That's not what the words you quoted were saying, and it's not correct, either. Profitable 3-bets derive their profitability from a combination of fold equity and actual equity when called. No hand should be able to profitably 3-bet solely on the basis of fold equity.

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.

No, all hands realize some of their EV from 3-betting when the SB calls.

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.

Any two cards are able to check-call post-flop.

What is KQ+? Does KQ+ = AA-22, AKs-A2s, AKo-A2o, KQs, KQo?

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?

What does it mean for a hand to "hit?"

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?"

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.

My BB defense range against a 2.5x open makes trips or better on 884 ~10.5% of the time.

Depending on how you define "bluff" and "value," this ratio is either a little higher or much lower.

The defending frequency depends rather critically on c-bet size. Against a pot-sized c-bet, defending only 40% might well be right. Against smaller c-bets, I'd defend more frequently (and check-raise less).

Whether this is true really depends on what you mean by "good flop" and "easy for the BB to defend." Because so many of the SB's semi-bluffs have such good equity against a large swath of the BB's potential "bluff-catchers," the BB cannot profitably continue with as many hands on 884r as he could on most other boards. However, because the top of the distributions are static - and because the BB's range is heavier in the hands that make up the top of the distributions - the BB can defend aggressively (i.e. by check-raising) much more often than he can on most boards. The ability to frequently raise and immediately bring an end to the hand is a powerful one, and its value should not be underestimated, even if exercising it necessarily lowers the overall frequency with which he can continue.

No, this is wrong. The opposite is true. The BB wants to defend as much as possible without unnecessarily diminishing the profitability of his strongest hands.

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.

You're committing an epistemic error here that has broad implications beyond just poker.

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.

If this is true, then all it demonstrates is that CardrunnersEV is worthless and wrong. It does not demonstrate that the threshold is not arbitrary.

If CardrunnersEV's max-exploit doesn't work for multi-street/full tree, then it doesn't work for poker. Poker is a multi-street game.

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.

No, it was 100% untrue because, as I've already explained, there are no spots where your entire range should consist of at least bluff-catchers. If you are going to check with some hands that plan on calling bets on later streets, then you also need to check with some hands that plan on folding to bets on later streets.

No, the 1-alpha threshold is 100% irrelevant in both of these spots.

It's not clear to me why you're having such a tough time understanding this.

Read my posts itt: http://forumserver.twoplustwo.com/15...stion-1387323/

The quotes from the book are completely correct. At no point in these quotes does the author state that it is important or necessary to prevent a player from betting profitably with ATC.

We can go through the nuances of how equity is realized into EV, but it's more or less the weighted average of all the strategic options (3-betting and getting folds, 3-betting and getting called and winning / losing 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".


AJ,AQ,AK KQ 99+
and balanced with some "bluffs"


yes I understand that the terms "value" and "bluffs" don't work perfectly before the river, but I know that you know what I'm saying. So yes, KQ sometimes works as a bluff when it gets better hands to fold preflop when AXo folds, and it also works as a bluff when it gets worse hands that it dominates to fold their little equity preflop. And yes it works as value when it's 3-bets preflop and outflops AA. These terms are a bit fuzzy, but since it's not practical too write out the solution to all of poker, I'm going to continue to use these terms unless you can come up with something better.

Fwiw, this process would go faster and better if you'd give the benefit of the doubt sometimes.


A hand like KQ hitting would mean that it makes a pair either the Q or K.

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.

When I say that KJ can be bet for "value", I'm really just saying it's going to be higher EV as a 3-bet because it'll be able to bet all 3 streets postflop if it makes a pair a very significant amount of time (like KQ can). And if a hand can be 3-bet and then bet bet bet postflop, it's going to be hard for you to convince me that it's going to play better as a call.

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.


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.


I read it the fist time and responded to it, so I'm not sure why you repeated it. I gave you a very favorable check-raising frequency and then you chose to just ignore my point.

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.


It does not imply what you're suggesting since I explained how much we need to defend in the follow up sentence which you quoted in your next point, so I'm just going to respond there.


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 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?

+1

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!

I would also be very interested in this.

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 [0,1] games with symmetrical ranges work fine with alpha. It also applies to static multi street situations. The problems with alpha start, imo, when ranges are heavily asymmetrical (this is often the case on river) and/or there are draws present (i.e. there are cards to come).

Not sure I follow the logic of the last sentence. Unless you mean "when villain bets huge, an increasing part of my continuing range is now so strong that it's essentially a slowplay / doesn't benefit from any protection"?

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.

My point is that this is likely true for every combination of cards.

There is not a single hand for which this is true.

Why would I try to convince you that taking a lower EV line for a hand is better than taking a higher EV line?

It is absolutely possible that KJo should be 3-bet against a min-raise 100bb deep, but this reason you've proposed for it being the case is nonsense.

What is a "bluff"

It's not that they don't work perfectly, it's that they don't work at all. So yes, it's true that I know what you're saying, if what you mean is that I know what you're saying is gibberish.

Getting worse hands that it dominates to fold = "bluff"?

So if I bet 32o on AK9 and the turn/river are a 4 and 5, the flop bet retroactively becomes a value bet? Good to know.

They're not just fuzzy, they're literally worse than worthless, because they encourage you to think incorrectly about how to play poker well.

I don't believe you've earned it in this area. You are clearly a bright guy, but you're also saying some very silly stuff.

That seems like a pretty terrible assumption, no?

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."

Are you factoring in the possibility of the pair not being top pair?

What does "a very significant amount of time" = ?

Any two cards can be 3-bet and then bet bet bet post-flop. Am I to understand that you advocate 3-betting 100%? I'm pretty sure that's wrong.

Any two cards can bet two streets post-flop.

My default bet size on this board (as the SB in a single-raised pot) would indeed be half-pot. I'm pretty sure it's not correct to bet often in this spot though for reasons I've laid out elsewhere in the thread.

What does it mean to say that the BB's flatting range "doesn't have lots of outs"?

I read your question the first time you asked it and responded, so I wasn't sure why you repeated it. I gave you a very comprehensive answer and then you chose to just ignore my point.

Ace-high or better + any two cards 5 or higher with a backdoor flush draw + gutshots.

The fact that all hands make +EV bets in no way implies that betting all hands maximizes EV.

That's less than I currently 3-bet, but I'm not sure my current 3-bet strat is optimal. Important to note that 3-bet strat should change based on the SB's opening size and stack sizes. The range of frequencies that I'd consider reasonable is something like 14-24%, so 17% is probably fine.

The starting point is always intuition. After that, work backwards from the river.

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."

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.

Fictitious play tho.

Cool, thx. What % of hands are you flatting with preflop, so I can guesstimate your continuing range.


Your losing the thread of the discussion. This point has NOTHING to do with whether we should bet our entire range on this flop... we weren't discussing this hand during this section. Instead, you asked me to explain why I thought that the BB can bet any two cards profitably on nearly ALL flops... and of course, just because he can doesn't mean that he should. You also think this is true based on what you've seem some limit bots do, my reason is different than yours. My reason has to do with the idea that the SB wouldn't be indifferent between betting and checking some mixed strategy hands if he wasn't able to bet any two cards profitably.