and putting a ton of pressure on us when the flop comes 776/654/889/79T etc..
Maybe we will want to add some hands to our open raising range from UTG to give us better board coverage. That way if we don't get action on AK8r we will have some bluffs to leverage our range advantage with and if the board comes 654 we can have the nuts on occasion.
You seem to be omitting all those other boards were we already have the best hand. That's where we make our money for the times we whiff. That's also where we lose our money when we start adding random opens to our UTG range that may or may not be profitable.
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Originally Posted by Donovan
Maybe hands like QJs and 87s will have about the same EV in a vacuum and maybe break about even over all. But, even though QJs is the objectively stronger hand, we will already have hands in our range that will do some work for us on QQJ, JJQ, QJT, KQJ, and even like AJT. But we won't have hands that can do work for us on 876, 765, 776, 872, 773, 988, etc.
Board coverage is something to consider but mostly only when stacks get deeper and having the nuts in your range is more important. If you and the new pro sitting to your left have 200+bb stacks then yeah you may want to worry about board coverage but there's so many other factors that influence the EV of a single hand at that depth board coverage is probably only a minor factor. And again tons of other boards that aren't so terrible for our range.
Quote:
Originally Posted by Donovan
I'm not so convinced that 76s belonged in our range in my OP but I can buy the idea that we may want to have some stuff like 87s in our UTG range when we play deep enough at full ring cash games and six max online cash games even though maybe we don't want to open some objectively stronger hand even if it has about the same EV as the other in a vacuum because we would want to include the hand that adds the most EV to our strategy at large.
Right?
Your EV for your strategy at large is just the summation of the EV of your individual hands. You maximize the EV of your individual hands and you will maximize your overall EV. It doesn't have a whole lot to do with board coverage. There are literally times where you will be caught with a weak range completely due to the chance nature of the game. That doesn't mean you try to throw in hands in your range to eliminate that possibility.
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