Hi, at page 97 the author says : ''B's MES in this case is to fold all the time if A bluffs less than 5% (because player A has 20% value in his range, the pot is 3, the bet is 1), obtaining an ex-showdown equity of 3x, where x is A's bluffing frequency''.

I really don't understand the meaning of this sentence.

Then the author puts two equations :

<B, fold> = 3x

<B, call> = x – 0.2

I understand from the explanations before what he calls 'ex-showdown equity' is the equity in the pot which is coming from a non-showdown source. But I really can't make sense out of these words.

How could B have any non-showdown equity if he's just have a bluff catcher ? He will either call and have some showdown equity, or fold and have zero.

How does these equation makes sense ? let's say A bluffs 5% as optimal, 3(0.05) = 0.15. So what is the meaning of this 0.15 ? The equity of B fold should still be 0%.

And if we try 0.05 - 0.20 = we get -0.15, But how can the EV of calling be -15%? 4 times he lose 1 bet, 1 times he wins 4.How could his equity be minus anything ?

I'm sorry I just try to make sense of this book. I know it's valuable but there are not much explanations.

hi

Conceptually, that page is teaching the difference between balance and optimal.

A balanced strategy may be +EV but may also be exploited by a MES response.

An optimal strategy may be less +EV than MES, but is purely non-exploitable, such as a Nash Equilibrium.

So, player A can bluff anywhere from 0 to 20 percent, and not lose money. Conversely, player B can fold full range when x<5%, and call full range otherwise. These are valid MES responses.

However, when player A bets *optimally* within a tiny margin (4.8 to 5.2) , there is no MES, and player A is guaranteed his best expectation.

The author points out that real poker is more complicated than this contrived situation. The point here is that sometimes all you can manage is balance, and true optimality will just be an educated guess.

this seems like all you need to know to beat no limit. like its fundamental theorem in raw form.

Hi, thank you, but I still don't understand what is the meaning of those equations exactly ?

Let say:<B, fold> = 3x

so if A bluffs 5% 3(0.5) = 0.15

so what means this 0.15 ?

And what is the idea behind multiplying by 3 player A's bluffing frequency ?

Sorry Kingkong352, but the text does not explain itself very well. The authors often use methods which are 'upside down' to me, and not very intuitive. Some of the numbers which are negative in my mind, are positive in the book and visa versa.

The almost cryptic nature of the book is sort of why so many people revere it. To really understand it, you have to decipher it as if it were written a lost language and found in an archaeological dig.

My personal opinion is that the book was simply in need of better editing.

My guess is that those equations are folding equity, or the portion of the pot that player A wins due to the bluff percentage.

So:

<B, fold> = 3x

When player B chooses to fold, then the fold equity is (Pot)x(Bluff) this is the percentage of the existing pot that player A wins due to having a bluff frequency x.

<B, call> = x – 0.2

When player B chooses to call, this is the equity gained by the call, since player A has a winning hand with frequency .2 and is bluffing with frequency x.

This is my best guess, and usually I am the only forumer willing to try to explain this book.

If the book is not teaching you well, it is not your fault. This book is not for everyone and there are other better edited books such as Matt Janda's first volume 'Applications of No Limit' which I gather has useful poker mathematics better explained.

Kingkong:

To me those symbols are the elements of a ratio.

A couple yrs ago I struggled w/ MOP for several weeks readingit Page by page and taking countless detours to learn the math from other sources. Finally I️ just decided to treat the book differently, and jump around learning about the different toy games and trying to absorb the concepts and the basic math.

This book rly frustrated me, partially because i wish there were more ‘keys’ or laymans breakdowns of the concepts. I have a ton of respect for bill Chen, but i also thought that he/editors did not make this book accessible even to a dedicated reader. I did a deep dive on juandas applications as well, i need to warn you that he agknowledges many of the formulas/concepts were slightly incorrect. He is a pioneer, what makes that books so great is that he proposed a way of thinking about ranges, defense, frequencies, etc that we take for granted nowadays. I think his latest book has more up to date ideas but I️ haven’t read it yet.

IMO MOT is a foundation theory book, but the math can be understood conceptually. For example bills 1-A equation for defense can be done in simpler ways, but the concept is what is valuable