Re: Good News/Bad News/Good News
 

For a classic and very readable text on game theory, see "Games and Decisions" by R. Duncan Luce and Howard Raiffa.

From the text:

"In the domain of mixed-strategies, every zero-sum, 2-person game has at least one equilibrium [strategy] pair, and when there are several, they are equivalent and the equivalent strategies are interchangeable."

Re: Good News/Bad News/Good News
 

[ QUOTE ]
For a classic and very readable text on game theory, see "Games and Decisions" by R. Duncan Luce and Howard Raiffa.

From the text:

"In the domain of mixed-strategies, every zero-sum, 2-person game has at least one equilibrium [strategy] pair, and when there are several, they are equivalent and the equivalent strategies are interchangeable."

[/ QUOTE ]

Are you saying that if a 2-player zero-sum game has 2 eqiulibria, A=(a_1,a_2) and B=(b_1,b_2), then e.g. C=(a_1, b_2) is also an equilibrium?

Re: The Mathematics of Poker
 

[ QUOTE ]
available now from sellers on amazon.co.uk if anyone's interested.

[/ QUOTE ]
High Stakes in London has copies.

chez

Re: The Mathematics of Poker
 

I'd like to thank everyone for catching our errors. I have to say that we didn't expect the book to be error-free. We read over it several times along with our editors and reviewers, but at some point you have to decide to release the book. During the editing phase we made sure the sections were as understandable to our outside readers as possible, and I hope our efforts paid off there. I don't mind saying most of the clearly written prose is Jerrod's and any typos in the equations are likely to be mine:-).

Bill Chen

Re: The Mathematics of Poker
 

On one extreme is the game where your opponents strategies are entirely known and they have no adaptive abilities. In this case it's relatively straightforward to calculate the best play. Jerrod dubs this the PlayStation (tm) approach to poker. We do go over several examples of this in Section II. Even though game theory is the biggest section in the book, the book is hardly all about game theory. It's just that in comparison the mathematics of playing against a known strategy is much easier. This is not to say that the sections on how to collect data against your opponent and Bayesian inference in tells aren't important--in fact, they are more useful against weak and unadaptive opponents.

But even in so called "soft" games the players are not this predictable. Even when it's claer someone plays badly because of a given play it's still unclear how badly they play. For example say you see someone make a bad call, do you know if it's the minimum hand they would call with or will they call with worse, or did they just make the call on a whim? There are certainly situations where game theory may still apply such as value betting on the end.

Even if you read your opponent perfectly for a mediocre hand--in the book we call this the clarvoyant game, if you don't have an idea of his calling frequency you may still want to play the optimal mix of bluffs and value bets at the end. This is the strategy that is the hardest for your opponent to play against.

Bill

Re: Good News/Bad News/Good News
 

Yes. In fact B can play any mixture of b1 and b2, which means that the set of all equilibria strategies is actually convex. All the strategies in this space are "optimal" and we can talk about the space of all equilibria as the cross product A0 x B0 where A0 and B0 are both convex strategy subspaces of A and B respectively.

Bill Chen

Re: Good News/Bad News/Good News
 

Oh thanks for explaining, I just got the book and it looks pretty good I have to say. A lot more rigorous than any other poker book I've seen.

Re: Good News/Bad News/Good News
 

I bought this book at The Gambler's Book Club in Vegas based on the kudos in this thread.

I opened it up in the middle somewhere. My head assplode. I suggest a degree in mathematics as a prereq for this book. I've got a film degree so I'm screwed, but this will be perfect for some of you guys.

Re: Good News/Bad News/Good News
 

[ QUOTE ]
I bought this book at The Gambler's Book Club in Vegas based on the kudos in this thread.

I opened it up in the middle somewhere. My head assplode. I suggest a degree in mathematics as a prereq for this book. I've got a film degree so I'm screwed, but this will be perfect for some of you guys.

[/ QUOTE ]

You certainly don't need a mathematics degree. Start from the beginning, and work your way through it. Don't be dismayed, they work through everything and explain it so it's fairly easy to understand.

If you start from the middle, your head may very well "assplode", but it really isn't necessary.

Don

Re: Good News/Bad News/Good News
 

Yeah since there are 382 pages not counting the roman numbered ones, I opened to 191. I see what you mean. But you aren't supposed to start reading from there. It's a little easier to start from page 1. The goal was to make the book understandable for different levels of math sophistication--I think understanding the conclusions is possible without understanding the derivation of the results, though I imagine there are lots of participants on this forum who will keep us honest on our math.

