Re: The Mathematics of Poker
 

Is this book worth reading? Or is it too theoretical?
I am playing Nl200 atm.

Re: The Mathematics of Poker
 

Jerrod, thanks for the reply. I'm not quite to chapter 20 yet, but I am about halfway through. Its incredibly difficult to resist skipping forward to the case-study, but I've managed not to do it so far. [img]/images/graemlins/smile.gif[/img]

Lots of the concepts are starting to illuminate each other, so I'll just finish the freakin book before asking anything else that's already explained in it. [img]/images/graemlins/cool.gif[/img]

thanks again!

Re: The Mathematics of Poker
 

recallme: theory is important in poker.

Re: The Mathematics of Poker
 

Does it seems ridiculous to anyone else that I haven't recieved my pre-ordered Conjelco copy?

Re: The Mathematics of Poker
 

For me it seems to spew around with numbers too much, can you give me a quick summary of it`s contents?

Re: The Mathematics of Poker
 

[ QUOTE ]
For me it seems to spew around with numbers too much, can you give me a quick summary of it`s contents?

[/ QUOTE ]

numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers

at least if you can't see the forest for the trees.

Re: The Mathematics of Poker
 

[ QUOTE ]
For me it seems to spew around with numbers too much

[/ QUOTE ]

There are lots of numbers involved in math. [img]/images/graemlins/confused.gif[/img]

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
For me it seems to spew around with numbers too much

[/ QUOTE ]

There are lots of numbers involved in math. [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]
maths is excellent, i am really looking forward to reading the book. [img]/images/graemlins/smile.gif[/img]

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
For me it seems to spew around with numbers too much

[/ QUOTE ]

There are lots of numbers involved in math. [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]

There is lots of mathematics NOT involved with numbers. [img]/images/graemlins/laugh.gif[/img]

Re: The Mathematics of Poker
 

[ QUOTE ]
There are lots of numbers involved in math. [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]
Almost all of them are.

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
There are lots of numbers involved in math. [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]
Almost all of them are.

[/ QUOTE ]

[img]/images/graemlins/blush.gif[/img]

Re: The Mathematics of Poker
 

I have a problem on page 78

<X check, Y check> = (15/45)(0$) + (30/45)(29/44)($300-$100)
= 65.15

It's not 87.9 ???

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
For me it seems to spew around with numbers too much, can you give me a quick summary of it`s contents?

[/ QUOTE ]

numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers numbers

at least if you can't see the forest for the trees.

[/ QUOTE ]

I have ordered the book (twice already, since the guys at Amazon are a bunch of donkeys). Numbers alone isn't what I am looking for. I am looking for answers. I hope this book provides answers to non-trivial questions and/or shows methods how to solve problems.

Actually I don't expect this book to be similar to Nesmith Ankeny's phenomenal book on 5 Card Draw, but I would love to see it discuss methods to create something similar.

Re: The Mathematics of Poker
 

252 posts in this thread and still no review. C'mon people, I am desparately waiting on sb to give short review or comment a little more extensively. I can't wait to get my hands on this book but I am in friggin Bulgaria, so who knows when and how this is going to happen...

So, pretty please - review? Anyone?

Re: The Mathematics of Poker
 

A question to Bill Chen. In "Jam or Fold Tables" for attacker (i.e. small blind) with KT offsuit strategy is "JAM" meaning SB should push with stack/BB ratio 50 or less. I've made some calculations using linear programming method and got another results:

stack/BB KTo % jam
50 41.08%
49 0.00%
48 0.00%
47 8.73%
46 100.00%
45 83.50%
44 100.00%
43 6.25%
42 21.70%
41 19.34%
40 20.33%
39 43.36%
38 38.07%
37 32.53%
36- 100.00%

Comments?

Andrzej Nironen

Re: The Mathematics of Poker
 

On page 268, the authors propose a preflop strategy of raising each time we enter the pot and to bet from a minimum a 2BB 5-6 off the button and 3BB on the button with an adequate distribution of hands that have to be defined.

I would like to know if the authors have already used this strategy with success playing online.

Re: The Mathematics of Poker
 

Yes, without going into numbers we've been much more successful than we thought we would be, although much of the success is over thousands of NL-multis. I don't think simply making lots of money proves what we are doing is correct though since a lot of the NL play is quite weak. There are probably many unsound opening strategies that would work.

