Pg51 Example 4.3:

"It is the flop of a $30-$60 holden game. Player A holds AdKd, and player B holds 7c8c. The flop is AcKs4c. There is just $75 in the pot (suppose the AK limped preflop). Now the AK bets $30. B has just eight outs in this case (as Kc makes AK a full house). So from an immediate pot odds standpoint, B should call if his chance of winning the pot is greater than 30/105, or 28.5%. So what is B's chance of making his flush on the next street? It is 8/45 on the turn. This chance is only 17%, and so we can see that B's chance of making his flush is not high enough to justify calling"

Know I see that this came from the principle that was stated earlier on the same page: "In made hand vs. draw situations, the draw usually calls if it has positive equity in the pot after calling and subtracting the amount of the call"

This principle is confusing me. It is to my understanding that from a direct pot odds standpoint, when facing a bet of $30 into a $75 pot, I should call if I expect to win more than 22.2%, not 28.5%. And I can't see how my hand being a draw or not should change this number. The odds are the odds no matter what hand we hold. If I expect my hand (either it being a bottom pair or a gutshot) to win at a bigger frequency than the odds given to me, I should always call.

So, what's going on here? What am I missing? *** I'm embarrased of asking such basic odds question, but this just doesn't seem to fit right to me.

The way I see, from this principle perspective and implications, the book would be suggesting for us to fold our draw hands that don't match the stated principle, but some of those hands would actually have an EV>0 and therefore call>fold. Consider the hand 3c5c instead the 7c8c and that we'r facing AdQd for a toppair hand instead of a two pair hand. Now we have 12 outs instead of just 8, giving us about 25% chance of improving, what would be more than enough to call profitably considering the odds given. But considering the principle, it would still be a fold because our chance is still less than 28.5%. So why should I fold 3c5c here if I'm getting enough odds to call profitably?

Thats a known book error. check out http://www.conjelco.com/mathofpoker/...ker-errata.pdf

Many thanks Pokerlogist for bringing that up, didn't know of the existence of that errata.

Unfortunately this did not solve my question. Apparently on this errata, they've changed a previous odds number (it was 30-75, 40%) to the number I've used in the example (30-105, 28.5%).

Quoting from the errata:

"Page 51: where it says "So from an immediate pot odds standpoint, B needs to be getting
more than $75 to $30 (or 40%) to win the pot." it should be "So from an immediate pot
odds standpoint, B should call if his chance of winning the pot is greater than 30/105, or
28.5%." (12/6/06)"

So my question was already considering the values that the errata are stating (the same ones that I find in my book). Which is really a super basic odds issue.

Why should I need better odds to call off when I have a draw than when I have any other hand? What really matters is the frequency that I expect to win, this frequency is the only thing that matters to a strictly pot odds standpoint.

To ilustrate this, the same example again. I have a draw with 12 outs on the turn for about 25% chance of becoming the winning hand. There is $75 in the pot, villain bets $30. To me, this is a clear profitable call, since I need 22.2% winning frequency here to breakeven, fold would be a clear misstake since calling has a higher ev.

But according to this principle on page 51 of the MoP. This should be a fold, since in reality I need 28.5% and not 22.2%. That's because the principle is stating that I should discount the ammount of the call, which I don't really understand.

p51
"Example 4.3 ($75 Pot)
It is the flop of a $30·$60 holdem game. Player A holds A+ K+, and player B holds 8~
The flop is A+ Ks 4+. There is just $75 in the pot (suppose that the AK limped preflop).
the AK bets $30. B has just eight outs in this case (as the K+ makes AK a full house). So
an immediate pot odds standpoint, B should call if his chance of winning the pot is greater than 30/105, or 28.5%. So what is B's chance of making his flush on the next street? It is 8/45 on the turn. This chance is only 17%, and so we can see that B's chance of making his is not high enough to justify calling."

After looking at it, I believe you may be correct. It should read 30/135=22.2%. So then immediate pot odds do justify a call with a 12 out draw which has about 12/45=26.6% immediate equity.

Yeah whoever corrected the error apparently got it wrong again. If opponent bets 30 into 75 you then have to call 30 into 105 getting 3.5:1 odds, so you need to win at least 1/4.5 or 30/135 = 22.2% of the time.

The book has so many errors that make it almost unreadable.

It seems so. 22.2% would be the odds we get facing a bet of 0.4psb.

Now I don't know if that 30/105=28.5% is just a typing error or if it is that principle stated earlier on the same page affecting the standard odds of the situation.

Principle again: "In made hand vs. draw situations, the draw usually calls if it has positive equity in the pot after calling and subtracting the amount of the call"

Didn't understand this principle tbh. What does positive equity mean in this phrase? Our equity must be positive (>0) after calling and subtracting from the equity this same bet size? I didn't get it at all haha. If ppl who did care to clarify would be nice.

To me the single principle I know of to figure out if draws should be called or not are the standard pot odds themselves and pot odds+implied odds.

Anyway, that might be the case that it is this principle in action making the odds 30/105 instead of 30/135, which don't make any sense to me.

I don't know either. I'm guessing they meant positive EV. Sounds like a very convoluted way of saying that a draw should call when it is getting correct odds to do so.