To be honest, there is some minimum math requirement, just as there is some minimum poker knowledge. If you don't know what a check-raise is, I would recommend reading something else and playing a little first. Similarly, familiarity with Algebra is a minimum. If you see "w = 3xy + 2" and don't know that it means the value of w is three times x times y plus 2 or see how that simplifies to "w - 2 = 3xy" then you may not get far with the book.

This is unfortunate as this does exclude a large portion of the population, I suspect even a large portion of the poker playing population. I feel pretty bad about this, but we can't put all prequisite material or the book will be several thousand pages long.

For the rest who meet these requirements we do feel you will understand most of the book if we have done our job well--in fact this is a good test for us as authors.

Bill

Re: Good News/Bad News/Good News
 

Kudos to the excellent book. This is the best book on poker I have ever read.

Re: Good News/Bad News/Good News
 

i think i might get this for xmas :>

Re: Good News/Bad News/Good News
 

[ QUOTE ]
Yeah since there are 382 pages not counting the roman numbered ones, I opened to 191. I see what you mean. But you aren't supposed to start reading from there. It's a little easier to start from page 1. The goal was to make the book understandable for different levels of math sophistication--I think understanding the conclusions is possible without understanding the derivation of the results, though I imagine there are lots of participants on this forum who will keep us honest on our math.

To be honest, there is some minimum math requirement, just as there is some minimum poker knowledge. If you don't know what a check-raise is, I would recommend reading something else and playing a little first. Similarly, familiarity with Algebra is a minimum. If you see "w = 3xy + 2" and don't know that it means the value of w is three times x times y plus 2 or see how that simplifies to "w - 2 = 3xy" then you may not get far with the book.

This is unfortunate as this does exclude a large portion of the population, I suspect even a large portion of the poker playing population. I feel pretty bad about this, but we can't put all prequisite material or the book will be several thousand pages long.

For the rest who meet these requirements we do feel you will understand most of the book if we have done our job well--in fact this is a good test for us as authors.

Bill

[/ QUOTE ]

Thanks for the reply. Although I made kind of a half-assed comment about it, you replied professionally. I will recommend this book to friends because you seem to care about your customer base.

Re: The Mathematics of Poker
 

Hey, I'm not sure if this is errata or user-error, but I've been plodding through this book, stopping to make sure I understand each equation and application fully. On page 26, they plug their example game into equation 2.4 to figure the standard deviation for the variance (2.61)

the equation is something like:

STDEV = 2.61 * SQRT 100

and they end up with an answer of 36.89. How? Isn't SQRT(100) = 10? so 2.61 * 10 = 26.1?

Note: I have a BA and clepped out of all my college math, so be gentle if this is a dumb question.

Re: The Mathematics of Poker
 

Yep it's in the list of errors, it seems you are getting the material.

Bill Chen

Re: The Mathematics of Poker
 

[ QUOTE ]
Hey, I'm not sure if this is errata or user-error, but I've been plodding through this book, stopping to make sure I understand each equation and application fully. On page 26, they plug their example game into equation 2.4 to figure the standard deviation for the variance (2.61)

the equation is something like:

STDEV = 2.61 * SQRT 100

and they end up with an answer of 36.89. How? Isn't SQRT(100) = 10? so 2.61 * 10 = 26.1?

Note: I have a BA and clepped out of all my college math, so be gentle if this is a dumb question.

[/ QUOTE ]

Yes, this equation should say sqrt(200) instead of 100. This and other errata can be found at:

http://www.conjelco.com/mathofpoker/...ker-errata.pdf

It's really really hard to find all the small errors in a book like this; we had several people all reading the book looking for this type of stuff, but things do slip through the cracks. In future printings the errors that we (or you!) find will be corrected.

Re: The Mathematics of Poker
 

I ordered the book today off amazon...if after 300+ pages you only have around 10 corrections that need to be made, then i am quite excited

Re: The Mathematics of Poker
 

I realize this is a week late, but the best calculator ever made is the Hewlett-Packard HP48GX or the older but basically the same HP48SX. You can get these off of ebay. They will last forever. There is pretty much no reason to have any other calculator for serious math.

You can get a Palm Pilot emulator for these machines for free on the web. My Treo 650 emulating my HP48SX is faster than the calculator is.

If you want to do real math on a computer, get yourself a copy of Mathematica or Maple, both of which do symbolic math. I prefer Mathematica. If you are a student, you can get a copy of this for only a hundred bucks. Pretty much a no-brainer for anyone who wants to do sophisticated math in any subject (or even unsophisticated but tedious symbolic math).

FWIW,

Jim

Re: The Mathematics of Poker
 

Figure 15.1 pg 163 is inconsistent with the following text on the next page,i.e. the graph does not show that f(x) is maximized at x=1 for P>2.

