Actually i tried to find articles dealing with 5b bluff and found that:
http://en.donkr.com/forum/optimal-3-...-part-1-533561

Interesting part:

"We include 5-bet bluffs in Bob's value range
Remember the definition of "value range" as the hands we 3-bet, planning to 5-bet all-in after a 4-bet. Some of these hands will be 5-bet bluffs, but for simplicity we'll refer to all the 5-betting hands as Bob's value range.

From the previous theory section, we remember that Bob wants to have enough Axs 5-bet bluffs in his value range to make Alice's weakest value hands break even. This accomplishes two things for Bob:


He forces Alice to fold more of her 4-bet bluffs
He makes it impossible for Alice to "cheat" by not paying off Bob's value 5-bets with {KK+}. If she tries to be "smart" and fold QQ/AK, Bob will just collect his profit with his 5-bet bluffs instead.


So Bob's 5-bet bluffs with some Axs hands attack Alice's 4-bet bluffs, and they also make it impossible for her to profitably tighten up her value range, even if she knows Bob's value range is the squeaky tight {KK+}. Keep in mind that Alice knows Bob's strategy, since this follows from her own strategy, which follows from her opening range, which both players know.

So she knows Bob only 3-bets/5-bets {KK+} for pure value, and if Bob's doesn't 5-bet bluff a bit, Alice can improve her 5-bet-calling strategy by folding the big underdog's QQ/AK from her value range {QQ+, AK}. And when one of the players can improve his/her EV by a strategy change, the original strategy pair can't be optimal (per definition). So Bob has to 5-bet bluff.

The next step for Bob is to add enough Axs to make Alice's weakest value hands break even when they call a 5-bet. Alice then calls off her last 73bb to win the blinds + Alice's 4-bet + Bob's stack =1.5 + 27 + 100 =128.5 bb. The pot odds are 128.5 : 73 =1.76 : 1, so Alice needs minimum 1/(1 + 1.76) =36% equity against Bob's 5-betting range to call profitably. - See more at: http://en.donkr.com/forum/optimal-3-bet4-bet5-bet-strategies-in-nlhe-6-max---part-1-533561#sthash.SDePMF6V.dpuf"

He won't be BE with his worst felting hands (QQ and AK being CO if i take your chart) versus our value felting range already (JJ+, AK). Actually JJ is used to be a value 3b (will be called by worse) and will be 5b as a bluff (underdog vs the value 4b range of CO).

Thus, you have no room to add new 5b bluff combos and have to 3b less than indicated in your chart.

That article is incredibly old so I wouldn't worry too much about it. Besides, a GTO strategy probably calls 3-bets and 4-bets OOP very often. There's also a ton of mixed strategies pre-flop that get messy very very fast that aren't really worth worrying about for the vast majority of players.

Well, the article may be old but the math don't change

If you don't mind i'll make these asumptions, just tell me if you think they're not right:

1) Our 3b valuerange is made of hands which have 50%+ equity vs vilain 3b calling range and 4b value range.

2) In the GTO framework, the worst value hand in a given spot BE

From asumption 1, given the CO a range of 99+,AJs+,KJs+,QJs,AQo+,KQo which either call a btn 3bet or 4b/c (the range is from your book), JJ has 52,2% equity so we 3b for value. TT has 47,5% equity so it's ok not to 3b it, same goes for AQ (actually it's not quite true cause CO will sometimes 4b bluff and as you pointed out we can sometimes use TT/AQ for the purpose of 3b/c).

Once we've 3b JJ vs CO, we know that 5betting it is profitable given the felting range of CO (QQ+, AK in your book) and our FE vs his 4betting range. So we 5b cause it's more profitable than folding and that's it for what we get from asumption 1.

Now if we try to add some 5b "pure" bluff into that (by "pure" bluff i mean hands we don't 3b for value but still include in our 5b range, namely A5s- type of hands or small pp). Asumption 2 tell us that we can add as much combos of 5b pure bluff as it makes the worst vilain felting hand BE. When vilain 4b and we shove (let's say he opens to 3, we 3b to 9 and he 4b to 24), he has to put 76bb in a pot which is 125,5 which give him pot odds of 125,5:76 = 1,65:1 so he needs minimum 37,7% equity versus our felting range to call.

QQ vs {JJ+,AK} already has 47,3% equity
AK vs {JJ+,AK} already has 40,5% equity

Therefore given asumption 2 we can't add any 5b bluff combo to btn felting range, which makes the 3b btn vs co range given in your book too much bluff heavy (vilain could theoritically 4b ATC and show an immediat profit).

