And as Pökerfu pointed out, the correct formula must be:

EV = ((r-a)/(r))*($50) + (a/r)*((c/t)*((2015)*(EQ)-890)-((t-c)/(t))*(110))

On way to see this, is by using the formula for calling an AI given on page 65.

Following up on Poker_Apprentice's confirmation of Pokerfu's observation that the formula should use 890 instead of 1000, I have rerun the numbers for the table of page 198.

The first column is what's in the book and is wrong.

The second column is correct calculations based on the wrong formula using 1000 that's in the book.

The third column is what the book should use in the next printing, since it's based on the correct formula using 890.

Many thx @poker_apprentice and xpxinvxpy!

Equation for the table on page 198 for the first line:

((0.15-0.15)/0.15)*50+(0.15/0.15)*((0.07/0.11*(2015*0.51-1000))-((0.11-0.07)/0.11) * 110) = -22.4045 (the books solution is $-29.82)

Now I plug in the new value of 890 instead 1000 (like poker_apprentice and me mentioned) and get this equation:

((0.15-0.15)/0.15)*50+(0.15/0.15)*((0.07/0.11*(2015*0.51-890))-((0.11-0.07)/0.11) * 110) = 47.60 a positive number for our EV!

Guess this is wrong too! Makes no sense, imo. If villain always 4bets (like in the example) and we fold some of the times to his 4bet. The 0.51% Equity when all in will not make the EV positive for the times we fold to his 4 bet. I guess. So I think there is something more wrong with the formula. Any help?

And btw Iam some kind dissapointed that Mr. Bakker or Mason Malmuth don't answer to to this topic. Because both already posted here and I think it should be no big problem to help us in this question. Or some kind of statement would be nice. Man there is nothing wrong with having one or two failures in a book like these. there are some more math fails in much more expensive Poker ebooks with less mathematics in it. So nothing to be ashamed off oO. Great book imo. But why can't the author just turn his PC on and post the right equations in this thread or give any advice? This is a 2plus2 book, so I think I am in the right forum?

edit: haha @xpxinvxpy posted at the same time ^^ thx for the new table

I believe the table on page 220 is in error. It is based on the Hero's
perceived range of 88+, AJo+, ATs+, KTs+, QTs+ after the flop.

The flop is Qc,5d,4s so Villain knows that Hero does not have Qc in his hand, and probabilities must be calculated based on Qc being removed from Hero's possible hands.

Below are the ranges with the number of possibilities given twice, first without card removal and then with card removal.

total hands with no removal: 42+36+16+12+8=114
total hands with card removal: 39+33+15+11+6

Let's calculate the probabilities of various types of hands as per page 220, using the "card removal" numbers.

SET:
QQ
3
3/104=0.0288
(agrees with the book's 3%)

PAIR OF QUEENS:
AQo,AQs,KQs,QJs,QTs
9+3+3+3+3 = 21
21/104 = 0.202
(does not agree with the book's 27%)

ANY PAIR:
88+,pair of queens
39+21 = 60
60/104 = 0.5769
(agrees with the book's 58%)

OVERCARDS:
AKo,AKs
12+4 = 16
16/104 = 0.154
(does not agree with the book's 14.0%)

NO PAIR, NO DRAW (presumably includes overcards):
AKo,AJo,AKs,AJs,ATs,KJs,KTs
12+12+4+4+4+4+4 = 44
44/104 = 0.423
(does not agree with book's 39%)

Of the five numbers in the table, I can reproduce two of them. Can anyone confirm/deny the other three? Maybe I made a mistake, but I can't figure out what it is.

just plugged your number in flopzilla. Your numbers are nearly exact! Books table is wrong. but there are just 57 combos for any pair -> Toppair 21 combos
88-JJ 24 combos, overpair 12 combos. So flopzilla gives me 54.8 % pairs of range.

edit: I want to apologize again for my bad english skills. ^^ In my last post there are some hard fails, hope you native speakers will understand at least some of the post. haha

Pokerfu you are correct there are 57 pairs. I erred in counting 88+ as 39, it should have been 36 because QQ makes a set not a pair! Thanks.