I calculate that at P=3 alpha = 1/2 and f(x) = 0 at x= 0 and f(x) = 1/12 at x=1 which looks like the P=1 line on the graph as printed, so the legend may be inverted, but I haven't checked each value of P.

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Bill,

Seeing as your a Pokerstars sponsored player any chance of you pushing them to put into the VIP store?

[/ QUOTE ]

[/ QUOTE ]

[/ QUOTE ]

Again: could you please answer this question?
Also when will there be a 2nd edition?

Re: The Mathematics of Poker
 

Correction: At P=3 alpha=1/4 so the graph line is correct ( f(0) = 1/12 and at f(1)= 1/24) but the characterization f(x) max'd at x=1 for P>2 is still suspect.

Guess I need to work through The Arithmetic of Poker before tackling this one :-)

Re: The Mathematics of Poker
 

Great book. I was familiar with some content (like most 0-1 games described in the book) but still its very good.
I will give my review when I finish the book. I am especially curious if some of my calculations for multi street bluff or nuts games weer correct.
For now minor typo :
page 89 KK,QQ,JJ,TT should be 24/42 not 6/42.

Re: The Mathematics of Poker
 

Maybe I'm paranoid, but I have a strong feeling that this book will become the bible for bot developers.

Re: The Mathematics of Poker
 

[ QUOTE ]
Maybe I'm paranoid, but I have a strong feeling that this book will become the bible for bot developers.

[/ QUOTE ]

I doubt it.
Techniques for programming poker playing programs are out there for a long time.

Re: The Mathematics of Poker
 

[ QUOTE ]
Correction: At P=3 alpha=1/4 so the graph line is correct ( f(0) = 1/12 and at f(1)= 1/24) but the characterization f(x) max'd at x=1 for P>2 is still suspect.

Guess I need to work through The Arithmetic of Poker before tackling this one :-)

[/ QUOTE ]

Maybe I'm just a moron, but posts like this are making me think this book might not be my cup of tea. I had some math in college, but I'm not a big fan of it. I am, however, willing to do whatever it takes to continue to improve as a poker player. Just worried that this book may be written in Greek to me...

Re: The Mathematics of Poker
 

Actually you can skip most of the math and still get the gist of the exposition. That's what I'm doing, at least on the first pass. That one I just happened upon since the graphs and the text didn't jibe so I decided to slog through the calculations. I think in this case the solution is reversed just after the graph, but later in the text when it refers to the results it seems to do so correctly.

After the math, which is 99% algebraic solving for when two expressions are equal, the authors usually take pains to explain why the results match, or do not match, one's intuition or customary advice.

There are bullet point items at the end of each chapter if you want the condensed version.

If you want to avoid the occasional glitch just wait a couple of weeks for the online errata list to fill out, or for the next edition in a few(?) months.

Hint to publisher for second edition: Do wish the type was larger though. Would make it a bit easier on the aging eyeballs.

Re: The Mathematics of Poker
 

seconded on the typeface thing. info this deep is all the more intimidating in little bitty letters. I also find my mind wandering a little too quickly when reading this smallish type. Maybe a monetary consideration though, as you can obviously fit more material in fewer pages with the smaller type.

other suggestions for the next edition:
a comprehensive equation appendix in the back. I'm finding myself wanting to go back to the original references to certain equations as I re-encounter them, but I'm having to rely on my note taking to get there. an appendix would be very helpful here.

<font color="gray">jopke: Q:why don't republicans use bookmarks? A:because they just bend the page over. </font>

things that I'd love to see in future series installments:
-exhaustive limit poker (specifically turn and river play)
-review of one's own statistics

thx for a great book!

Re: The Mathematics of Poker
 

don't think this has been mentioned yet, but on pg 135 in the headsup jam or fold section you said "continuing to raise the temperature" and then went on to lower the temperature by increasing the stack sizes.

Re: The Mathematics of Poker
 

"For now minor typo :
page 89 KK,QQ,JJ,TT should be 24/42 not 6/42. "

Each of the four listed pairs having the identical frequency of 6/42. So "6/42 for each pair" might be less ambiguous?

Re: The Mathematics of Poker
 

Yes, f(x) is the value to Y, not X as was said on the top of the page. In all these games, we calculate the value to Y. Hence X is trying to minimize f, so in the sentence maximize should be replaced by "minimize."

Good, youa re the first person to catch this.

Re: The Mathematics of Poker
 

anyone take a snapshot? I still have a few days till mine arrives, Im curious to see what intimitading looks like.

