100NL Coolers or bad play?
What you may have meant to say is that our weaker profitable 3-bets have a higher EV when our opponent folds than when he calls. If this is what you meant to say, then I agree.
What you may have meant to say is that our stronger profitable 3-bets have a higher EV when our opponent calls than when he folds. If this is what you meant to say, then I agree.
If a hand can profitably continue against a 4-bet, then it is +EV facing a 4-bet. If it cannot, it is 0EV facing a 4-bet. In general, if a hand cannot profitably 5-bet, then its EV is higher when not facing a 4-bet than when facing a 4-bet. If a hand can profitably 5-bet, then its EV is probably higher when facing a 4-bet than when not facing a 4-bet.
I'm sure you're being sarcastic. But another way of putting it is that even if you only 3-bet KQ+, then you're opponent would be able to likely 4-bet ~11% of hands. In other words, by adding KJ to your 3-bet range, you only add an additional 1% of a range to your opponents 4-bet range. It's just not drastically different when you add KJ.
In any case, the question of how wide the SB can 4-bet "for value" is not relevant to anything I've said about the decision to 3-bet or call KJo.
It's still not clear to me what KQ+ means. Please clarify?
What's a value range?
Doesn't the frequency with which you can bet depend rather critically on how big you bet? And doesn't it also depend rather critically on what your 3-bet range is?
With what frequency does the flush get there or some other terrible run out occur when a hand "hits?"
Any two cards can sometimes check-call in a 3-bet pot.
That your claim is absurd should be obvious from the fact that it logically implies that we should fold everything but the nuts to a bet, thereby preventing our opponent from betting for value with the second nuts.
Why? This seems like an arbitrary and indefensible claim. I'm pretty sure there are some boards where the SB should simply c-bet 100%. I've given 222 as an example.
I claim that there are space aliens on Jupiter who want you to give me all your money. If you don't, they're going to destroy our planet. As long as you don't have any proof whatsoever in one direction or the other regarding whether what I'm saying is true, how come it doesn't make sense to give me all your money?
The answer is that one needn't possess proof nor certainty in order to act on the basis of a judgment. Bayes' theorem ftw.
This isn't really relevant to your question concerning thresholds though because we actually do have proof that they're not relevant.
The reason none of these minds jumped in to make a stand is that they all recognized how obviously wrong you are. Every bright mind that bothers to comment here will confirm this, and none will agree with the position you are taking. Most won't bother because it's too obvious to be interesting.
I don't understand how it can be arbitrary(?!?). Just playing around with CardrunnersEV will show that when applying max-exploit to a strategy which, in some random decision node, folds more then threshold, the betting/raising range in that spot of the exploitative strategy shifts to 100%. So its clearly not arbitrary...
On the other hand, I can accept arguments on how the EV gained by switching to the 100% betting/raising range as a result of max-exploit on that particular street may not generate the highest EV overall for the exploitative strategy (as far as I can tell CardrunnersEV's max-exploit doesn't work for multi-street/full tree) but I would say it will def be higher then the EV of not switching to betting/raising more as a bluff in that spot.
Insanely tight. Not sure it's possible to be a winning player defending that tight. Try ~80%.
I see GntlmnsHndshk, icoon, and Rei have been doing the Lord's work in my absence. Thanks guys.
2 scenarios:
We are in SB (srp pot) and
1) BB leads flop we call, BB leads turn
2) BB c/c flop and leads the turn.
In case (1) our total call freq should coincide with the 1-alpha threshold, both on the flop and on the turn, but in the 2nd case on the turn this is no longer true because we polarised our ranges by betting the flop and so the amount of bluff catchers we arrive on the turn no longer coincide with our entire range.
We are in SB (srp pot) and
1) BB leads flop we call, BB leads turn
2) BB c/c flop and leads the turn.
In case (1) our total call freq should coincide with the 1-alpha threshold, both on the flop and on the turn, but in the 2nd case on the turn this is no longer true because we polarised our ranges by betting the flop and so the amount of bluff catchers we arrive on the turn no longer coincide with our entire range.
It's not clear to me why you're having such a tough time understanding this.
Originally Posted by Matthew Janda
For example, suppose we want to compare how much money our opponent must put into the pot if we bet 0.5 PSB, 1 PSB, or 2 PSB on the river and our opponent does not want us to be able to profitably bluff any two cards.