Let's have more fun. See my next post later today.

working on page 223 of Bakker's Anayltical NLHE

[Pokerfu, maybe you can Flopzilla this problem?]

flop is 9s 7s 6d

for each component of the range, the number of possibilities
without card removal and with card removal are given

AJs-4/4
ATs-4/4
KQs-4/4
KTs-4/4
QJs-4/4
QTs-4/4
JTs-4/4
T9s-4/3
98s-4/3
77-TT 6+6+6+6=24/3+6+3+6=18

total number of possibilities without card removal:
4+4+4+4+4+4+4+4+4+24=60

total number of possibilities with card removal
4+4+4+4+4+4+4+3+3+18=52

SET:
3+3=6
6/52=0.1154
(agrees with the book's 12%)

STRAIGHT DRAW:
open ended is anything with an 8 (98s and 88): 3+6=9
gutshot is anything with a T (T9s, JTs, QTs, KTs, ATs, TT): 3+4+4+4+4+6=25
9+25=34
34/54=0.6296
(disagrees with the book's 40%)

ANY PAIR:
flopped pair is anything with a single 9 (98s, T9s): 3+3=6
pocket pair is 88 and TT (because 77 and 99 make sets): 12
6+12=18
18/54=0.3333
(disagrees with the book's 36%)

I conjecture that there is some overlap that is not being accounted for properly.
E.g., 88 makes both a pair and a straight draw, how shall it be counted?


If STRAIGHT DRAW is STRAIGHT DRAW WITH NO PAIR
then
open ended is 98s (88 doesn't count because it makes a pair): 3
gutshot is anything with a T except TT (T9s, JTs, QTs, KTs, ATs): 3+4+4+4+4+=19
3+19=22
22/54=0.4074
(agrees with the book's 40%)

If ANY PAIR is ANY PAIR WITH NO STRAIGHT DRAW
then
flopped pair is only T9s (98s doesn't count because it makes a straight draw): 3
no pocket pairs count because 77 and 99 make sets, 88 makes an open ender, and TT makes a gutshot: 0
3+0=3
3/54 = 0.056

There is a lack of precision in how "any pair" and "straight draw" are defined,
and it leads to confusion. Perhaps I have missed something, but
I must say that I am confused about the percentages reported on page 223.

Looking for your next post. But the topic is not fun at all for me. I really get nuts over the problem on page 198.

Like we said the table is wrong anyways. But the EV of $47 for line1 makes no sense to me. I guess the $-22 make more sense, because we fold 64% percent of the time to a 4bet. So the EV shouldnt be postive with just 51% Equity but already invested $110 for the 3bet. I really hope some more give their opinion to this topic.

I can say the other formulas in the books are correct. I checked them with some tools and by computing by myself. But there is another formula I have problems with. It is the formula on page 68. I can't remember exactly what it was, but I think the plugged in numbers don't match with the formula above exactly. These both formulas are the two I left beside. But it is a little bit sad because both handle preflop 3betting...

edit: haha posted again at the same time. Will c what I can do with flopzilla, but Iam some knd of tired. Maybe not just right now ^^

set 6 combios 12 %
overpair 6 combos 12%; toppair 6 combos 12%, pocket pairs below toppair 6 combos 12%
oesd 9combos 18%; gutshot 23 combos 46 %

It is included any gs with and without pair and any oesd with and without pair

89s and TT for example are counted both in the pair group and in the straight group. But that are just combinatorics. I dont see a big problem in it . I can think he is not counting the combos twice, but flopzilla does for every category counting the combos new. So the maybe he is alright and we are wrong, because I didnt look for that effect of flopzilla. anyways Iam sure you can get a free trial for flopzilla and count on your own. ^^

Sorry this is my last spam.

Okay Iam out. I hope I can forget about this. It is just not good service. Iam a glad user of pokerstrategy.de and will stick there. I will post the formulas in the german forum some day, when I forgot about this stupid topic. Just cracks me up.

Hey I wanted to write a nice cool feedback for your book in pokermedia forum on ps.de. Saying it is my favorite book for me, besides, 'Pokerblueprint', 'MOP' and 'exploiting regulars'. Well after there was a neutral review by "ghostmaster" already. A very well known german PS. moderator delievering high quality content day for day. I think a nice feedback would have sellt at least some books for you.

But I really can't understand what is happening here. I spended a whole lot of time figuring all the math stuff out on my own in the last half year. And well I made it through MOP and uderstand the most stuff by Alix M.^^. I know there are some fails in the german PS math articles and it is for me hard to understand, they write it in some complicate ways. So I only use the english sources for my math education. Deuces cracked, BFP and mainly daily variance books and 2plus2 books. So I was really happy to read this book because the math Bakker teaches is very clear and easy to understand and it is the only book out there really covering the most Pokermath besides MOP. But sadly there is this page 198 and it is somewhat the main formula in the book besides the other one I mentioned on page 68.

But hey just a little statement like: "Pokerfu you are a complete tard- the math is correct. or well maybe you are right we will handle it out..." But no response at all makes me really angry because I worked for some days on the book and really a little statement or any advice would be nice. This is no rocket science...

