I received the second link so thank you for that. The first link was in my Junk folder (Hotmail) and I didn't spot it, cheers.

I actually purchased your EHUNL video pack, I will re watch that video and hope it clears things up for me.

I guess I'm just struggling to find practical ways to incorporate GTO concepts into my poker game? It seems the more I learn the less I understand? I've read MOP, EHUNLH, and am working my way through Janda's book. The thing I like about Janda's book is that he appears to have worked out a framework that can be applied in practice that is based on GTO concepts.

You stated....

"First of all, the original indifference argument can break down for a lot of distributions (eg what if villain doesnt even hold any air or not much) Second those ideas about the EVs of bluffing and not bluffing are pretty much always wrong. ATC have like 20perc chance to pair up if they check back and get a couple free cards, bluffs and esp semibluffs can still win a lot if they bluff and get called, etc. And it turns out that these things can have a v big effect on the estimated gto strats. So the naive estimate found by calling to make complete air indiff is usually completely wrong."

Does the fact that a GTO strat includes a calling range and approximating those frequencies address some of these concerns?



On p.69 of Applications of NLHE Janda writes...

"We know it's necessary to defend wider against a raise first in if we defend by calling instead of 3-betting since calling lets our opponent see the flop. Therefor, it should come as no surprise the same concept applies when we open and face a 3-bet. That is, when we call our opponents 3-bet, he's guaranteed to get to see the flop and have the opportunity to either make a strong hand or profitable bluff. This forces us to defend many more hand combinations than if we only 4-bet or folded."

Let's start by assuming we use a 45 percent button opening range-a reasonable button opening range used by many winning players. When we open to 2.5 big blinds and our opponent 3-bets from the big blind to 9.5 big blinds, he risks 8.5 big blinds to win 4 big blinds. And as we've already shown, this means the big blind's 3-bet cannot be allowed to succeed more than 68% of the time. Put another way, it's important to defend at least 32% of our opening range and since our opening range is 45%, this means we should defend at least 14.4% of all hands.

0.144= (0.32)(0.45)


However, the 14.4% is correct if we only defended by 4-betting, but now we need to figure out how many additional hands should be added in if we also defend by calling."

He then goes on to discuss methods to solve for reasonable calling ranges. Is this a solid approach in your opinion?


I've been watching some of DC's video series on GTO and it seems that they are working on the basics with the promise that it will all build to something useful. Frankly I'm starting to lose faith. When asked for specific application, the default response seems to be that NLHE has not been solved...so we can't answer that.

Is there a video where someone is playing and discussing their decision process(live) while applying GTO concepts? I think this would be very helpful for many of us to understand this whole approach. I find the theory interesting, but would like to see how an expert applies it in real time.

After spending a bunch of time going down the GTO rabbit hole I'm starting to get a bit frustrated with my lack of understanding, and my personal inability to apply concepts. Maybe I'm taking things too literally, and would be better off playing my normal exploitative game, with an emphasis on ranges/distributions and just being aware of broad GTO theory to avoid spots where I'm easy to exploit.

Any suggestions?

Ah great, yea video 4 is basically a critique of the "make Villain's air indifferent" approach to estimating unexploitable frequencies.

I'm not sure I understand your question?

Yea that all looks right (up to card removal effects), but I guess the trick is in those methods that he goes on to discuss. I mean, I'm sure Matt understands the relevant issues, it's just that there can be a lot of quite subtle effects that make it difficult to achieve useful results.

Interesting questions, I reflected on them a bit, and I have a couple suggestions that may or may not apply to you, but probably apply to a lot of players...

So, as we've been talking about, it can be difficult to get exact results, but overall, a study of game theory can give you a lot of insight into what your frequencies and ranges should be in various spots. And it can do that whether or not you're trying to play exploitatively or unexploitably.

But -- is knowing what your frequencies should be useful info? IMO, there's an important prerequisite to being able to make much use of the kind of info game theoretic work often gives you -- you really need to know what your ranges look like in various spots. Knowing that you should be calling a bet X% of the time does you no good at all if you don't know what your range looks like when you face that bet and where your current hand fits into that range. And it's also not good enough to be able to figure out your ranges given 15 mins away from the tables -- for practical purposes, you need to be constantly and more or less effortlessly aware of it in every hand you play.

This isn't as hard as it might sound at first. Most players these days are in the habit of thinking about opponents' ranges at all times. Knowing your own ranges should be way easier, since you know yourself and it's not something that changes as much with every new opponent -- it's just that most people have not gotten into the habit.

