In post 299, the above appears

I think this says you need not know earlier round betting sequences for GTO play. You bet and villain calls is no different than V bets and H calls.
In describing Cephus, a GTO-like bot for LHE, Neil Burch notes it’s a pre-computed strategy and requires you to input the betting to have it show its next move. Here is the quote:

In order to act, Cepheus needs to know the public cards on the board, as well as the betting that has occurred.
Here is the link:

http://poker-blog.srv.ualberta.ca/20...uery-tool.html

Any comment?

Thank you for the comment and you've clearly put in a lot of work to this, I unfortunately had a bit of trouble following it and I don't think I have too much to add.

Feel free to keep posting though if you decide to keep working on this and think you've found something interesting or new. GL!

What I'm saying is if you know both players' ranges, then previous betting action does not matter.

In reality, the only way you'll know both players' ranges is if you know the previous action and bet sizing. So, in actual poker it's absolutely crucial to know the previous action, or you won't know what each players range is right now and what the right action is to take with your specific hand.

Probably best if you just make a few more posts then shoot me a PM.

Hello Matthew,

I'm re-reading Application of No Limit Holdem (AoNLH), best poker book ever read and Im looking forward to read your new book, but i have a doubt about a line in AoNLH.

In the section: sample hands, in hand number two i can not understand our bluffing line OTR.

In details:
- we are out of position in the UTG and villain is BTN.
- I'm focusing on our 3 barrel line after we raise first in pre-flop.
- The board is: [8c, 4h, 2s][2d][Tc]
- OTT our bluff betting range is composed by: [AQ,76s, 65s, AJ] (while our value betting range is: [AA, KK-QQ, TT]).

--> OTR we identify some combo of [AQ] as a bluff bet for balancing our value bets, that are: [AA, KK-QQ].

My question is: given the fact that we have 65s in our bluffing range OTR why do we use AQ as a bluff? isn't it more efficient to use a low show down value hands as a bluff? Moreover with AQ i think that we can not make an argument about blockers, i.e AQ is more efficienti as a bluff thanks to blockers, therefore i can not figure out why we use some combo of AQ as a bluff and not 65s...

I'm sure that you can help me to figure out this and thanks for your time Matthew, really appreciated!

Cheers
pksmv

Hi,

Can someone explain to me where does 0.57 number come from ?
I saw this number in the book page 111 too.

If we want to go all in on the river we have 16R^3 = 200 <=> R = 2.32

So we have S + 2B = SR <=> 16 + 2B = 2 x 2.32 <=> B = 10.56
So we should bet 10.56BB on the flop.

Then we can calculate the % of the bet/pot.

16BB -> 100%
10.56BB -> 66%

So we should bet 66% of the pot on the flop, turn and river.

If we check this % we have a 200BB pot on the river.

Flop: pot 16BB, 66% 16BB = 10.56
Turn: pot 37.12, 66% 37.12BB = 24.49BB
River: pot 86.1BB, 66% 86.1BB = 56.24BB
Total : 86.1 + 56.2 = 198.5 BB

So I guess I am missing something ....

Thanks

Sorry about the late response.

I'm confused, aren't we bluffing both the 65s and AQ?

Either way, I was probably just trying to include enough combos, and the weakest combo I could see including after we already bluffed the 65s and friends was AQ. Though realistically, at the time I wrote this I mostly would just go "Ok, I want to value bet 30 combos on the river and bluff 10 combos, so what are the weakest 10 combos I have in my range on the river I can bluff with?"

But the better your opponents are, the more removal effects will matter on the river. The weaker your opponents are, the most your actual showdown value will matter, because even if you should never win with checking AQ on a 8422T board against an optimal opponent, at the end of the day sometimes you will.

Based on just the numbers I'm seeing, it looks like it should be a 66% PSB to me too. But it's early in the morning and maybe I'm missing something youthebest was referring to as well.

It's figuring out how much we lose on average when our bluff is called.

So let's say we go all-in for 60BB and villain calls. The final pot is 200BB. But now, if we have 15% equity with our bluffs once called, we really didn't lose the 60BB we put in the pot. On average we'll lose less because sometimes we'll be called and get lucky and win a massive pot.

So on average, we only lose:

60 - 200 (Bluffs equity) = 60 - 200(0.15) = 60 - 30 = 30BB

That's because we on average get 200(0.15) = 30BB back from the pot, since we end up winning the 200BB pot 15% of the time.