Hope i've been clearser, i'm really not trying to mess with you, just want to be sure i understand the concepts exposed in your book ;-)

Hey Matt! Love love love the book and a big fan of videos (you haven't made one in a month!).

Would it be possible for you to update your ranges every so often? I know you speak a lot of the ranges in your videos and how they are constantly evolving but wondering if you can give us an update of ranges you provided in the book? Thanks!

#1) This isn't true in the sense that GTO poker doesn't look at hands as "value bets" or "bluffs" pre-flop.

Basically, the terms "value bet" and "bluff" just don't work all that well in a lot of spots. Pre-flop is one of them, so if you start out trying to classify hands as "value 3-bets" or "3-bet bluffs" then I think you're greatly oversimplifying things.

Calling hands as "bluffs" or "value bets" pre-flop does work pretty well when people never flat 3-bets or 4-bets OOP (which I believe this BUGS model assumes, but could be wrong as I have not read the entire article), but that's not true in theory even though this advice was commonly accepted several years ago.

#2) For 3-betting this probably isn't true OOP (see my post #62 in this thread) and this may or may not be true in position.

I already explained a bit of how I'd overall update the ranges on post #62 and it's been discussed quite a bit in recent CardRunners videos.

I actually don't have all the ranges updated even on my computer. I'm mostly concerned with button and blind play at the moment and probably will make a series on CO/BTN/blind play later. I'm just less interested in ranges dealing with MP and UTG since those spots occur much less frequently, they're overall a bit simpler, and they probably involve lots of mixed strategies which will get messy (for example, since you have fewer combos hands like AK will make up a larger chunk of your range post-flop, which probably requires you to do more different things with it post-flop).

Toy games are so much easier than actual poker. Do you consider it reasonable at all to try to model the EV of a call with bets left to play, or the EV of you betting/raising and your opponent calling from a GTO perspective (assigning a betting range + continuing range on possible future streets as well as a calling range + range for all possible future actions)? The process seems rather "messy" as you say, even for a "simple" discrete situation. The general approach seems to be to go by experience (as in a large database) to evaluate the EV of such situations when we compare them to a line ending in an all-in or a fold on the current street. At least, that's what HU SNG players tend to do by looking at their winrate with various hands and comparing that to either their winrate when they 3bet them (or even possibly try to calculate the optimal getting in range based on ~GTO calculations).

Looking at line EV based on past success has two disadvantages though. It can only tell us how well we're doing, without telling us how well we could be doing, or how much worse we'd do at higher stakes. Basicly it says "with my current skill vs my current field this works better than using this hand to get it in" which certainly is effective at telling us what would currently earn us money but fails rather hard at improving our understanding of the game and reasons for what we do. Also we have the issue of database size. If our database is modest, then we have to rely on someone else's who may not have the same postflop game quality we do... Also, even with a large database, we have played differently over the past 150k hands than we did over the 500k hands before those (hopefully better).

TL;DR: can you think of a reasonable way to evaluate the EV of taking the action to future streets rather than pressing the issue immediately if given the chance, other than through experience and past winrate in similar situations? I'm particularly curious about this given the modern way of defending more 3bets and 4bets with calls.

Your book certainly sounds great and has been strongly advised so I really look forward to giving it a good few reads!

From reading this thread, I'm very interested in buying and studying the book.

I really also would like to read Will Tipton's book.

If anyone here has read both, can you please give a very basic analysis on how these books are different, and which one might be better to read first?

Edit: you can leave out the obvious in that Will's book is aimed at heads up.

Thanks a lot Matth, your enlightments are precious. I still have one question though which is not treated in the book i think: how do you calculate the right 5b "bluff" frequency ? Is there a "formula" like two bluff raise for every value raise talking about flop play ? Tried to find it on my own but can't and didn't find any literature dealing that matter from now on ...

It's really hard for me to answer this without going off on a tangent. I'll just start with saying that if I had to re-write a section of the book it'd be the pre-flop section and if I had to recommend an already very good player skip a section it'd be the pre-flop section. It was already the most difficult section to write (by a *lot!*) and I think it made a lot of assumptions which already haven't aged very well (remember, it takes a long time to write a book and get it into print, so even though the book is less than 1 year old most of that section was written over two years ago).