I don't really know of any way to get good at this other than to practice. Ofc there's too many spots to tell you what your ranges should be in every spot, and ofc it depends on your style/knowledge, your reads on the pop tendencies and your opponent, etc. So maybe just a readless example --

First hand of the match, in whatever games you usually play and at whatever stacks you usually start out with. You're in the SB -- what do you minraise? BB calls, flop comes QsTh4s and BB checks to you. Whats' your cbetting range and what's your checking range? Given those ranges, what are your frequencies with which you take each action? Suppose you get c/r'd, whats your flatting, 3-betting, folding ranges and what are the corresponding frequencies? If you check back the flop and face a turn lead on a Jh, what are your calling, folding, and raising ranges, and what frequencies do those ranges lead to?

Being able to answer these questions quickly, at least to good approximation, is an important prerequisite to making good use of game theoretic approches to the game. I'm confident that this can be easy for any player who practices away from the tables and forces himself to make it a habit at the tables.

Hi Will, could explain this equation to me from 2.2.1

EV83,B > EV83,A =S-1

I get that our EV is greater after a limp, but how do both A and B "=S-1"

That equation says, first, that the EV of holding 83o at decision point B is greater than the EV of holding it at decision point A, and, second, that the EV of holding it at A equals S-1.

Of course, the two EVs can't both equal S-1 if one is greater than the other.

Got it, thanks

Sorry, that is confusing. What I wanted to know, is your "issue" with the concept of defending enough to ensure that villain cannot auto profit with ATC's because it is often presented in either...

1.) A raise X% or fold context.(Neglecting that a GTO strategy should have a calling range?)

2.) A raise/call/fold framework with the raise+call frequencies equaling X%. (Neglecting the fact that if we incorporate calls in our strategy we need to increase X% to account for the added EV that villain gains when we allow him to see a flop.)

Can we approximate GTO ranges by making educated guesses as to what X% should be, and how that portion of our range should be split between raising and calling, based upon preventing opponents from auto profiting?

Or is the issue more to do with the "auto profit defense approach" neglecting the importance of the distribution of equity in post flop situations?

I'm sorry, even my clarification is awkward.





Thanks for this Will, definitely applies to me, and will help get me back on track. I think my approach has been flawed in that I started to focus too much on constructing some sort of comprehensive strategy before I started playing again.

I think I will start playing again and try to apply the theory I have learned spot by spot and my play should improve as I discover places I'm making fundamental mistakes.

This was a post you made earlier that is similar, and it helped me understand how Game Theory could be applied...

"It'll help you identify spots where you're losing money and need to adjust. As an easy example, if you get to some spot with a mediocre-ish hand, face a bet, and decide it's best to fold, then that's that. But if you get to a spot with a range full of mediocre-ish hands, face a bet, and decide it's best to fold all your hands, then it's a really strong indication that you need to make some adjustments. Or at least become aware of the possibility that you're being exploited, so that if it happens a couple more times, you can realize that you need to adjust. And by the way, keep in mind that your opponents don't have to be smart for their strategies to be exploiting you. Sometimes guys' default strategies just happen to stack up well versus yours. It doesn't mean they're thinking, but you still need to be able to realize what's going on and then adjust to prevent it."

Do you know of a video where someone is applying these concepts in a live flow? Don't you think that would be helpful?

Keep up the good work Will, you have handled yourself very professionally, and I'm looking forward to your next volume.

Only in spots where it makes sense to. For example, I think you would agree that no player should ever be able to auto-profit with a raise (either by 3/4/5-betting ATC pre-flop or raising/check-raising ATC post-flop). If this is possible then you definitely aren't playing GTO. Exactly how many more hands you should be defending isn't clear, but we know there is a lower bound.

I probably gonne regret I posted this, but:

This is only true if 2 conditions are furfilled.

Firstly our street starting range is not allowed to be too weak.

You figure this out by looking @:
the equity distribution (@ start of the street of the player that is defending by calling) (vs the range of hands our other player is betting) does not drops below the following curve:
X - [0,1]
Y - [0,1]
line Y = [(1-X)/X] / [1+2*(1-X)/X] = (1-X)/(2-X)
Found by
GTO call freq = 1/(1+frac)
min required EQ = frac/(1+2frac)
Frac = fraction of pot that is betted
(this curve can be approximated by drawing a straight line through (0;0.5) and (1;0.0)

The above is the graphical quick look solution simular to:
a) bet-fraction known,
b) then my GTO call freq is know & my min required EQ of my bottom defending hand is known
c) i look @ my EQ distribution to see if my bottom hand has the min required EQ
IF not; I cannot defend the required hands & I have to call tighter

Secondly, our street starting range is not allowed to be too strong

you figure this out by looking @
the equity distribution (@ start of the street of the player that is defending by calling) (vs the range of hands our other player is betting)
X - [0,1]
Y - [0,1]
line Y = [(1-X)/X] / [1+2*(1-X)/X]

But now you draw a line vertically upon the bottom hand
Then you meet the above curve
Then you draw a line horizontally to the right
If the equity distribution does not drops below this horizontal line; you can call your complete start flop range.

