Yes, this is always correct and there are no exceptions. You always have to take the most +EV line.

Look at it like this-- if we pretty much never have a nut type hand, we'll often get our opponent to make very large overbets if we're deep (in theory). So it may be more profitable to slowplay a strong hand even in a risky spot if we'll sometimes get a massive overbet from our opponent. If our opponent won't do this, or if it happens at too low of a frequency to justify slowplaying, then we should go ahead and play our nut type hand aggressively rather than slowplay it and we'll just have to deal with sometimes having a capped range.

FWIW, most people don't overbet anywhere nearly enough, so it's fine to constantly have a capped range and you'll very rarely get punished. Even in theory it's fine to often have a capped range, but it's especially fine in practice vs most players.

A GTO opponent does not change his strategy based on what you're doing. So playing your nut type hands differently won't change the EV of your medium strength hands, which is why you always need to take the most +EV line with your nut type hands.

Matthew,

Thanks for your response.

If you decide to do a volume 2 I think you should do a workbook with say 50 hand examples.

You have pretty much explained the concepts in as much detail as possible except maybe expanding on calling 4 bets and maybe 5 betting small as with min raise opens this may be possible to do now.

On page 399, let's say we know our opponent will raise exactly 25% of the time when we bet 40% of the pot, then we'd be going all-in with all our nuts hands since it has higher EV.

But he will now be able to raise shove AJ and KJ balanced with some bluffs and our KJ hands will lose a ton of money compared to being included in a range with some nut hands where our opponent cannot raise us with AJ/KJ/bluffs.

I understand the higher EV route needs to be taken with any hand, but I don't understand how it can be correct and make us unexploitable (if we were to play perfectly in all spots) to play this way.

Going back to my example, losing a tiny bit of value with our nuts hands and gaining a lot of value from our non-nutted hands seems a far better adjustment than just maximizing our EV with our nuts hands.

Thanks

Usually when you change one thing it will cause several other things to change at once. So let's just go one (or two) steps at a time.

#1) Do you agree with me that when playing against a GTO opponent, he will never change his strategy no matter what we do?

#2) If so, do you agree that it's impossible for the EV of your medium strength or weak hands to change regardless of what you do with your nut type hands?

I agree with #1, not #2. We don't know what strategy the other GTO will be using since we can't solve for it.

Basically it doesn't make sense to me that playing a hand in a way that always maximize our EV with this particular hand would be GTO. The way I see it, it would be much better to maximize the overall EV of our range, and this example is perfect to express my point.

How can the rule that says we need to play a hand in a way that maximize his EV guarantees us that we are unexploitable? Playing it differently can be better overall for all our hands in our range, and maximizing our overall EV is IMO the way to be unexploitable.

I'm sorry if there's something obvious that I don't get, this stuff is just really messing with my head.

It doesn't matter if you know what his strategy is. As you've conceded by agreeing with #1, his strategy will never change no matter what you do. Therefore, regardless of what you do with your nut hands, he will always respond in the same way to any particular action, even if your range for taking that action consists of only medium strength or weak hands, theoretically leaving you vulnerable to further exploitation. Agreeing with #1 means you agree that he will not be exploiting you in this way.

Maximizing the overall EV of our range requires maximizing our EV with every individual hand in that range. Failing to maximize the EV of any particular hand renders it impossible to maximize the overall EV of our range.

What's confusing you is that you aren't actually imagining yourself playing a GTO opponent - you're imagining yourself playing a real person who will adjust to any change in strategy that you implement. The wording in the problem you posed makes this very clear. I'll bold the important part:

See what you did there? You imagined yourself playing one hand in the way that maximizes EV, then imagined your opponent adjusting in order to exploit your strategy. But this isn't something a GTO opponent would do, as you acknowledged by agreeing with #1. You proceeded to disagree with #2, but this was irrational, because #2 follows directly from #1.

Hope this helps!

But how is that possible? If your opponent's strategy doesn't change, then it won't ever matter what you do with your nut type hands. You can always check-fold your sets post-flop, and it still won't change your opponent's strategy. And if your opponent's strategy isn't changing based on what you do with your nut type hands then it won't effect the EV of your medium strength hands.

It sounds like you are incorrectly thinking "I don't care about maximizing the EV of every single hand in my range. I care about maximizing the EV of my entire range." But it's only possible to maximize the EV of your entire range if you're taking the line with the highest EV with every single hand in your range.

Put differently, if you ever take a line that doesn't have the highest EV you'll always have an incentive to change. And if you have an incentive to change against a GTO player, then you're not playing GTO yourself.