Re: The Mathematics of Poker
 

Sorry the FPP Store will be carrying the book soon. I can't confirm just yet, but there will likely be an event where you can get a signed copy of the book at the PCA in the Bahamas.

Re: The Mathematics of Poker
 

Thanks Bill, will definitely be spending my FPPs on your book when it becomes available and look forward to reading it.

Re: The Mathematics of Poker
 

[ QUOTE ]
Maybe I'm paranoid, but I have a strong feeling that this book will become the bible for bot developers.

[/ QUOTE ]
That was my continual thought as I read through the book: Computers can't beat (very good) humans at poker yet, but whenever they get to that point, it will be by using the concepts presented in this book.

Re: The Mathematics of Poker
 

whens the study group gonna get going..i get my book on the 23 and i have a feeling im gonna need help applyin this to the variety of games

Re: The Mathematics of Poker
 

a question:

should one use basic hand-reading in conjunction with optimal bluffing?

example:

If a player checkraises two people on the turn in holdem and then leads the river should we even bother doing the bluff math?

In 2-7 tripledraw if a player is pat on the second round and has been betting the whole way, should we bother looking at the pot size to determine whether or not to bluffraise on a third-round brick, or should we just make a categorical fold?

intuitively I think that the answer is to be sure that you're in a situation where the opponent is capable of folding at least sometimes, and that mixed bluffing strategies are categorically exploited when our opponent is a non-folding situation. I guess the key is identifying those situations.

I could be wrong though. [img]/images/graemlins/smile.gif[/img]

Re: The Mathematics of Poker
 

On page 77, it says

&lt;X, bet turn&gt; = (29/44)($200)-$50
&lt;X, bet turn&gt; = $54.55

Doesn't it equal $81.81? What am I not figuring in?

N

Re: The Mathematics of Poker
 

[ QUOTE ]
On page 77, it says

&lt;X, bet turn&gt; = (29/44)($200)-$50
&lt;X, bet turn&gt; = $54.55

Doesn't it equal $81.81? What am I not figuring in?

N

[/ QUOTE ]

Yeah, this isn't terribly clear.

p 77. "X still has a clear call, getting more than 3 to 1 from the pot" should be -&gt; "Y still has a clear call, getting 3 to 1 from the pot."

then below that:

&lt;X, bet turn&gt; = [p(Y misses flop)][p(X wins)(new pot value) - (cost of bet)]
&lt;X, bet turn&gt; = (30/45)[(29/44)(200) - (50)]
&lt;X, bet turn&gt; = $54.55

(81.81 is the equity for X when Y misses the flop, but the equity of playing it this way is 54.55 beacause sometimes he just loses the pot immediately on the turn).

Thanks for pointing this out.

Re: The Mathematics of Poker
 

Thanks for the quick response. Wouldnt it be clearer to say something like

"The value of checking the flop if Y checks behind, assuming that X bets the turn when it doesnt complete Y's hand is

&lt;X, X checks-Y checks flop&gt; = [p(Y misses turn)][p(Y misses river)(new pot value) - (cost of bet)]"

I'm really enjoying the book. If I come across anything else thats unclear to me, I'll make a post about it. I appreciate the authors' hard work.

N

Re: The Mathematics of Poker
 

[ QUOTE ]
a question:

should one use basic hand-reading in conjunction with optimal bluffing?

example:

If a player checkraises two people on the turn in holdem and then leads the river should we even bother doing the bluff math?

In 2-7 tripledraw if a player is pat on the second round and has been betting the whole way, should we bother looking at the pot size to determine whether or not to bluffraise on a third-round brick, or should we just make a categorical fold?

intuitively I think that the answer is to be sure that you're in a situation where the opponent is capable of folding at least sometimes, and that mixed bluffing strategies are categorically exploited when our opponent is a non-folding situation. I guess the key is identifying those situations.

I could be wrong though. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

Well, in an optimal strategy, there really shouldn't be very many places where you wouldn't fold. Assuming that your opponents won't snow (which is your assumption in the case where you claim that they are in "non-folding situations") might allow them to exploit you by doing just that. It's easy to see why. Suppose that you never bluff-raise the river. Then they can just exploit you by folding the worst hands that they would play in this manner instead of calling your raise. Then your strategy isn't optimal.

So no, you shouldn't use "hand-reading" of that type as a tool in generating optimal strategies. The tone of your post also suggests (by your use of "optimal bluffing") that you may not understand some things about the nature of multi-street play - that is, that the solution to a game considered in isolation on the river is not necessarily (or even often) the solution to the same game carried forward from previous streets. We have a clear example of this idea in our book (ch 20) which considers a holdem hand where the flush comes in on the river and one player is known to hold a mixture of flush draws and bluffs.