SO if the equity distribution drops somewhere below the curve;
- there exists a bet-size where the frequency forms an upper bound (meaning every time a bet-size is used @ right of this intersection you have to call tighter & cannot call the 'GTO freq')
SO if the equity distribution does not drops below the curve;
- there exists a horizontal line (representing a maximum allowed bet-size) where you can call ATC as your range is too strong for the used bet-size

The above storry only takes into account freq with which you call and the minimum required equity with which you call.
In his book in his first flop chapter he points towards a 222 flop example where you have to fold more then the frequency dictates. Arriving at same conclusion.
Thought I posted this quickly as it incorporate the concept equity distribution / range to weak to enable following GTO / range to strong to enable following GTO / graphical quick look

You can by yourselve draw easily a random equity distribution around this curve:
- first above the curve
- then drops below the curve
- at end above this curve

And then you are even in a different situation;
- the first area where you are above you call wider but not ATC
- the next area you cannot call GTO but tighter
- the last area you can call wider and there will be an area where you call ATC because there exist a horizontal line

So things are quickly hard and difficult

This is false; betting and raising are different things. As I said, no player should ever be able to auto-profit with a raise (either by 3/4/5-betting ATC pre-flop or raising/check-raising ATC post-flop). This is true regardless of the strength of either player's range. If either player can profitably raise ATC at any point, we know that the original bettor/raiser must be making a mistake.

Your comment would be sensible/correct had I used the word "bet" instead of "raise," but I didn't because then what I said would have been wrong.

Not entirely sure if this has been asked yet in the thread, but I was wondering if that equity distribution tool took into account card removal effects. For example if I give him the A high diamond FD, and I then put the board as 8d7x2d, and the Ad on the turn, the equity distribution does not count these A high diamond draws I put into the range as flushes?

Book Review:

The first poker book I read was Play poker like the Pros by Hellmuth. Reading the introduction immediately put my mind at ease:

Phil was going to teach me "exactly which hands to play, when to bluff, when to call a bluff, when to raise and when to fold." - A pretty good start! - So I kept on reading, I learned about the different player types, the "Phil's top fifteen" and more...

Now since this "review" is not about Phil's book, I will simply say that to describe me as a "Pro" after I finished reading it, would have been a little bit of a stretch. I just wasn't quite there yet. Even with Phil's recommendations poker wasn't easy - I found that tilting off my stack however, was easy enough. You know how that goes:

You've been playing for an hour or so, a nutcase is running over the table. Actually, when I say playing, I really mean you've been sitting there for an hour, you've raised two hands, and sure enough he's 3b you twice, forcing you to fold. But you decide to be patient, play solid, trying very hard not to get annoyed by this guy. Then at last you wake up with a premium hand, AK UTG. You open for a raise and obviously, he 3b. Smiling to yourself, you put in 4b... he calls in the BB. Flop comes KT5r and he instantly check/minraises your cb. You decide to take a stand and, get snap called by T2o. Turn is a blank but sure enough the river is a 2. At this point your new best friend tells you he wasn't sure his flop call was +EV but that he's a fan of Doyle's and you barely manage a "nh" before punching your keyboard.

I guess my point is that poker is not an easy game and that you can't play good poker by simply following a fixed set of rules.

Sauce considers that there are 2 main types of books, practical books and theory books, you can read about it here: http://www.leggopoker.com/blogs/sauc...list-9065.html


Expert HU No Limit Hold'em is a theory book. It shows/explains how to devise a strategy, what factors you should consider when you're building your ranges."Range based" thinking is a key concept in this book, but I guess you can get a pretty good idea of the content by checking the table of contents.

I will tell you what I thought about it:

About the style of the author: Some people have criticized his style, saying it was too dry and not concise enough. I think that's harsh: Sure it's not a thriller, it's a book about poker and Game Theory. It's well written, I'm not saying it's an easy read but I think most people would agree that the concepts that are introduced here are pretty advanced and he did a great job at making them accessible. About conciseness, often the author tries to "build intuition", so he will describe what's going on in plain english. Some people don't like it, I think it's great. You will find a few errors/typos but most of them have been corrected in the errata or addressed in this thread.

Some people were wondering if microstakes players could benefit from this book. I'm a microstakes player and I think the answer is definitely yes. In fact, I wish this had been my first book. I tried M.O.P, but gave up after a few chapeters. This book is so different from other poker books... See I first bought the paperback version. After reading a few pages, I quickly realized taking notes was probably a good idea. Halfway through chapter 2, I decided to buy the PDF version, just because I had so many questions/comments. I remember reading Phil's well and people asking him about his 'aha moments', well... I've had so many reading this book. That's what I mean when I say it's so different from other poker books: This book makes you realize how beautiful/complex/fascinating this game is.