Re: The Mathematics of Poker
 

Bill:

I haven't had the opportunity to fawn over you since the WSOP, as you already know I am the president of the Bill Chen fan club. I haven't picked up the book yet, but I hope that you have left signed copies with Gamblers Book Club or the Gamblers General Store for me to buy myself as a new years present [img]/images/graemlins/smile.gif[/img]

Would love to discuss Badugi math with you sometime soon, but I'll wait till I am done with your book before bugging you.

TT [img]/images/graemlins/club.gif[/img] - aka Bill Chen Fanboy #1

Re: The Mathematics of Poker
 

P.48:
<B,call> = p(A has nuts)(-1) + p(A has a bluff)(+5)
<B,call> = (0.2)(-1) + (5)x

Shouldn't it be:
<B,call> = p(A has nuts)(-1) + p(A has a bluff)(+5)
<B,call> = (1-x)(-1) + (5)x

Re: The Mathematics of Poker
 

[ QUOTE ]
Bill:
I am the president of the Bill Chen fan club...I haven't picked up the book yet

[/ QUOTE ]

lol

[ QUOTE ]

- aka Bill Chen Fanboy #1,126

[/ QUOTE ]

FYP.

Re: The Mathematics of Poker
 

[ QUOTE ]
P.48:
<B,call> = p(A has nuts)(-1) + p(A has a bluff)(+5)
<B,call> = (0.2)(-1) + (5)x

Shouldn't it be:
<B,call> = p(A has nuts)(-1) + p(A has a bluff)(+5)
<B,call> = (1-x)(-1) + (5)x

[/ QUOTE ]

There is a problem in the original text. The correct formulation follows from conditioning on the right information set. I previously posted the correction here:

http://forumserver.twoplustwo.com/sh...age=0&vc=1

The authors' general conclusions are unchanged by the correction even though the value function (and graph thereof) becomes non-linear.

Re: The Mathematics of Poker
 

I just finished my first complete reading of the book. It is absolutely extraordinary.

Those looking for specific advice playing particular forms of poker will not be happy with the book (with one important, and possibly extremely profitable exception). Those who are looking to really understand the depths and complexity of the game, in all its forms, will be rewarded with an absolute masterpiece.

I've read and studied everything worth reading (and many others not worth reading!) about poker many times. In my opinion, nearly all of the worthwhile stuff is 2+2 books, with a few exceptions. As stellar as I believe the 2+2 books are, I feel that MoP deserves its own category.

Its major departure from most good poker books is to explore the notion of "optimal play" in a great deal of depth. The most powerful tool of this exploration is game theory, and the book contains an extremely rigorous application of game theory to poker using exemplifying "toy" games that illustrate strategic principles of real poker games. Except for what Sklansky has briefly written on the subject (ToP), this is the only book containing this kind of information that I am aware of.

While the game theory sections seem to be causing the most comments, MoP also contains excellent sections on what the authors call "exploitive play". While optimal play intends to make our own play unexploitable, exploitive play intends to maximally profit from the deficiencies in our opponent's strategies. To do so, we must ourselves deviate from optimal play, which opens us up to be expolited ourselves (what the authors call counter-exploitation). The discussion of identifiying opponent's strategic weaknesses and developing maximally exploitive strategies is fantastic. Related to this whole discussion is the notion of strategic "balance", which is the bridge to the discussion of optimal play -- and the defense against counter-exploitation.

I can't say the book has taught me any new "plays" or given me any one specific thing to improve about my game (I am not a tournament player, the domain of the important exception I mentioned above). Instead, this book has given me something orders of magnitude more valuable: a more sophisticated way of *thinking* about poker. One reading has already prompted me to think about some pretty important aspects of my game -- balanced strategy on the turn in cash NL holdem, in my particular case -- in an entirely different paradigm. This is absolutely NOT just another book showing you how to calculate pot odds and reminding you to consider future action or the chance you'll catch and lose (my opinion of Yao's "Weighing the Odds"). There is some new and very sophisticated stuff here.

The book has introduced me to thinking about poker at the level beyond what's described in the existing literature. As soon as I finished the last page, I started reading it again...