1.For 0.5 PSB, our opponent must call or raise 66.7 percent of the time to keep us indifferent to bluffing. He thus ends up putting in on average at least 0.334 pot-sized bets.
0.334 = (0.5)(0.667)
2.For 1 PSB, our opponent must call or raise 50 percent of the time to keep us indifferent to bluffing. He thus ends up putting in on average at least 0.5 pot-sized bets.
0.5 = (1)(0.5)
3.For 2 PSB, our opponent must call or raise at least 33.4 percent of the time to keep us indifferent to bluffing. He thus ends up putting in at least 0.668 pot-sized bets.
0.668 = (2)(0.334)
1.For 0.5 PSB, our opponent must call or raise 66.7 percent of the time to keep us indifferent to bluffing. He thus ends up putting in on average at least 0.334 pot-sized bets.
0.334 = (0.5)(0.667)
2.For 1 PSB, our opponent must call or raise 50 percent of the time to keep us indifferent to bluffing. He thus ends up putting in on average at least 0.5 pot-sized bets.
0.5 = (1)(0.5)
3.For 2 PSB, our opponent must call or raise at least 33.4 percent of the time to keep us indifferent to bluffing. He thus ends up putting in at least 0.668 pot-sized bets.
0.668 = (2)(0.334)
Originally Posted by Matthew Janda
So to start, let’s first examine how often we would have tofold to a flop bet before our opponent can profitably bet twounwinnable cards To help do this, the following equation shows,in terms of pot-sized bets, how often a bluff needs to suceed toassure that the overall bet is guaranteed a certain profit.
Minimum bluff success rate =
(bet size in PSB) / (bet size in PSB + 1)
or
Y=X/(X+1)
where
X is the bet size in terms of pot-sized bets, and
Y is the frequency the bluff must succeed to show an immediate profit.
For example, suppose our opponent bets 50 percent of thepot. This means bluff rate should be 33.3 percent of the time
0.333 = 0.5/(0.5 + 1)
Similarly, the proper defending frequency can be solved forwhen expressed in terms of the opponent’s flop bet sizing.
Y=1/(1+X)
where
X is the bet size in terms of pot-sized bets.
Y is the frequency the potential caller must defend toprevent his opponent from being able to profitably bluff with pure air, and
So in this example where X = 0.5 (pot sized bets) the potentialcaller needs to defend 66.7 percent of the time.
0.667=1/(1+0.5)
Minimum bluff success rate =
(bet size in PSB) / (bet size in PSB + 1)
or
Y=X/(X+1)
where
X is the bet size in terms of pot-sized bets, and
Y is the frequency the bluff must succeed to show an immediate profit.
For example, suppose our opponent bets 50 percent of thepot. This means bluff rate should be 33.3 percent of the time
0.333 = 0.5/(0.5 + 1)
Similarly, the proper defending frequency can be solved forwhen expressed in terms of the opponent’s flop bet sizing.
Y=1/(1+X)
where
X is the bet size in terms of pot-sized bets.
Y is the frequency the potential caller must defend toprevent his opponent from being able to profitably bluff with pure air, and
So in this example where X = 0.5 (pot sized bets) the potentialcaller needs to defend 66.7 percent of the time.
0.667=1/(1+0.5)
Originally Posted by GntlmnsHndshk View Post
I would make the same argument that some of our hands are going to work best as a 3-bet because of a combination of the reasons above AND they'll be able to check-call postflop.
I would make the same argument that some of our hands are going to work best as a 3-bet because of a combination of the reasons above AND they'll be able to check-call postflop.
My point is that I'm assuming that some hands will maximize their EV by 3-betting postflop, and then check-calling on some future streets postflop. Otherwise, if everytime our hands "hit" the flop that we maximize our EV by bet-bet-bet, then our checking range is going to be very weak and open to exploitation by the opponent, so we would then adjust by adding stronger hands to our check-calling range. Now while all hands can check-call, if it's higher EV for a hand to bet the river after betting the flop and turn, then it's going to be hard for you to convince me that it should be played as a check-call (ignoring capped ranges for now).
My guess is that KJo at the very least would fall into this category in that it should be 3-bet preflop otherwise our range will be too weighted toward strong hands which will want to bet bet bet all 3-streets postflop when they "hit".