One last thing: All the examples are actual poker hands/situations. One of the things I didn't like about M.O.P was the fact that to illustrate some of the concepts that were being discussed, they used toy games. I guess it's not a big deal but still, I prefer to analyze actual poker hands/spots.

Cliffs:
- People who liked Play poker like the pros may also like this video:http://www.youtube.com/watch?v=oDQLUq8Krh4
- People who prefer Galfond's and Sauce's videos will prefer this book: Phil's and Sauce's videos stand out, so does this book
- Clearly the best book I've ever read.

(And I have nothing against Phil Hellmuth, I think he's a very nice guy and a great player)

What software do you use for calculating equities?

I've tried to use the command line version of ProPokerTools and it is very slow. I haven't been able to get it working in server mode. 8(

Hi Will any other software for Visualizing Equity Distributions for those with macs? Thanks

The non-auto-profit with ATC thing is essentially based on the assumption that we make Villain's ATC indifferent between two actions and that we can accurately estimate the EVs of those two actions as a function of our strategy. Neither of those two things is true in general.

I always think of Phil Galfond as a video maker who is always very conscious of his own ranges. He spends about as much time talking about them as he does about his opponents, and considerations of his own range factor heavily into his decisions. I'd recommend his vids v highly.

"Autoprofit" means that the bluff makes strictly more money by betting/raising than by checking? And ATC means a 0-value hand? Then, I disagree. Your intuition might come from studying over-simplified toy games. It often turns out that, facing a bet or a raise, Villain will continue enough to make some non-pure-air bluff of ours indifferent. In that case, our actual air could strictly prefer to bluff, i.e. autoprofit.

Yea, there's a few different card removal effects we can imagine. First, if you select hands in the ranges that conflict with the board, they're removed from the ranges automatically. So, they shouldn't show up in the distribution on the right, or in any of the equity calcs, etc. Of course, card removal effects our equities too, and the equity calcs are all correct.

There is one subtle remaining issue though, and that is that Villain's range actually affects our range. For example, suppose we take some line in a hand every time we have JJ and 55, and only when we have one of those hands, and the board has no jacks or fives. Then, we'd say our range contains 100% of all the JJ and 55 combos and nothing else. So, on the equity distribution, JJ is gonna get half the horizontal space and 55 is gonna get the other half.

But, if Villain's range contains a lot of JJ and relatively few 55, then when we get to this spot, then we're actually more likely to hold 55 than JJ. So we should draw the equity distribution to indicate that we hold more 55 than JJ, even though we play both of them this way 100% of the time we're dealt them. The EDVis utility does not account for this.

Thanks for the nice review unlimited.

If I'm just doing a one-off sort of calculation, and I want a GUI, I use PokerStove, which is a very solid utility.

Sounds like you're trying to do something automated though? I use my own software for that sort of thing and don't really know what to recommend...

Hi visualizer, I believe the holdemresources.net calculator does this and has a Mac version. Not free, though.

The EDVis utility works with wine (kind of a windows emulator) under Linux, so I imagine it'd work with wine on a Mac, too, although it's not something I've tried.

So our non-air bluffs with some equity would make a 0-EV bluff raise (comparing to max(call,fold) ), but raising 2 napkins could make a profitable bluff? Unless you're talking about some very heavy card removal, I'd like to see an example.

It's not that raising gets us more money with the napkins, it's that checking gets us less.

This happens in most of the [0,1] model games in Vol1. For example in the SB bet-or-check game (pg 248), we have a 1/2-street river situation where SB can bet or show down. In the case of a pot-sized bet, we found that BB calls 4/9 of the time. This is just right to make SB's 1/9th percentile hand indifferent to bluffing. But since this is less than 1/2, SB's complete air does strictly better by bluffing than by giving up.

Things can also be the other way around, where some non-air bluffs are indifferent, but complete-air bluffs do strictly worse by bluffing than by checking. For example, maybe before the river, we bet a polarizedish range where our bluffs are actually draws (ie semibluffs). Then, Villain might have to call a lot more than the naive approximation would suggest in order to make our draws indifferent, since they can still win money after they bluff and get called. But if Villain's calling a lot, our actual complete air is strictly unprofitable to bluff. So the naive approximation where we try to make air indifferent can break down in either direction, sometimes v drastically.

edit: I guess Spladle was focused on raises not bets, so the model game I mentioned doesn't provide a good example. The issue with semibluffing, however, still shows why making air indifferent doesn't serve to give us a good estimate or bounds on the equilibrium frequencies.

Is this book relevant for building a 6-max nlhe strategy?

Well, as you noted in your edit, that's very far from the original Spadle post.

Yeah I agree with all that. I still find your comment on Spladle's post confusing.

Hi,

what is the status of the 2nd volume?