One final comment about the math. I have an extremely strong math background (though not post-graduate level), and I am comfortable reading ideas in a textbook style of writing. However, the math is not difficult in this book, and the most "advanced" math employed is probably finding a minimum by finding the zero of the first derivative. That is calculus, but anyone who's taken basic differential calculus will be able to follow all the math in the book (this includes quite a few high school students). If you're someone who thinks that NL Holdem is a "people game" and so you don't need to know about equity of hands, pot odds, and draw probabilities, skip this book. This book is for people who have that stuff down cold, don't need any clever new ways to think about it (DIPO?!?), and want to go to the next level.

The beginning of the book has a nice introduction to probability and statistics, but I feel that a good understanding of how the authors analyze poker will require some basic training in statistics, particularly a degree of comfort with the idea of distributions. I think that studying the first half of a first-term college statistics book is valuable for gamblers whether they read MoP or not, but it will definitely help you with this book.

Jim

?=1.61 on page 34. Question for authors.
 

What on earth is the quantity that equals 1.61 on page 34? [img]/images/graemlins/mad.gif[/img]

Re: ?=1.61 on page 34. Question for authors.
 

"As we calculated above, the standard deviation of a sample of 16,900 hands is 1.61 units/100hands" Thats what it is. Or is there something in the quote that is unclear?

Re: ?=1.61 on page 34. Question for authors.
 

thylacine said:[ QUOTE ]
What on earth is the quantity that equals 1.61 on page 34? [img]/images/graemlins/mad.gif[/img]

[/ QUOTE ]


Oct0puz said:[ QUOTE ]
"As we calculated above, the standard deviation of a sample of 16,900 hands is 1.61 units/100hands" Thats what it is. Or is there something in the quote that is unclear?

[/ QUOTE ]

Yes, we are looking at the same book. The quote is about as clear as pea-soup flavored porridge in a thick fog.

Let me ask again. What on earth is the quantity that equals 1.61 on page 34? What is the precise mathematical meaning of each of the quantities in this calculation?

Re: ?=1.61 on page 34. Question for authors.
 

thylacine said:[ QUOTE ]
What on earth is the quantity that equals 1.61 on page 34? [img]/images/graemlins/mad.gif[/img]

[/ QUOTE ]


Oct0puz said:[ QUOTE ]
"As we calculated above, the standard deviation of a sample of 16,900 hands is 1.61 units/100hands" Thats what it is. Or is there something in the quote that is unclear?

[/ QUOTE ]

thylacine said:[ QUOTE ]
Yes, we are looking at the same book. The quote is about as clear as pea-soup flavored porridge in a thick fog.

Let me ask again. What on earth is the quantity that equals 1.61 on page 34? What is the precise mathematical meaning of each of the quantities in this calculation?

[/ QUOTE ]

thylacine says: Even more to the point: What exactly is being done to a random variable with standard deviation 2.1 to produce another random variable with standard deviation 1.61?

Re: ?=1.61 on page 34. Question for authors.
 

[ QUOTE ]

thylacine says: Even more to the point: What exactly is being done to a random variable with standard deviation 2.1 to produce another random variable with standard deviation 1.61?


[/ QUOTE ]

The 2.1 is the SD/hand, 1.61 is the SD/100 hands. They want to compare the WR (in BB/100) to the SD so they need to adjust the units of SD from /hand to /100 hands.

Edit: Uh, yeah. So shouldn't the converted value be 27.3, not 1.61?

Re: ?=1.61 on page 34. Question for authors.
 

[ QUOTE ]
thylacine said:[ QUOTE ]
What on earth is the quantity that equals 1.61 on page 34? [img]/images/graemlins/mad.gif[/img]

[/ QUOTE ]


Oct0puz said:[ QUOTE ]
"As we calculated above, the standard deviation of a sample of 16,900 hands is 1.61 units/100hands" Thats what it is. Or is there something in the quote that is unclear?

[/ QUOTE ]

thylacine said:[ QUOTE ]
Yes, we are looking at the same book. The quote is about as clear as pea-soup flavored porridge in a thick fog.

Let me ask again. What on earth is the quantity that equals 1.61 on page 34? What is the precise mathematical meaning of each of the quantities in this calculation?

[/ QUOTE ]

thylacine says: Even more to the point: What exactly is being done to a random variable with standard deviation 2.1 to produce another random variable with standard deviation 1.61?