Basically the theory behind pre-flop play is very complicated and you can't even really begin to explain it very well unless someone already has a reasonable understanding of theory. Terms like "value bet" and "bluff" don't work almost at all and optimal ranges almost certainly require flatting many 3-bets and 4-bets OOP using very aggressive ranges that will not be very good in practice for probably 99%+ of readers (many more players play low stakes than high stakes and hands which are slightly +EV calls for very very good players vs. very very aggressive 3-bettors will almost certainly be -EV for the vast majority of readers).

Ok.... so to kind of answer your question:

#1) 3-bet ranges should still probably be pretty "polarized" in position, but much less polarized when OOP. My BB 3-betting range still has some polarized component to it (for example, I like 3-betting hands like K2s vs a BTN open since any KX hand I make fold has K2s dominated and K2s gives me some hands that can check-call later on certain board textures), but my SB 3-betting range is super non-polarized since I don't have a SB flatting range.

#2) As 3-betting ranges get less polarized, the question now becomes "Wait, are 4-betting ranges polarized?" Yeah, for the most part they are (at least more polarized than a 3-betting range and clearly more polarized than an opening range), but they might not be completely "nuts" or "air" like 4-betting ranges were in the past. As we 4-bet small in say a BTN vs BB situation, it may make sense to 4-bet AQ some or all of the time even though AQ is very far from a "nuts" type hand.

#3) As 4-betting ranges get less polarized, now the question becomes "When we 5-bet against a 4-betting range, are there any hands we should make indifferent to calling the 5-bet? Or is it ok if our opponent's entire 4-betting range consists of hands that either snap call or snap fold against the 5-bet? Also, should any hands in our 5-betting range be neutral EV (indifferent to 5-bet jamming or folding) or should we believe every hand we 5-bet should be +EV like we believe every hand in a BB vs BTN 3-betting range should be +EV?"

Suffice to say stuff gets pretty messy pretty quickly.

For 100BB stacks with multiple streets left to act, probably not unless you are very good and spend a very lot of time working on this stuff. I imagine some really good HSNL guys could painstakingly write out every possible action and turn and river combination when looking at a flop situation, though I think this would take a very long time and I'm not sure how many people actually do this (though some might).

When stacks get really small and the situation very simple ("I have a disguised straight draw on the turn and my opponent made a 1/2 PSB and I will have 3 PSB left on the river") then yeah you can probably estimate the EV of calling.

Hey Matt! Two related questions here regarding GTO:

1) Given a GTO strat is a fixed strat who comes from a pair of strats who are maximally exploiting each other, how does GTO responds to a line that his pair strat never takes? Like suppose that a GTO strat will never lead on the flop in BB after calling preflop heads-up, how would GTO respond to that line?

2) We are heads-up in the button, on the flop, vs BB who flated our raise pre. 100 bb deep. From a GTO perspective, how should our flop raising range (if any) roughly be composed of when BB donks bet with a "standard" size like 2/3 pot on lets say AQ8; 863 K73; T97 ?

So Im not asking about any adjustments given population reads or anything similar, just from a pure GT POV

hey Mat, didnt read whole thread, but page 343
shouldnt say Y = 1/(2*(1+X)^2) ?, but doesnt matter much, since you never use the formula again

Also, general solution of the quadratic given Y has an easy solution. You dont give it to encourage work?

Hey Forrest Gump,

Firstly, loved the movie. Good stuff.

I think you are correct about this and I believe it was already addressed (though I forget where, there's been a lot of posts in this thread). I do think it should be put in the first post so give me a few days to look into this and try to get it updated.

Can you show me what you mean? I definitely didn't try to make things more complex to encourage work, I probably just didn't see a simpler solution or a simpler way to explain something.

I tend to not spend much time in spots where I know the opponent is making a clear mistake. Usually you'll have some idea of how to exploit said opponent if he's making a clear mistake you wouldn't see a good player make.

I would still just do the same basic stuff against someone who donk bets in a spot where they shouldn't donk bet (raise very strong hands for value, call with medium strength stuff, bluff raise stuff with little showdown value and some robust equity, etc).

I just wanted to say I really enjoyed your book Matthew.

I learned more from this book than any other book I have read.

Pros

- The section explaining the benefits of using blockers on the river was fantastic. Previously I used missed flush draws which was not as effective as using blockers.

- You demonstrated how to effectively defend a checking range which many skilled players have trouble with.