I have some questions on section "Maximum 3 betting ranges" on page 41.
First it says that there are 5 players left to act after the UTG player opens. this suggests we are dealing with a 6-MAX table. Are all discussions in the book handling 6-MAX and not full ring ?

Then given the preflop opener needs it to work 70% of the time to be immediately profitable we first derive the percentage all 5 players cant three bet for that to work and that comes out to 0.93. We then call the complement of that (6.9%) the maximum 3 bet frequency.

Why is this a maximum frequency? If we 3-bet more aren't we also denying the open immediate profitability?

Hey Mathew,

thanks for writing this new great book.
it has helped me a lot.
i have a question and would be grateful if you answer.

after finishing your new book you mentioned the most of the concepts which were in application already (as you mentioned in the book).
i want to take my game to next level.
i am not sure after reading your new book, should i read application as well or not.
my own idea was to read will tipton heads up books.
please comment on my idea.
or if you think other books will be better.


thanks a lot
Amin

I think my book is worth the $25 or whatever it cost on Amazon, but I don't think you need to rush to read Applications. I think you can probably buy/borrow it and then just read the sections one at a time that interest you whenever you have some free time and are interested in learning poker theory in some more depth.

It's also a harder read, so it's not likely something that's necessarily bestto read cover to cover. A section or two at a time is fine, and if you find a section feels outdated (after reading the new book) you definitely shouldn't feel bad about skipping it and then if you choose to coming back and reading it later.

Hope that helps and glad you liked the new book,

-Matt

If villains 3-bet more frequently than that, you would never open and fold to a 3-bet. You'd simply be getting 3-bet too often (and thus having to fold pre-flop after putting money in the pot) to make opening with anything but hands strong enough to at least call the 3-bet profitable.

Hi Matt

A couple of general questions about your first book, Applications of No Limit Holdem..

Firstly, can you explain the title? "Applications of no limit holdem" has never made sense to me as a title, because it seems to suggest that you are applying NLHE to something. In the same way that if we talk about "applied mathematics", the implication is that we are applying math to something like engineering or physics problems... so in what sense did you feel you were "applying" no limit holdem to something?

Also, and unrelatedly, can you explain how this book compares with Bill Chen's Mathematics of Poker? I understand that Chen's book is probably the most mathematical of the books that are widely available on poker theory.. but is this additional amount of mathematical rigour the main difference between his work and yours? And more generally, did both his book and yours come to the same conclusions about what it means to play theoretically sound poker? And also, was your book influenced by Chen's since his was published a few years before yours?

Many Thanks

Pg. 59 says that the range's weakest hand has an EV of -.82 but then you later state that the hand expects to get back 1.68 big blinds from the pot. The two contradict each other don't they? Maybe I'm confused on something simple

I think the title was originally longer but it got shortened to what we have now.

Mathematics of Poker is much more math based than Applications and focuses more on precise solutions to toy games whereas my book focuses more on using models to simulate NLHE situations.

I think our book came to a lot of the same conclusions regarding bet-sizing and defending checks, but neither book (or any book for that matter) can get you close to playing GTO.

I definitely have read Mathematics of Poker and it's one of my favorite books, but a lot of my poker knowledge and where I learned it from all blends together. So it's hard to point out any one specific thing I learned from one specific source, but I think I learned a lot from Mathematics of Poker regarding bet sizing.

Did we put 2.5BB in overall for the hand? If so, then if our EV is 1.68BB on the flop we'll still expect to have lost 2.5BB - 1.68BB = 0.82BB overall for the hand since we invested 2.5BB pre-flop to have a 1.68BB EV spot post-flop.

Hi Matt:

The Applications of Theoretical No Limit Texas Hold ‘Em; A Guide to Understanding the Math and Language Behind Theoretically Sound Poker

Best wishes,
Mason

Love the full title, Mason. Maybe consider putting it in smaller font on the cover, or in a splash page inside.

This book and Mr. Janda's follow up are basically the pinnacle of NLHE theory at this time!

Warning: *****Longer than I intended Thank you if you get through it******

Ok I'm really trying to understand this GTO concept. FWIW I am in the best poker coaching program and we are taught to exploit, exploit, exploit - so I definitely understand exploitative play. We are trained to ignore GTO until the point in which we need to use it. (versus villains who are competent, winning players and who are exceptional at exploitative play.)

