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.

Set up a situation in CREV, have the oop player bet flop, turn and then checks the river. The in position player then bets half pot on the river. What frequency do you think the oop player needs to defend?

Check your results in CREV and get back to me.

I dont understand exactly what are you trying to say. Create the situation yourself and put it here...

If I defend 55-60% of my hands in the BB when facing a minraise, would you call me tight, loose, or something in between?

PREFLOP:
SB/BU opens to 2x, BB 3-bets to 7.5x. BU flats.

FLOP ($15) Q T 6
BB bets half pot. BU calls.

TURN ($30) Q 7 6 2
BB bets half pot. BU calls.

RIVER TURN ($60) Q T 6 2 2
BB checks. BU bets $30.

How often should BB defend here?

Come up some reasonable ranges for the river.

@fityfmi: tight

BB's strategy, in order to be *in the spirit* of GTO, should be to call with up to 66% of his bluffcatchers if that means he will reach the threshold of 66% of his entire range by doing so OR to call with all his bluffcatchers if those represent less then 66% of his entire range.

So you say, did you put it into CREV and solve it?

This isn't in the spirit of GTO at all. Defending ~66.67% of our bluffcatchers would ensure half-street indifference (of villain's "air")*, but poker hands have more than a half-street of play.

ETA: It might turn out that the solution is to defend ~ that % of them, but the crude sort of calculation you're referencing is often way off.

ETA 2: *Provided we can't raise.

I had a feeling this was the case. Then I think there is no wonder Spladle will have to fold enough on the flop to make it profitable to cbet any two. I'm not saying that makes defending your BB with 70-80% of hands wrong though.

fwiw, as i've defined the question, it is kinda a half street game. But this doesn't change the fact that you don't need to defend enough even if it's on the river and it's a half street game.

When you think about the weakest part of the BU/SBs range on the river, the weakest hand is going to have decent equity against the BBs range. When most people fabricate a half street game, they make the bluffs have 0% equity, but this isn't always the case as is here. So the BB doesn't need to defend enough to make the BUs bluffs have EV of 0, the BB only needs to defend enough to make the SB indifferent between betting and checking -- which can be quite a bit less.

Yah, that too.

You should really do a game tree in CREV. Take the villain you have the most hands against and start plugging ranges into it. Just estimate one bet size for each decision, it's close enough and a sh**ton simpler. It takes a while but you'll quickly see how bad folding a hand like J7o is to a min raise pf even considering how often that hand gets folded otf vs a cbet.

OK. Suppose you play this river vs 3 unknown opponents: BU1 bets $60; BU2 bets $30 and BU3 bets $1.

a) Does your river defending range changes from one to another?

b) If yes, why?

yes, your river defending range changes based on your opponents size because you're going to need to make you're going to need to defend enough so your opponent is indifferent to betting vs checking with some hand(s). The smaller the BUs bet, the more likely we're going to need to have a wider defending range.

So you agree that the 1-alpha threshold (where alpha=pot/(pot+bet)) forces you to change your defend range.

And somehow using this thresholds as starting point to develop a [bayesian] balanced strategy vs common bet sizes in common spots it's still outrageous.

where did I say anything about a 1-alpha threshold?

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).

We can safely assume that in every spot we never want to defend a wider range against a bigger betsize than against a smaller betsize, but just how often we want to defend depends on the exact situation. We simply want to defend with the range that minimizes the ev of our opponents maximally exploitative strategy.In the polar vs blufcather on the river this happens to be 1-alpha, in almost every other situation this will be a totally different number.

What we can do is check if the ideas we have about SBs and BBs strategys are consistent with each other. For example, if we would somehow know for sure that SBs GTO strategy involves openfolding some hands on the button preflop, than we also know that BBs strategy should be such that SB can not play those hands he folds profitably for any other line than folding, thus we can deduce that BB should defend >50% time against a minraise, >33% of the time against a 3x, play aggresively enough against a limp, etc. If we know for sure that SBs GTO strategy involves folding every hand worse than 63o, continuing with every hand better than 63o, and folding and minraising with 63o a nonzero % of the time, we can deduce that BB should play such that SB is indifferent between folding and minraising 63o. If we know for sure that SBs strategy involves openfolding no hands on the button, than we can only deduce that BB should play such that SB can profitably play any hand. We cant figure out the exact defending percentage withouth solving the game, withouth making more assumptions it could be 80% or 4% for all we know. Like Spladle said many times, there is no fundamental reason why the SB shouldnt be able to bet 100% of hands profitably in a lot of spots. So,defending exactly 50% preflop against a minraise or 33% against a 3x is completely arbitrary.

No, this is wrong. The SB should defend those hands that can profitably continue against the BB's betting range and fold those hands that cannot. The threshold you keep referring to is irrelevant.

No, you can't just arbitrarily set the "value" range at top pairs+; the range that the BB can profitably bet the turn with is a function of the range that the SB checks behind on the flop with. The weaker that range is after the turn comes, the more frequently the BB can bet for value, and vice versa.

No, this is wrong, the SB doesn't have to defend any particular %.

Because almost every hand will still have some equity when called, the SB calling 50% of the time is not sufficient to prevent the BB from profitably semi-bluffing with any hand he can actually hold. However, even if the BB can profitably bet all of his hands after the SB checks behind on the flop, that doesn't necessarily mean that he should. Just as the SB should almost certainly check back the flop sometimes even when he can profitably bet ATC, the BB should check the turn sometimes (after the SB checks behind on the flop) even if he could profitably bet with ATC.

Poker is more complicated than you think it is.

What job is this calculation supposed to do? It has no relevance whatsoever to poker.

Oh well I think realise now where my mistake was...

In the AKQ, BB check/calls with the K at the frequency (50%) of the threshold otherwise SB should deviate from betting at equilibrium. But BB's call freq coincides with the threshold because he doesn't have hands that are losing vs. SB's bluffs.

IMO, the AKQ toy game should be presented rather like the AKQTJ toy game where BB has {K,T,J} and SB has {A,Q}.

Now its becoming clear that BB should call only with his bluff catchers at a freq of 50% to be at equilibrium! So in this new AKQJT game, BB's TOTAL check/call freq is ~16.7%.


Nevertheless, what i said was not technically untrue because in many spots, usually in those where we didn't bet anywhere, our entire range is at least a bluff catcher. But this doesn't obv apply when we already bet somewhere and polarised our range.

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.

Also this quote is from "Applications of No-Limit Holdem" by Matthew Janda (recommended by sauce) - its about raising a flop bet:

How do you guys comment on that?

Those are raises, not bets. That isn't just a minor detail--it drastically changes the nature of the situation.

Think about it.

Ok,
same book about facing a bet:

about defending vs a bet in position

You're framing those excerpts in a misleading way.

http://forumserver.twoplustwo.com/sh...&postcount=193

http://forumserver.twoplustwo.com/sh...7&postcount=25

Damn spladle is doing some serious work in this thread. Very enlightening