Originally Posted by GntlmnsHndshk View Post
Well let's say that you're 3-betting KQ+
Well let's say that you're 3-betting KQ+
It's still not clear to me what KQ+ means. Please clarify?
and balanced with some "bluffs"
Originally Posted by GntlmnsHndshk View Post
so KQ is the bottom of your "value" range
so KQ is the bottom of your "value" range
Fwiw, this process would go faster and better if you'd give the benefit of the doubt sometimes.
Originally Posted by GntlmnsHndshk View Post
I'm guessing that you'd be able to bet flop, turn and river over 50% of the time when you hit (assuming the flush never gets there and not any other terrible run out).
I'm guessing that you'd be able to bet flop, turn and river over 50% of the time when you hit (assuming the flush never gets there and not any other terrible run out).
Doesn't the frequency with which you can bet depend rather critically on how big you bet? And doesn't it also depend rather critically on what your 3-bet range is?
With what frequency does the flush get there or some other terrible run out occur when a hand "hits?"
The frequency we can bet does depend on the bet size which I was assuming to be 50% on all streets. And the 3-bet range is what I described above.
The frequency that the flush gets there or another bad run out is ~45% of the time (maybe a little closer to 50%), if I remember correctly.
Originally Posted by GntlmnsHndshk View Post
It's not clear to me what you mean by "3-bet __ 'for value'," but I have already stated that KJo can be profitably 3-bet (see: post 53). The relevant question is whether calling is better than 3-betting.
Any two cards can sometimes check-call in a 3-bet pot.
And if this is the case, it seems that one of two things are then true:
1) you could either 3-bet KJ for value
or
2) you should 3-bet KJ so you can have hands which will sometimes check-call in a 3-bet pot.
1) you could either 3-bet KJ for value
or
2) you should 3-bet KJ so you can have hands which will sometimes check-call in a 3-bet pot.
Any two cards can sometimes check-call in a 3-bet pot.
OR
And if it can't bet-bet-bet postflop frequently, then it can likely can bet two streets postflop, and it seems like we're going to need some hands which work well for this.
Originally Posted by GntlmnsHndshk View Post
At most you'll have a 36% check-raising range, and then a pretty close to 0% check-calling range. I'd be surprised if the BB could defend more than 40% of the time.
At most you'll have a 36% check-raising range, and then a pretty close to 0% check-calling range. I'd be surprised if the BB could defend more than 40% of the time.
Originally Posted by GntlmnsHndshk View Post
If this is true, I don't understand how you could think that this flop is a "good flop" for the BB OR easy for the BB to defend.
If this is true, I don't understand how you could think that this flop is a "good flop" for the BB OR easy for the BB to defend.
I think it's just going to be a lot easier if you write out your defending range, but I just don't see how you're going to be able to defend nearly as much as you say that you are.
Originally Posted by GntlmnsHndshk View Post
The BB is going to want to defend as little as possible because the wider he defends the thinner the SB will be able to value bet.
The BB is going to want to defend as little as possible because the wider he defends the thinner the SB will be able to value bet.
That your claim is absurd should be obvious from the fact that it logically implies that we should fold everything but the nuts to a bet, thereby preventing our opponent from betting for value with the second nuts.
Originally Posted by GntlmnsHndshk View Post
Now the BB doesn't need to defend enough so that the BB cannot bet any two cards, he just needs to defend enough so that the SB has both a betting and checking range.
Now the BB doesn't need to defend enough so that the BB cannot bet any two cards, he just needs to defend enough so that the SB has both a betting and checking range.
The vast majority of boards where the the GTO equilibrium includes the SB having both a betting and checking range, there will often be hand(s) which will be indifferent between both betting and checking. By definition this means that the EV of these hands will be equal. Similarly, since when the SB checks back ALL of his hands will be +EV because even his weakest hand has some equity to draw out and has fold equity. So since all of the SBs hand are +EV, the BB cannot defend so much that the SBs weakest betting hands are 0 EV because then they wouldn't be indifferent to checking.
The difference is that when your opponent raises your c-bet, we're assuming that he's going to have a folding range (otherwise there would be no reason for you to bet). So if the Villain has a folding range, then the EV of his folding range is 0. So if when your opponent raises, if he can raises any two cards profitably, then he wouldn't have a folding range, and then we wouldn't be at equilibrium. So as suggested, the difference between defending your bet against a raise, and defending when oop are strikingly different.