Ahh Spladle responded while I was typing, thanks for that and hopefully reading his response will help you as well (it's good to hear two different people explain the same concept in different ways). Bonus points for the bowling analogy.

Yes thanks guys, I now understand what you mean when playing someone who will not change his strategy. But if the opponent isn't GTO and actually adjusts to us, how can we be sure that we're unexploitable using your strategy?

If by "my strategy" you mean the ranges/ratios/simplifications etc in the book, you can't. As long as we're not playing GTO ourselves (and no one is even close to being able to play GTO) then there's always the chance we're the one being exploited.

Realistically, if you're playing a game closer to GTO than your opponent then you'll probably have the edge on him and it will be pretty hard for him to exploit you (and you can always adjust to exploit him as well).

How can we know that taking the action that maximizes the EV of each hand will result in us playing GTO? We can't protect some hands in our range and it will decrease the EV of those hands when we only try to maximize the EV of other hands.

So basically, only looking at our actual hand (and not our range, unless we want to bluff and justify it by making our opponent indifferent to calling, etc) and maximizing the EV of this hand is the way to play GTO?

I actually deleted the bowling analogy because I decided it might be more confusing than clarifying.

You can't be sure, and in fact it is virtually impossible that you will ever play unexploitably.

First, it's important to note that maximizing the EV of each hand against an opponent playing GTO will result in playing GTO. Maximizing the EV of each hand against most real-world opponents will not.

As for why, well, it's simply true by definition. Playing GTO means playing in such a way that you maximize the EV of every hand you play (assuming your opponent plays GTO as well). How can we know that scoring more points than our opponent in a football game will result in us winning? Because that's how winning is defined.

This is false. Refer back to points #1 and #2 above:

#1) When playing against a GTO opponent, he will never change his strategy no matter what we do.

#2) It's impossible for the EV of [a hand] to change regardless of what you do with [other] hands.

If we are playing GTO, then maximizing the EV of some hands will not decrease the EV of other hands; any attempt by our opponent to exploit us will by definition fail. If you identify a way that your opponent could exploit you, then you know you aren't playing GTO and should modify your default strategy to remove this vulnerability. But if you are already playing GTO, then no such vulnerabilities will exist and no such modification will be required.

Remove the text in parentheses and you've got it, but remember that in order to maximize the EV of your hand against a GTO opponent, you need to know the GTO strategy yourself. In practice, this is impossible, so it makes sense to think about your range as a whole in order to develop reasonable approximations of what we think GTO ranges should look like. But actual GTO play would only look at our actual hand and never our range (not even when bluffing and making the opponent indifferent to calling).

Matthew,

I was reviewing the sample hands at the back of the book.

When you are the preflop raiser and get a bad flop eg low and connected like hand no 9.

It's hard to check call so you check raise all your sets.

But by doing this when u bet you are capped at overpairs/two pair.

So when you get raised by sets how are we defending?

3 betting into a polarised range is bad especially when we have no nut hands and calling with overpairs will let our opponent have a chance to improve their bluffs. Our opponent can also over bet with sets.

Wouldn't it make more sense to not have a check calling range and just try to bet more often with some check raises to punish an opponent who bets any two when checked two.

Hope all that makes sense just having a hard time with this spot. These flops oop are a nightmare.

Any differences between the ebook and paperback?

No footnotes for ebook

I've hinted at it throughout the book and in some CardRunners videos, but this is a bit too complex and detailed for me to discuss in one lengthy post. Hopefully this should get you on the right track though.

#1) Ask yourself "Does putting sets into my betting range really change my opponent's incentive to raise or call certain hands?" For example, imagine I never CB sets (or even two pairs) on a T 9 3 board, but bet a lot of top pairs and overpairs.

If my CB range is capped at overpairs, what kind of hands will my opponent usually raise "for value" on the flop? Probably his two pair and sets. What if I start betting some sets on the flop as well now? Well, it probably won't change much. He'll still just raise two pairs and sets.

In other words, there's no way we're ever realistically going to design a CB range where our opponent can't raise sets and two pairs for value very comfortably. Even if we bet all our sets on this flop, if our opponent looks down at T9 he'll almost certainly say "It doesn't matter what my opponent's CB range is, T9 loses to very few hands (only 5 set combos total) and there are way, way more than enough overpairs, top pairs, and draws to justify a raise.