There are ebooks out there which are very expensive and they have some fails in it. But at least they response directly on the forum and help their customers. I really wanted to buy Ducy but hey I will go for Killer Poker by the numbers. :/

And I am sure Mr Malmuth has at least noticed some of our problems in this thread because this book his his new baby. Speaking in high tones about it for weeks. And now there is no response at all whether by the author or the producer to a simple basic question?

I just want to thank xinvxvy and the other german user for their response again. @xinvxvy I hope you are not disapointed, it wasn't meant harsh that I don't want count combos. But I do alright with some fails in counted combos or obv. fails but not with fails in the basic equation formulas and I really can't see the book anymore.

This is the forum where Red Joker, Besarius and other very skilled people delievering high math content. But no other user can figure out the solution to a simple math equation? pffffff

Hi: Poker--

I took a look at this and my comments are below.

Best wishes,
Mason

The formula looks correct to me. See my comments below.

I too get different results from what is in the table. Specifically, when I recalculated the EV of 3-Bing for the first three lines of the table, my results were -$22.40, $7.50 and $27.65 respectively. This compares to the table entries of -$29.82, $6 and $27.65 respectively.

However, even though this is the case, I believe the table entries are correct. What has probably happened is just simple rounding error. For instance, on the second line, if the percentage for the equity was 49.93 percent, then it would come out to $6 as is given in the table. So it seems like the source of confusion is that the equity column should have been given to two more decimal places, but the calculated EVs are most likely correct.

I think what's happening here is that the author, Thomas Bakker, is computing the expectation for the specific startegy from the start of the hand to the finish of the hand. That's why the number $1,000 is used. On the other hand, if you were to compute the expectation at the point where your opponent four bet shoves, then you would use the $890 figure. So again, the book looks correct to me.

The formula on page 65 is for deciding whether to call at the specific point in the hand. That's normally the way you think about poker problems. But the formula on page 198 is looking at a complete strategy from start to finish. Thus the difference.

Best wishes,
mason

Please see my previous posts. I believe what's in the book is correct.

Mason

Thank you Mason. I will wait what others say but your explanations make some sense to me. I take a little break and go over it later the day. Thx for your response. I will soon order the Ducy book ^^

Hi xpxinvxpy:

It looks like this table has some errors and your numbers look correct to me. I suspect the 27 percent for a pair of queens is a type-o. It looks like the overcards was calculated without taking into account the removal of the Q, and the same for the no-pair number. Also, for your any pair, QQ should not be included. I suspect the author made the same error.

Best wishes,
mason

I am very sorry for the confusion caused by my wrong answer (apologies to pökerfu in particular), and thank Mason for correcting it.

Referring to the table on page 198 again, I don't understand how the numbers given in the column 'Our Equity When All-in' have been calculated. If we take the percentages given in the columns 'Opponent 4b' and 'Our All-in Range', and then plug them into pokerstove, we get different results.

Possible errors in Table on page 223

The range and number of possibilities with card removal (accounting for the 9s 7s 6d flop)

AJs 4
ATs 4
KQs-KTs 3*4=12
QJs 4
QTs 4
JTs 4
T9s 3
98s 3
TT-77 6+3+6+3= 18
============
total number of hands = 56

set (77, 99; 3+3=6) 6/56 = 0.107 (disagrees with book's 12%)

Since the only pocket cards with this range that make sets are 77 and 99 for a total of 6 possibilities,
the book's 12% implies that there should be only 50 possible hands (6/50=0.12). So maybe I counted the possiblities incorrectly, but I don't see where.

any pair (T9s, 98s, TT, 88; 3+3+6+6=18) 18/56 = 0.321 (disagrees with book's 36%)

If there are only 50 possible hands then 18/50=0.36 which agrees with the book.
Again, I don't see how there are only 50 possible hands.

overcards (AJs, ATs, KQs-KTs, QJs, JTs; 4+4+12+4+4+4=32) 32/56=0.571 (disagrees with book's 52%).

If there are only 50 possible hands then 32/50=0.64 which again disagrees with the book.

Perhaps someone can find my mistake and resolve the discrepancies, or confirm that I am correct.

bump this book any good, apart from being filled with typos?

Finally read it completely. To be honest I was expecting to be disappointed due to mixed reviews in this thread so the book was a very good surprise.