Cons

- The pre flop section is a disappointment. I understand that you started the book 2 years ago but I really think that section needs to be re-written.

Examples of this

- You use a 3.5x open raise size which nobody uses anymore.

- The pre flop hand chart is full of errors.

- You can easily exploit the 3 betting/4 betting ranges used in the book.

I think that this book will be very useful for intermediate/advanced players as they already have a solid foundation and can improve their knowledge acquired from this book.

Beginner players will struggle to know where to start as the pre flop section is dated, there is incorrect information regarding 3/4 bet ranges, and the pre flop hand chart is a mess.

Kyle

Thank you for your comments and the brief the review.

FWIW, with regards to the bolded I mostly agree with this (it's the chapter I'm least happy with and would most want to re-write), but it's really hard to stress just how difficult that chapter would be to write even now after having learned a lot in the last 2 or 3 years. In retrospect trying to write out all the ranges was probably too ambitious and if I ever do re-write it I'll likely only include ranges that assume UTG and MP fold and won't go past 3-bets.

I also just want to mention I think it'd be very hard to not make ranges which can't clearly be exploited pre-flop unless you use mixed strategies (and even then I'm skeptical someone could realistically do it, though it wouldn't shock me). The problem is ranges with mixed strategies would get very messy very quickly, which just further showcases why if I ever do re-write that section I'll likely only focus on button vs blind play and/or CO vs button and blind play (and not deal with 4-bet pots).

Try to solve with the quadratic formula and you have at least a positive solution when Y > 0.5 and its: X = -1 + (2Y)^(-0.5)
The other solution is always negative

Also, from the opening/defending preflop charts there's no 3B in BB vs SB open. But if you look at what's not in the defending range you have AA-JJ, AK-AJ, KQ
that is 1.8% and not polarized. Is that ok?

I didn't do SB vs BB ranges as I thought I had little idea as to what they should look like. Seeing as the PF chapter gets 80%+ of the complaints directed at the book, that was probably a good decision.

In general I would say I like 3-betting pretty polarized ranges IP but not OOP (again, have talked about this a bunch throughout the thread as it's more complicated than that). So if I had to pick the "value" part of the 3-betting range in SB vs BB right now I'd just go with something like AJ+/KQ/TT+ and then for 3-bet "bluffs" I would emphasize 3-betting with hands that have robust equity (suited connectors and such) as well as hands that make mostly dominated hands fold (I personally like 3-betting hands like Q2s sometimes but others do not).

page 26 of this thread there're some corrections, you have to put them in the OP. Very good work btw, I have a lot of things to test now

Hi Matthew, first of all thanks for the book.

I just started reading it and I have a question on Part two: preflop play. On page 59 we calculate the EV of the BTN getting called with the bottom of his opening range and we get -0.82bb. Then on page 61, we use the same formula but with slightly different values: 0.278 probability of getting 3-bet instead of 0.234 and 0.217 probability of getting flat called instead of 0.243.

So an increase of the total frequency of being 3-bet and a decrease of the total frequency of being flat called, which gives us an EV of -0.29bb when we get flat called.

1) Why should we open the bottom of our range if it has a negative EV?

2) Why does our EV when flat called increases when the blinds call less often and 3-bet more? Wouldnt that make their range a bit more narrow when they flat call?

3) Random question: I'm not sure to completely understand to term ''indifferent'' as stated in Part one when we want to make our opponent indifferent of calling a river bet. Does this mean that giving our opponent a 0bb EV situation is the best we can do?

Ty.

Finally finished reading thru the whole thread after a week lol. My friend mentioned gto to me this week and just from what he explained to me, I'm sold. Will be getting a copy of the book soon so i can study with him. Probably because i haven't read the book yet but i cant see why its impossible to reach perfect gto since we are basing it on the bet size. But i guess I'll have to wait and see. It's really ground breaking stuff IMO and I'm looking fwd to studying. I was curious however for someone who needs to completly change my strategy is there an order of sections i should implement? I was about to start working on my game one concept at a time and this came to my attention at the perfect time. Does pre flop ranges need to be worked on first? I kinda feel post flop should be first so I'm not lost if i do pre flop first and now have to play a diff range post flop that i have no experience with. So start with the flop? Or should i work backwards and start with the river and work my way to pre flop?

I have an interesting question. Lets say we reach river with a stronger range than our opponent (we're merged) and we're oop. Do you still bluff with the bottom of your range? (or just below your valuebetting range maybe?)