Matt was asked how to adapt GTO for micro stakes and he replies:

The answer is to take the most +EV line. It is very obvious to me at least that GTO is not the most +EV line is so many situations. GTO is most clearly NOT the best at every stake because it's NOT the most +EV line. Or I should say it's clearly NOT the most +EV line against villains who are highly exploitable.

Extreme examples. Villain is a huge nitty nitty nit nit and gets extremely uncomfortable with calling flop raises OOP even with TPWK hands like AT on a Ah2hJs flop. Their fold to flop raise OOP is 75%.

The GTO approach is to raise your value combo's (22, JJ, AJo, A2s) and some premium flush draws (KhQh, KhTh), etc. along with some bluffs.

This GTO approach assumes villain cares about being exploited themselves. Maybe they are happy living in their world of nit and continue folding TPWK.

This also means that CLEARLY you can go outside of the GTO bluff strategy and begin to raise more bluffs (backdoors flushes, 3rd/4th pairs, broadway gutshots without backdoor equity, etc) because villain can be exploited hard

On the opposite side of the spectrum, you have mr. WHALE STATION and they open 50% UTG and fold to flop raises 20% of the time. Here you would NEVER want to raise bluffs (one could argue you still should at a very rare frequency to let the whale who is probably one tabling not get the idea that you are only attacking them with value every time)

But the main point is that you can begin to raise the flop with lower value hands like AQ or AT maybe even A9.

If Player A and Player B both play perfectly GTO poker, and they play 1 million hands against each other, shouldn't the expected winnings of each player be the 0bb/100? (assuming no rake is paid)

Meaning GTO is only a system to prevent you from losing money but also prevents you from winning money? It is a 0 sum system?

Because if GTO is simply a preventative maintenance to counter exploitation then is assuming villain exploits and doesn't play GTO, therefore also implying that now you are being exploited because now you can't take exploitative lines because now villain is adapting to your exploitations by becoming more and more GTO.

So you have 2 villains that are both exploitative villains. They want to study how to play against their opponent (A vs B and B vs A), so they move more and more into GTO play instead of moving more and more into exploitable play - So eventually in a perfect system, they both end up having 0 net profit vs each other.

In other words, GTO seems to be a system that only works if the villain also plays GTO.

If villain knows you fold to much to 3bets, then the correct solution for the villain is to 3bet you more. This is not GTO, correct? Because villain should just be 3 betting their normal range.

I don't understand how Matt can claim GTO crushes all limits.

It also confuses me that if you play GTO it assumes villain exploits. Instead of counter exploiting, like x/raising flops more often when you see they float bet IP more than average but fold a lot to cbets.

If no villain is exploitable and everyone plays perfectly GTO, nobody would make money in poker.

Also some villains do not purposefully exploit, because they could exploit by cbetting 80% OOP so it is an exploit vs someone who folds a lot IP, but sub optimal vs someone who calls down to river with 2nd and 3rd pairs.

So I really fail to see how GTO is some game crushing theory - because in my head it seems clear to me that it is quite the opposite - it is a system which prevents being exploited and ALSO prevents you exploiting the villain, therefore making your win rate 0bb/100.

Is not GTO simply a system to prevent yourself from bleeding too much versus better than average exploitative players and NOT a system that allows you maximize EV in all situations?

Because it seems to me that maximizing EV is simply playing good, logical, reasoned and most importantly exploitative poker and GTO cannot give you this.

Maybe some people are using "GTO" and "Taking the most +EV line through intense study of range vs range, flopzilla board texture connectivity, combo counting, a solid understanding of poker equities and what not" as the same thing. GTO does not necessarily equate to the other. Or so I argue.

I do hope the book forces me to study some poker math and reason/think on new levels but the overall concept of GTO is really something I tend to find some huge issues with.

If anything I wrote is answerable and made any sense, I thank anyone who can clear some of this stuff up.

Ok so I came up with a ridiculously obnoxious extreme example.

Let's say that we have a fish at the table who is calling 100% of 3bets, 4bets, etc. We then believe that fish might even call a 20x or 30x open. They call these too. We the find ourselves with AA UTG.

We have 300bb's and fish has 300bb's. We believe fish is so bad ( or so good hehe) that they might just call a 150x raise pre flop.

Well, this is obviously not GTO to raise 150x. Because we aren't balancing this with bluffs or weaker value.

And it would be ridiculous to make GTO a definition about "A line that offers maximum EV compared to all other lines"

Because you can't just define GTO to mean the most EV play in any given situation because that is not what GTO is.