I've constructed a new range of about 75% now. It's surely possible to be a winning player with a 60% VPIP from the BB, as this is relative to how your opponent playes. One can for instance look back at the games a couple of years ago where pretty much only sauce123 defended 80% from the BB (at highstakes). It seems obvious that he was not the only one crushing the games. However, I have now adjusted my default, and am in agreement with you that we are probably getting too good odds to fold >25-30% of hands preflop. What do you think of 3betting around 17%?
I think that typically occurs though at 100bb with a 3x 3 bet sizing when villain is folding >70-75% of his opening range, ie you can start 3 betting hands that can't profitably defend because they actually benefit more in terms of EV than 3 betting a hand like 89o. That can be an especially big deal vs habitual 3x openers.
FWIW you do actually see these guys a fair amount a NL50.
Hey Spladle, you've must been spent hours replying to this thread, educating me and prob a few others, for which i thank you, so please answer me to one more question, actually to my original question itt:
How do you construct a defending range from BB in srp on a 222 flop, both c/c and cr? Whats the starting point from a GTO perspective? Maybe you'd like to expand it and share some GT fundamentals on other flops too?
How do you construct a defending range from BB in srp on a 222 flop, both c/c and cr? Whats the starting point from a GTO perspective? Maybe you'd like to expand it and share some GT fundamentals on other flops too?
Spladle (also Kaby and others i forgot), you are doing a helluva job here. This is one of the best threads i've read on 2+2 so far!
As of now i try to start by guessing a range that the sb can triple barrel and get called by 50% worse hands, adding bluffs, and then see what hands can/should call down in BB's shoes. The problem with that is obviously that:
a) the board changes (sometimes a lot, making it very difficult to construct good ranges for 752ss for example compared to A72r)
b) both player's ranges are a function of the other player's range, which sometimes results in many, many steps of adjusting both player's ranges back and forth.
c) this approach completely disregards chk-raising, which can't be right, lol.
I know that this procedure is very cumbersome and probably there exists a superior way of coming up with a good range for either player, but unfortunately i haven't found one yet
Highly appreciate any input
The 1-alpha threshold is only relevant in a very specific situation, namely a river spot where one player has a polar range with sufficient bluffs and the other player has a blufcatcher. You can not generalize this result to other situations. (Even in most river situations it would be completely wrong to defend 1-alpha).
On other boards (like 884r), I believe the relationship is very different - against smaller bets, you should continue more frequently but check-raise less frequently. As bet size increases, you should fold more often but check-raise a greater proportion of the hands you do continue with. As bet size increases still further, though, the relationship switches again, and check-raises should become less frequent.
Same principle as facing overbets I assume. That is, villains range should be so polarised there's no incentive to raise any part of your range.
then our checking range is going to be very weak and open to exploitation by the opponent, so we would then adjust by adding stronger hands to our check-calling range. Now while all hands can check-call, if it's higher EV for a hand to bet the river after betting the flop and turn, then it's going to be hard for you to convince me that it should be played as a check-call (ignoring capped ranges for now).
What is a "bluff"
You didn't describe a 3-bet range above any more than I have here:
"Oh, you know, some good hands and some bad hands."
Yes of course. Fwiw, I think Kaby nailed it earlier when he said that the correct way to play this spot is to bet often and small. This is the logical bet sizing adjustment on this board, if your opponent is check-raising often and that his flatting range doesn't have lots of outs. So for the sake of simplicity, lets assume that if the Villain could only have one bet size that it would be half-pot.
What does it mean to say that the BB's flatting range "doesn't have lots of outs"?
Of course, there are boards that the SB should bet 100%, the irony being is that I'm arguing that this is one of them. The point isn't to say that it's exhaustive, it's to show the logic why the SB should be +EV for the SB to bet any two cards. I'll explain another way.
The vast majority of boards where the the GTO equilibrium includes the SB having both a betting and checking range, there will often be hand(s) which will be indifferent between both betting and checking. By definition this means that the EV of these hands will be equal. Similarly, since when the SB checks back ALL of his hands will be +EV because even his weakest hand has some equity to draw out and has fold equity. So since all of the SBs hand are +EV, the BB cannot defend so much that the SBs weakest betting hands are 0 EV because then they wouldn't be indifferent to checking.