Playing against short-stackers is a straightforward section where the author provides optimal and exploitive methods to play against short stackers. The biggest shortcoming of this section is the equilibrium charts where the author suggests that the raiser bets 3.5bb against short-stackers, contradicting himself after he wrote earlier that against short-stackers, the raiser should open to about 2bb. I suspect it shouldn't make too much of a difference against a 20bb short-stacker to open to 2bb or 3.5bb in terms of the range we should play against them but against a 5bb short-stackers, the charts probably become completely incorrect. In practice I don't think it has a negative impact: 5bb short stackers are probably fish playing any 2 cards, not pros. Moreover, if we are the caller and the short stacker is the raiser, you will find some short-stackers routinely open-raising to 3.5bb, making the charts more valid.

My favourite section by far is the section "playing against bad players". One reason is that this section can easily be applied to any stakes. I love the fact that the author goes further that the typical classification of "loose aggressive/weak tight/loose passive". It didn't take me long in my short poker career to identify several types of loose passive players different from what I was reading in books and devise different strategies against different types. I was glad to see that the authors did the same work with loose aggressive players. He also explains and provides examples on how to exploit the bad regulars (the one with good pre-flop stats who don't seem to win much money due to bad hand reading skills), players making incorrect bet sizes, players folding too often, etc…

The 3-bet Pot section was also better than I expected. The author rigorously and quantitatively approached 3-bet pots both pre- and post-flop. The section was a good reminder for me that I should approach every decision based on the EV of my strategy instead of relying of some vague intuitions, videos or more qualitative books. Surely, one could complain that the ranges or the bet sizes the authors chose in this section weren’t completely representative of today’s mid-stake games (which is somewhat debatable) but his method of approaching problems (calculating EV) is what make the section good and timeless: the ranges and bet sizes can be changed but the method stands and the reader can always make calculations with its own data with the help of PokerStove and Flopzilla.

There are other various interesting topics at the end of the book like “Optimal bluffing” or “The Path to Success” which is a reminder to those who don’t seem to succeed even though they know all the basics and some advanced concepts or for those like myself who aspire to beat bigger games than those they are currently playing at.

The parts that I found the least useful (to me) was most of Part 3 (Post Flop Play in single raised pots) and all the bits about ranges, probably because I had already given the topic a lot of thoughts on my own.

Another “shortcoming” which isn’t really one is that readers who aren’t mathematically inclined may not benefit from the book as much as those who are. At the minimum, I advise potential readers to be comfortable with EV calculations/equations before reading the book.

Cliff: The short-stacking section should pay for the price of the book in due time despite minor errors. Even if you disagree with some of the author’s ranges, bet sizes or examples, his rigorous approach/methods is what makes the book valuable.

Do people think this book would be suitable for me as a live player who started online, i'm mainly looking to improve my fundamentals, get better at being aggressive.

So the book is full of typos and you disagree with the ranges, bet sizes and examples but apart from that it's a good book right?

I don't disagree with the author that much. I was just summarising (badly) some of the criticisms.

From some books, I only remember the conclusions but have forgotten all the calculations leading to the conclusion after reading them. But in Analytical No Limit Hold'em, I feel the Author's methodology is actually more valuable than the conclusions he draws in some particular cases. In some sections, what he is giving you are tools to improve your work away from the table if you are ready to redo some of his calculations with your own ranges and stats. This can allow you to devise specific exploitive strategies against various opponents. I feel these tools are more important than knowing if you should 4-bet raise the pot or 3/4 of the pot (for example).

Although some bits can be reusable, the book often implicitly assumes that you have reliable stats on the other players. It is really a book on online poker. If amping up your aggressivity is your objective, you will be better served with more practical books (like Dusty Schmidt's last book) or watching videos.

I liked this book more than others like it. Unfortunately most players are looking for systems. "In order to win you should 3bet this range, you should make exactly this bet size, etc." What they don't realize is even if the bet sizes or ranges were completely representative of today's midstake games probably they wouldn't be representative anymore after 4 years. A book should have value for many years not just for a year or 2. I think those who want systems should watch videos instead of reading books.

Hi,

I am thinking of buying the book but im not sure because its alrdy 2years old, is it still useful? (for me useful)

MYSELF:

So I am grinding at nl100 8-12 tables and iam a winning player.
I didnt really read much about poker just Harrington on Online CG, which gave me the basics about Holdem Manager and how to interprete stats and crush nl25.
After this i started watching videos on DeucesCracked where I improved to the point that i am able to play nl100 as a winning player.

Now I am searching for a new book to read, I guess my biggest leak is poker-maths (and im good at reading stats and exploiting leaks i find there) and in this book is some maths and also some other concepts right and because of this its maybe not that dry to read what I am afraid of :P

So can you recommend this book although its alrdy 2 years old or is there any better book which is helping me more!?
My goal is to move up to nl200+!