This is an obvious form of non GTO exploitative play by open raising 150xbb.

If we combine the following:

Bad Play<------------------>GTO<------------------>Exploitative Play

With the following...

Most negative EV <----------->BE EV 0bb<------------>Highest possible EV

I don't see how GTO could ever provide higher EV than exploitative play.

GTO provides the highest possible EV for your range against anything any villain could do, not against specific lines taken by hypothetical villains you pull out of a hat.
Obviously explo will make more money vs fish but GTO will still crush.

There are different degrees of villains
there is the super nits who play 10/8 at 6 max, 15/12, 18/9, 20/8, 24/6, 24/18, 26/18, 32/14, 35/0, on and on and on

There are also Regs who if you found 20 regs who all have 24/18 stats, each reg could likely have pretty different stats than another Reg.

One reg may begin to tilt and begin to play wildly different than their normal stats. One reg may 3bet a super polarized range BB vs BTN where another reg might be a 3 bet nit and 3bet only 6% SB vs BTN.

Once you discover how a Reg plays outside of the GTO standard, then that is where you can begin to exploit.

You can exploit vs passive fish by over folding your top pair hands to their x/raises and jams. You can exploit a tight 3 bettor by folding more hands because they aren't going to exploit you for tightening your 3bet call range vs them.

Someone who does not bet river a lot you don't need to call with all your capped range because they aren't going to begin bluffing you more often because their value combo's are still outnumbering their bluff combo's to where if they bet river 3/4 pot, you have 29% equity to call...but still it's a bad call if you know they most likely bet hands that are stronger than yours.

So GTO seems to be a ZERO SUM system in which it only makes sense vs a non GTO perfect bot who is able to exploit you perfectly. But by doing so, you are now no longer able to exploit this bot therefore putting your winrate at 0bb. They can't win money vs you because you are perfectly balanced and you can't win money vs them because they have forced you to be GTO.

2 players who are both perfectly GTO cannot win money from each other.

If this is a true statement then it implies the only way to win money is to deviate from GTO assuming another villain is also not perfectly GTO because if they don't play GTO then you can exploit them.

Playing a range vs 10 different hypothetical opponents prevents you from gaining maximum EV vs each different opponent.

It may in theory be the most maximal EV line vs 10 different opponents but it isn't the most maximal EV line in reality because you aren't playing each situation vs 10 opponents at the same time...it's usually 1 maybe 2.

So your definition doesn't really say anything at all. You can actually reword by saying

"GTO is how to not lose the most money with your range playing against 10 different opponents"

This would also assume each opponent out of the 10 is a reg and also assume they will begin to exploit you in every way possible.

If a reg doesn't exploit you and just plays their range the same way every time (this doesn't mean they are GTO just means they are playing the way they feel comfortable playing) then there is no need to be GTO vs them - if they fold to 3bets a lot, you 3bet bluff them more.

So I'm still left wondering...what IS GTO? What is a complete and internally consistent definition GTO? If 2 perfectly GTO players play vs each other for 1 million hands HU , don't both players have a theoretically break even winrate? Isn't GTO just prevention to being exploited? If the villain doesn't exploit you then there is no need to play GTO?

And if the villain does exploit you, then GTO is a way to prevent loss of your money because you balance everything to perfection to allow them no chance to exploit you.

GTO naturally exploits imperfections in sub optimal strategies and wins EV. it's a common misconception that GTO only makes a little to no money.



You may be interested in 09:40

Right but Doug Polk is defining GTO as a "good sound strategy"

Well yes obviously a "good sound strategy" is going to win a lot of money but does everyone define GTO this way?

Game Theory Optimal seems to suggest that you are playing optimally. But this also means that sometimes you are exploiting and sometimes you prevent exploitation by balancing your ranges.

So in another sense you could define GTO as "exploitation and exploitation prevention dependent on villain and structuring your strategy in such a way that you maximize your profit vs some villains and decrease your losses vs other villains"

But then GTO is defined as "How to win the most money in any given situation"

And if poker isn't solved, this just means that the "optimal theory" has not yet been discovered for x situation which I'm totally fine with that makes total sense.

"Maximizing your EV with your entire range vs multiple opponents" is not the same as the definition I provided above.

If GTO is universally accepted as "maximizing your EV in every possible situation" then it's the same thing as saying GTO is "playing perfect poker"

Great video by the way, I already subscribed this guy speaks a lot of common sense.