#2) Ranges are never perfectly polarized. So if the opponent knows you're never going to 3-bet since you refuse to CB/3-bet two pairs and sets, then he'll probably start raising you very aggressively with a lot of bluffs and draws. In other words, it's pretty reasonable to sometimes say "Well.... my range is pretty capped here, but I don't want to give a ton of free cards. So even though it's far from ideal, I'm going to 3-bet here since I think my opponent has way more bluffs than value hands and I think he'll have to 'float' me with some bluffs. Also, I don't mind putting more pressure on his draws, especially if he's raising with some relatively weak draws."

The above is an oversimplification, but hopefully you get the idea. I could go into more detail but I'd rather not as I don't think it will be overly useful, especially since the terms "value" and "bluff" won't work perfectly in a lot of spots (like super wet boards on the flop).

Thanks a lot Spladle, I now understand and agree with all the stuff you're saying. I appreciate it!

I have footnotes in my ePub version. Or do I have end notes and I'm missing footnotes?

nah i don't have endnotes either, that could possibly be it

Klever, not sure if it help you at all, but in my ePub version I have 26 hyperlinks (numbered 1-26) that follow after various sentences throughout the e-book. When I click on them a separate page with a one to two sentence explanation/clarification/expansion (take your pick they vary) appears. There is a "back" hyperlink, which takes you back to the page you were on. These to me function as e-book footnotes. I only mentioned end notes, because once you are in the 1-26 and if you don't click "back" you can page forward and back through the different notations, which is more of an end note style.

np, happy to help. =)

Nah it doesnt work but its alright though thx

I have just went through the entire book from start to finish during the past 10 days or so, taking notes.
So obviously it was a lot of things to cover.

One thing I cannot seem to wrap my wits around fully - river betsizing. Two concepts clash, and even when I try to combine them the outcome doesn't seem elegant enough.


Scenario a is as follows - I am in the SB, taking a bbb line. HU play.
Villain has a more or less capped range OTR (due to a turn overcard with draws out there).
On the other hand, I am holding a hand which I know how often it is best (and it is not the nuts).
Those two seem to get me to two different ideas on how to proceed.


Example, flop was J74, and turn was a Q - an overcard. He will not have any Q other than Q7 and possibly Q4 in his flop xCalling range. It is very likely that the few Queens that he does hold will be raised on the turn (since they'll turn twopairs), together with his sets, when I do bet there.
It is a common HU situation, where turn overcards typically completely miss BB's flop xCalling range.
So on the river his range is pretty much capped to Jx, other than rare rivered two pairs and rare slowplays.

Let's assume the river bricks off, and this is our scene:




Now, how should I then proceed? Ignoring the xR possibility (ie those few 2pairs and sets in his range on the screenshot), if we could work it out specifically, it'd be great.
Flopzilla tells us how often we are ahead. If I remembered to exclude sets and most twopairs before taking the screenshot, it'd be about 78% ahead and 22% behind.


My best guess, after going through the book, for our entire range is -
- bet big (pot or even overbets, overbets are theoretically better as we can bluff more then) with TP+
- fill up the range that bets that same big size with the "appropriate" number of bluffs (so for PSB we add in half as many bluffs, etc. for different sizings, depending on his pot odds after we bet)
- and, bet the "optimal size" with TP, like J3 on the screenshot, as per the maths in the equation in the book.
(I think that range will often be quite small? Nothing other than a J would fit in this spot.
And there are no bluffs to be included there to counteract it, as the bluffing part of the range is covered by Jacks which happen to be behind his Jacks when we are called)


But it feels kind of crude, and even a bit transparent.... and aside from that crudeness, I might be missing something else in the situation, as well?
Is that how we approach the situation? The Pinpointing river sizing chapter is for our "good but not great, and definitely non-nuts" hands only?


If we weren't into multiple sizing but wanted to use one size, how does that fit with our knowledge of how often we are beat/good and what our sizing should be according to that, as opposed to the bet-big-to-bluff-more concept? it appears as if it simply does not.


If we could work out the specifics, in a typical single raised pot with the percentage our hand is ahead from the screenshot, that would be great.
Pot on the river is 34bbs, we have 83 bbs each, we can ignore huge overbets or math that isn't as consequential here with too many overbet sizings as I'm more into the concepts. The river bricks off, like a 2h.




Scenario b, let's assume he isn't capped (maybe some draws he might have hit OTR, a 2s would make for some interesting changes in our scenario as several flop gutters or A highs turned a flushdraw) - how do we betsize then, in a nutshell?


That's a lot of parts of the picture, I know, but I felt each of them is necessary to complete it and see it clearly!