The vast majority of boards where the the GTO equilibrium includes the SB having both a betting and checking range, there will often be hand(s) which will be indifferent between both betting and checking. By definition this means that the EV of these hands will be equal. Similarly, since when the SB checks back ALL of his hands will be +EV because even his weakest hand has some equity to draw out and has fold equity. So since all of the SBs hand are +EV, the BB cannot defend so much that the SBs weakest betting hands are 0 EV because then they wouldn't be indifferent to checking.
I've constructed a new range of about 75% now. It's surely possible to be a winning player with a 60% VPIP from the BB, as this is relative to how your opponent playes. One can for instance look back at the games a couple of years ago where pretty much only sauce123 defended 80% from the BB (at highstakes). It seems obvious that he was not the only one crushing the games. However, I have now adjusted my default, and am in agreement with you that we are probably getting too good odds to fold >25-30% of hands preflop. What do you think of 3betting around 17%?
The starting point is always intuition. After that, work backwards from the river.
As of now i try to start by guessing a range that the sb can triple barrel and get called by 50% worse hands, adding bluffs, and then see what hands can/should call down in BB's shoes. The problem with that is obviously that:
a) the board changes (sometimes a lot, making it very difficult to construct good ranges for 752ss for example compared to A72r)
b) both player's ranges are a function of the other player's range, which sometimes results in many, many steps of adjusting both player's ranges back and forth.
c) this approach completely disregards chk-raising, which can't be right, lol.
I know that this procedure is very cumbersome and probably there exists a superior way of coming up with a good range for either player, but unfortunately i haven't found one yet
Highly appreciate any input
a) the board changes (sometimes a lot, making it very difficult to construct good ranges for 752ss for example compared to A72r)
b) both player's ranges are a function of the other player's range, which sometimes results in many, many steps of adjusting both player's ranges back and forth.
c) this approach completely disregards chk-raising, which can't be right, lol.
I know that this procedure is very cumbersome and probably there exists a superior way of coming up with a good range for either player, but unfortunately i haven't found one yet
Highly appreciate any input
Not sure what that means exactly, you left the interesting part off the quote because those hands benefit more in terms of EV than 3 betting a hand like 89o
Maybe that's lol or lolobvious. You're certainly much smarter than me if it is.
Maybe that's lol or lolobvious. You're certainly much smarter than me if it is.
You've basically got it. Highly dynamic boards are indeed much more difficult to "solve" and require more work away from the tables, and ignoring check-raising isn't right, but to my knowledge no superior method exists to "intuition + simulations + poking/prodding strategies for weaknesses."
Ace-high or better + any two cards 5 or higher with a backdoor flush draw + gutshots.
OOriginally Posted by GntlmnsHndshk View Post
Of course, there are boards that the SB should bet 100%, the irony being is that I'm arguing that this is one of them. The point isn't to say that it's exhaustive, it's to show the logic why the SB should be +EV for the SB to bet any two cards. I'll explain another way.
The vast majority of boards where the the GTO equilibrium includes the SB having both a betting and checking range, there will often be hand(s) which will be indifferent between both betting and checking. By definition this means that the EV of these hands will be equal. Similarly, since when the SB checks back ALL of his hands will be +EV because even his weakest hand has some equity to draw out and has fold equity. So since all of the SBs hand are +EV, the BB cannot defend so much that the SBs weakest betting hands are 0 EV because then they wouldn't be indifferent to checking.
Of course, there are boards that the SB should bet 100%, the irony being is that I'm arguing that this is one of them. The point isn't to say that it's exhaustive, it's to show the logic why the SB should be +EV for the SB to bet any two cards. I'll explain another way.
The vast majority of boards where the the GTO equilibrium includes the SB having both a betting and checking range, there will often be hand(s) which will be indifferent between both betting and checking. By definition this means that the EV of these hands will be equal. Similarly, since when the SB checks back ALL of his hands will be +EV because even his weakest hand has some equity to draw out and has fold equity. So since all of the SBs hand are +EV, the BB cannot defend so much that the SBs weakest betting hands are 0 EV because then they wouldn't be indifferent to checking.
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