[/ QUOTE ]

The SD of 1.61 is a renormalization of the standard deviation of a 16,900 hand sample into BB/100h terms. It's not the standard deviation of a 100 hand sample, of course! It's actually not a random variable, either.

Maybe this would be clearer if we said the following instead -- we won 1.15 BB/100 hands in 16,900 hands, which is 194.35 BB. Our standard deviation for a sample of this size is 273 BB, and change all the confidence interval stuff to read "194BB +/ 273BB" etc.

It's just that it seemed that people are more comfortable with BB/100 as a metric than large raw numbers of big bets over 16,900 hands.

Jerrod

Re: The Mathematics of Poker
 

[ QUOTE ]
A question to Bill Chen. In "Jam or Fold Tables" for attacker (i.e. small blind) with KT offsuit strategy is "JAM" meaning SB should push with stack/BB ratio 50 or less. I've made some calculations using linear programming method and got another results:

stack/BB KTo % jam
50 41.08%
49 0.00%
48 0.00%
47 8.73%
46 100.00%
45 83.50%
44 100.00%
43 6.25%
42 21.70%
41 19.34%
40 20.33%
39 43.36%
38 38.07%
37 32.53%
36- 100.00%

Comments?

Andrzej Nironen

[/ QUOTE ]

Checking these against our results for specific stack sizes, your results match ours. In formulating the jam or fold tables (which are sort of a simplification of this type of thing) we had to choose which oddities to report on and which to sort of ignore, so I think that here we simply decided to mark the hands as JAM as it is jammed above 50 at least sometimes and it can't be terribly costly to jam it when mixed.

Jerrod

Re: The Mathematics of Poker
 

So is this book in Barnes and Noble/Borders yet?

Re: ?=1.61 on page 34. Question for authors.
 

[ QUOTE ]
[ QUOTE ]
thylacine said:[ QUOTE ]
What on earth is the quantity that equals 1.61 on page 34? [img]/images/graemlins/mad.gif[/img]

[/ QUOTE ]


Oct0puz said:[ QUOTE ]
"As we calculated above, the standard deviation of a sample of 16,900 hands is 1.61 units/100hands" Thats what it is. Or is there something in the quote that is unclear?

[/ QUOTE ]

thylacine said:[ QUOTE ]
Yes, we are looking at the same book. The quote is about as clear as pea-soup flavored porridge in a thick fog.

Let me ask again. What on earth is the quantity that equals 1.61 on page 34? What is the precise mathematical meaning of each of the quantities in this calculation?

[/ QUOTE ]

thylacine says: Even more to the point: What exactly is being done to a random variable with standard deviation 2.1 to produce another random variable with standard deviation 1.61?

[/ QUOTE ]

The SD of 1.61 is a renormalization of the standard deviation of a 16,900 hand sample into BB/100h terms. It's not the standard deviation of a 100 hand sample, of course! It's actually not a random variable, either.

Maybe this would be clearer if we said the following instead -- we won 1.15 BB/100 hands in 16,900 hands, which is 194.35 BB. Our standard deviation for a sample of this size is 273 BB, and change all the confidence interval stuff to read "194BB +/ 273BB" etc.

It's just that it seemed that people are more comfortable with BB/100 as a metric than large raw numbers of big bets over 16,900 hands.

Jerrod

[/ QUOTE ]

Okay let me try to reverse engineer what you are saying. Tell me if this is right.

The question is what is the significance of the quantity

S(\sigma,N,K) := K \sigma / \sqrt{N} ---(EQ1)

(Note \sqrt{N} in denominator.) In particular you had \sigma=2.1 N=16900 K=100. This quantity is also given by

\sigma \sqrt{N} / H where H=N/K ---(EQ2)

(Note \sqrt{N} in numerator.) In particular you had H=169.

When K=N, H=1 then the quantity is

\sigma \sqrt{N} ---(EQ3)

which is what is in your equation (2.4) so no problem there. (Note \sqrt{N} in numerator.) But if K=1, H=N then the quantity is

\sigma / \sqrt{N} ---(EQ4)

(Note \sqrt{N} in denominator.) The question is, what is the significance of this quantity and why can we scale by multiplying by K to give a per-K-hand version, which is clearly quite different to your equation (2.4).