This book might give you some good ideas to study and research on your own, but giving too much attention to minor details will have you pulling out your hair. If after double-checking and thinking it over something still seems awry, most likely it's just an error on their part. In at least one case (the one that I mentioned in post #175) their argument itself is just plain wrong.

yea you r probably right. Should go easy on details and seek more for conclusions and main ideas of each chapter.
tkz =)

when does this book become good ? I'm on page 143 and they are inventing situations all long the book until now

This book is a mathematical mess. It's not really practical kind of extreme if you ask me


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Pre-Calculus is the most advanced math class I've taken.

My goal is to fully digest the information and math in MoP (eg. be able to solve the equations on my own)

What books and/or courses would you recommend for self-study?

I don't like the way Bayes' Theorem was explained in this book. In high school we did this via probability trees and it was a hundred times easier to calculate than just putting everything into the complex formula.

Not even close to being true.

Not what he ask.

OH PLEASE, more BS.

Well whoop-de-doo! Doesn't mean it's any good. Also doesn't mean it's any good for poker.

Agreed. Most of the high-math books are, at best, esoteric and beyond meaningless in play.

The math is there for the proof...

Dont you like arguments when you read a theory ...
If you think that is esoteric, you have a long way to go imo ...
No hard feelings!

I think this book is amazing.
And the year it was written....
Crazy

How much of math needed to digest? How much of statistics?

I am doing khan academy because seriously I forgot a lot of what I saw in high and college, and I never tough I would need math like this to a subject I really like

Right now studying precalculus

Can anyone answer this. I am wondering the same!

Somebody should write a book called "mathematics of poker made easy" which would be a simplified version of the original with practical applications.There are lot of important ideas in it that get missed in its sea of algebra. Not sure if there is still much market for those type of books though.

brilliant book.......... takes complex issues and breaks them down into smaller components.

as per math, i haven't looked at book in awhile....... but i'd algebra and probability theory.

I'm considering making the effort of learning this book. I was wondering, if I mastered every corner of this book, would other books such as "Winning poker tournaments", "The raiser's edge", "kill everyone", etc.. become useless or meaningless? I'd love to hear "yes".

I mean, this one's tough, but I'd love to just read 1 or 2 more books instead of 7-10 with theoretical approaches in most cases.

ty in advanced

it will not help you much for poker if you knew all the maths in the book.
Its like any math book, the calculation are there for proofs !
yes this book is not a religious book...

just try to understand on the why it works and the conclusion of the chapters, that is what is important and some basic algebra too of course because sme formula will always be needed, like probabilities in poker

Hire a mathematician. They cheap

This answer probably comes late, but I got intrigued by the same passage.

The Half-Street No Limit Clairvoyance game is solved for y = 1/2 (fraction of winning hands for Y). In the general case, solving for b the fraction of dead hands that Y bets as a bluff, we get (making X indifferent between call/fold):

b = s/(s+1) * y/(1-y). This respects the general result that Y bluffes s/(s+1) as many hands as he bets for value.

If s = 5 and y = 3/5, this yields b = 15/12 > 1 which shows that Y cannot make X indifferent between calling and folding. The best Y can do is bluff all of his dead-hands (b=1), but since Y is still "under-bluffing", the best action for X is simply to fold all the time.

Now if we set s = 1 both for bluffing and value betting, then we would have a valid Nash Equilibrium if Y wasnt allowed to vary his bet size. The authors are saying that if Y can vary his bet size, then the bluffing frequency b and calling frequency c alone do not guaranty a Nash Equilibrium, because Y can unilateraly increase his expectation by increasing the bet size without changing his bluffing frequency:

Indeed we have y = 3/5, b = 3/4 and c = 1/2. By locking these values and letting s "float", the expectation of Y is:

Ey = y*c*(+s) + (1-y)*b*(c(-s) + (1-c)*1) = 3(s+1)/20. Same goes for s=1%.

So Y can unilateraly increase his expectation by simply betting more chips. This new bet size will lead to new values for c and b, and so on until we reach b = 1 (starting from s = 2), at which point X does better by simply folding all hands.

Summary:
I think the authors are simply saying that there is no Nash Equilibrium at s = 1% if Y is allowed to vary both b and s. On the other hand, if s is set in stone at 1% then we have the usual optimum, and X would be correct to call with frequency 1/(1+s).

Remember that in this example, player Y is clairvoyant and knows the cards of player X. Player X is not clairvoyant, but knows that player Y is clairvoyant. This leads logically to player Y shoving full stack 100 percent of hands, and X folding to any bet.

The authors are, imho, laying groundwork for the later non-clairvoyant half street and full street toy games.

Hi all,

I've been reading this book and enjoy it as an exercise in logic. So far I feel that (despite the editing mistakes, which in a way help because they act as a reality check) I understand the assertions. However, I have hit a wall on one assertion and can't break through.

In my edition, on page 222 (chapter 18, discussion of game value for Y of game [0,1] #6) , the authors have ascribed equity G to the player Y in the special region [0, x1]. They then state that when both players have a hand on the range [0, y2] that the equity of Y is -G (and this situation reverses based on who made the last raise).

I don't understand why the equity in this region is -G and was wondering if someone could point me in the right direction. From their discussion of the next game value, I assume the reason is obvious, but I'm not getting it.

Thanks in advance.