1/(1+t) - 1/2 isn't the probability that he calls with a king. It's the total number of kings that he needs to call with in order to make the other guy indifferent to bluffing.

#calling hands = #acescalls + #kingscalls = (1/(1+t)) by usual arguments
#acescalls = P(dealt an ace)P(call with an ace) = (1/2)(1) = 1/2
#kingscalls = P(dealt a king)P(calls with a king) = (1/2)(??)

so to find the (??) value - the probability of calling when you are dealt a king - solve these equations. You get that #kingscalls = (1/(1+t))-1/2, and so on back to the original text.

i have been a professional player for 9 years; i want to start sharpening my math foundation. I mostly play sngs/mtt, so would this be a very useful book? how does it compare to "poker math that matters" by Owen Gaines.

I have never read either of these books nor do i own either. Some of the stuff on the last few pages looks quite advanced, all of these matrix and stuff; i havent saw this stuff for like 7 years and cant say i liked it much then. If i stay dedicated to the book and eager to comprehend it, will i succeed? My math background is not bad, I am certainly better than average and can problem solve half decent but again, some of this stuff posted just looks crazy

I don't think anyone can answer that but yourself. The more mathematically esoteric sections may escape your comprehension at first, and possibly even after much studying, but the conclusions that the authors arrive at are what is most important. These conclusions are often explicated in the text. there is only one way to really know the answer to the question of "do I have what it takes to understand these concepts?" And that is to find out for yourself.

I am going through this excellent book as a one time eager calculus student but the intervening years are proving caustic to my abilities.

On page 156 the authors had derived a formula involving an integral from 1 to ∞.

I can't write it quite right but just imagine the integral is from t=1 to ∞

x₀∫(t-1)/(t^4) dt

And from that the authors make some kind of algebraic transformation to

x₀∫1/(t^3)-1/(t^4) dt

I was having trouble thinking of what operation leads to that solvable form.

(t - 1) / t^4 = (t / t^4) - (1 / t^4). Now note that t / t^4 = 1 / t^3.

Slick. Gracias.

I'm having a few problems with equation 3.2 (P36).

I understand equation 3.1 but I don't understand the progression onto 3.2. It looks like you should be able to get 3.2 by substituting some values into 3.1.

Can anyone explain it?

Thanks in advance.

We get the new numerator in 3.2 by substituting P(B)P(A|B) for P(A^B) in 3.1, as explained just above in the text.

We get the new denominator by noting, as the text explains, that since either B is true or !B is true (and so B + !B = 1), P(A) is just the sum of the ways A can be true if B is true and the ways A can be true if B is false. So P(A) = P(A|B)P(B) + P(A|!B)P(!B)

Got it?

Think so.

I need to go over it a few more times (Math doesn't come easy to me) but that's certainly helped.

Thanks mate.

Chapter 11 Pg.117 bottom equation. I don't understand.

When this is positive, he will call.
(P + 1) (y1 - x1) - 1(x1*) > 0
(P + 1) (y1) - (P + 2) x1* > 0
x1* > y1(P+1)/(P+2)

So X would call with a fraction of Y's betting hands, such that the ratio of Y's bets to X's calls would be (P+1)/(P+2).
Intuitively, this makes sense. Let's say that the pot is 1, so the bet is pot·sized. Then X would need to have a 1/3 chance of having the best hand in order to call. The threshold such that he would have such a chance is 2/3 of the way from 0 to y1.

I do not understand the bolded parts. Why does this make sense?
The author is saying if the pot is 1 then:
x1* > y1(1+1)/(1+2)
x1* > y1(2/3)
x1* > 0.50(2/3)
x1* > 1/3

So I understand why he says X would need a 1/3 chance of having the best hand, but I do not understand why it is 2/3 of the way from 0 to y1?

Or is he stating that because it is a pot size bet, we need 33% equity regardless (risk 1 to win pot + Y bet + X call = 1/3).
And the threshold such that X would have such a chance is defined by the equation y1(P+1)/(P+2), which in this case would be 2/3 of the way up from 0 to y1?

I just don't understand why the threshold should be 2/3 of the way from 0 to y1 (intuitively) or is he only getting this number from the equation?

+1 recommendation for this book, but with the clause that you want to already have a good understanding of mathematics (or an extreme will to learn it) and are willing to put the effort into deriving its value, which is not always easy simply by the nature of the content.

Personally I have found it to be the best poker book I have ever read. However by this I don't mean the best in terms of the direct strategic value it has added to my game. It certainly has some to be gained if you work for it, however there are better, simpler books out their that convey the information in a more accessible way.

What I did gain was that it changed the way I think about the game both in terms of my strategic justification and how I deal with poker related data. I think these are the skills that this book provides successfully over all others I have read.

i have a question about the equation on page 152. Why is the calling frequency with kings 2*((1/1+s) -1/2) i understand that the calling frequency with kings given a bluff from a queen is (1/1+s -1/2) but i don't see why we multiply the expression by 2. Any thoughts would be appreciated.

Someone else did a post about page 152 a long while back:

X always calls with the A
X calls overall 1/(1+s)

How often does X call with the K? Call this number c, like in the book.

X gets an A or K equally often, so (1/2)*1 + (1/2)*c = 1/(1+s),

or c = 2*[1/(1+s) - 1/2]

Saying "Subtracting 1/2 from this expression for the aces with which X always calls", is not a very clear way of putting it. He's just working backwards from total call frequency to call frequency with a K, given that we know the call frequency for an A, namely 1.
.

Thanks for the clarification

for reference bill chen and co-author are on twitter, they were kind enough to reply to me directly before when i tweeted them with a question from the book

hi guys i got the book....lol........guess its gonna be a tough read lol

Subbed

Also I sometimes come around here (more occasionally than in the past).

--co-author

Hi there, I just started reading this book.

I foud what could be an error:

Page 48, example 4.1:

A never bluffs, B calls = -0.2 (Shouldn't be -1?)
A always bluffs, B calls = +3.8 (This is ok)
A bluffs 5%, B calls = +0.05 (Shouldn't be +0.2?)
A bluffs 4%, B calls = 0 (This is ok)

P.D: Books says "B's calling strategy only applies when A bets, so the probability values below are conditional on A betting", on that case if A never bluffs, then when A bets he will be 100% nuts, thus B should lose -1 when calling and not -0.2.

Could someone help me please?

Hello. Anyone knows how many editions this book has? Thanks.

does this book cover the math in LHE?

This book covers poker math in a more generalized way that is usually not specific to any game, so it is up to you to figure out how to apply the math.

Yeah, it's an error.

Their equation for <B,call> assumes his betting range always contains 20% nuts, but he won't bluff all his air so the % of nuts in his betting range is dependent on x (% of his total range on river that are bluffs and that he decides to bet).

so <B, call> should equal (5x-.2)/(x+.2)

Also, I have no idea how they came to the conclusion on page 148 (paragraph right below the graph) that X should fold 100% even if Y bets only 1% of the pot. Makes no sense to me whatsoever.