So I guess it is this. With K=1 or 100 or 16900 or anything you like, from the statstics gathered (and using "classical method") the "best guess" for the "true underlying mean" is 0.0115K per K hands (which scales as you would expect for the mean of the sum of K samples) and that you could represent your uncertainty about what the "true underlying mean" is as a "standard deviation of the best guess of the "true underlying mean" per K hands" is the abovementioned quantity

K \sigma / \sqrt{N}

(which equals)

\sigma \sqrt{N} / H

The scaling factor K is what you would expect for a mean (or a variance) but not a standard deviation. But since it is actually a "standard deviation of ... mean" it makes sense.

Does this make sense?

Do you understand why the factor K bothered me?

Re: ?=1.61 on page 34. Question for authors.
 

Yes, this seems right. The key is that *all* the samples we're talking about are 16,900 hands -- since we're not changing the sample size, we can talk about the standard deviation of a sample of that size in whatever units are convenient. But I get why this isn't terribly clear.

jerrod

Re: The Mathematics of Poker
 

[ QUOTE ]
So is this book in Barnes and Noble/Borders yet?

[/ QUOTE ]

My wife saw it in our local Barnes and Noble, and both have it on their web sites.

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]
So is this book in Barnes and Noble/Borders yet?

[/ QUOTE ]

My wife saw it in our local Barnes and Noble, and both have it on their web sites.

[/ QUOTE ]

Must be dependent on location. Neither store near me (southwest CT) had it.

Re: The Mathematics of Poker
 

Starting on page 272, for NL hold'em, the authors describe an optimal strategy on the flop OOP and facing a preflop agressor.

What I understand is:

1)on the flop we check 100% of the time even against opponents who don't autobet.
2)as a consequence, betting on the flop is a dominated strategy so we never bet into our opponent.

Am I right?

Re: The Mathematics of Poker
 

[ QUOTE ]
Starting on page 272, for NL hold'em, the authors describe an optimal strategy on the flop OOP and facing a preflop agressor.

What I understand is:

1)on the flop we check 100% of the time even against opponents who don't autobet.
2)as a consequence, betting on the flop is a dominated strategy so we never bet into our opponent.

Am I right?

[/ QUOTE ]

The strategy we outline is not optimal! If we had an optimal strategy for NL holdem we sure wouldn't publish it in a book. Instead, it's a case study of applying the principles of optimal play to an actual game. So hopefully the strategy is at least sorta balanced and not that exploitable.

In the case we describe, it's a multiplayer scenario (as there is an "early" raiser) which further prevents there from being an "optimal" strategy.

In any event, supposing that we treat the hand from the flop on as a headsup game where the opponent has some fixed distribution, our contention is that an early raiser in NL playing against the blind should probably autobet as his strategy on the flop (as an equilibrium). If this is the case, then likewise the blind should autocheck to the bettor. This is true regardless of who the player is or what weaker strategy they will employ -- if autobetting and autochecking are the ~optimal strategies, then the raiser can't improve by checking on the flop.

But betting out is not necessarily dominated - in order for that to happen, checking instead of betting would have to have higher or equal expectation against every possible opponent strategy, which is not the case. For example, suppose the opponent played normally if you checked, but automatically folded unless he had the nuts if you bet. Obviously this is a stupid strategy, but betting out would be superior in this case. It's that against the ~optimal strategy, checking has a higher or equal expectation against the opponent's optimal strategy than betting -- hence we check all hands.

That make sense?

Jerrod

Re: The Mathematics of Poker
 

[ QUOTE ]
[ QUOTE ]


My wife saw it in our local Barnes and Noble, and both have it on their web sites.

[/ QUOTE ]

Must be dependent on location. Neither store near me (southwest CT) had it.

[/ QUOTE ]

Same here. In Austin I haven't found it at ANY bookstores and I frequent 4 or 5 (3 B&N's and a couple of local bookstores). Further, in Arkansas, I went to the local B&N and they didn't have it either.

Re: The Mathematics of Poker
 

[ QUOTE ]
This and other errata can be found at:
http://www.conjelco.com/mathofpoker/...ker-errata.pdf


[/ QUOTE ]

p. 41: Typo in heading of last column of first table. Instead of P(B), it should be P(not B).

Wow, I read slowly.

Re: The Mathematics of Poker
 

I saw the book at the Barnes & Noble in Cary, NC today.

Re: The Mathematics of Poker
 

Yes, that makes sense.

I missed the point that our opponent hands distribution is constant in the checkraise scenario from the book.