Hi everybody, as discussed in this thread, BryanC and I are starting this study group for "The Mathematics of Poker", by Bill Chen and Jerrod Ankenman. This material might be a little heavy, so we're going to try and start with what we hope is a little lighter load than in previous study groups of other books.

The week I reading is as follows:

Part I: Basics

Chapter 1: Decisions Under Risk (pages 13-21)
Chapter 2: Predicting The Future (pages 22-31)
Chapter 3: Using All The Information (pages 32-44)

We're planning to start the next week's reading on Sunday, January 20th.

We'd like to encourage anyone to pose their questions, share their thoughts, and have a good discussion of Part I of the book. Who'd like to start us off?

Just remember that 'The Basics' are not really basic and don't let that first chapter kill this group, chapter two is where the fun starts poker wise!

Chapter 2, or Part 2 (Chapter 4)? "The Basics" covers chapter 1-3, just want to clarify where the fun really kicks in.

My mistake .. the fun starts in part two

How does the study group work? Is the idea is to read the chapters by the deadline -- and then discuss?

Does anyone care to post a "heads-up" before we start reading? What to look for, what might be difficult, what is especially important? Maybe a quick set of bullet-points?

Or are we all reading from scratch, so to speak?

These threads should be in the poker theory forum. There'll be greater participation.
Then the three groups should be beginners, intermediate, and advance.
Beginners start at part 1. Intermediates start at part II. Most of part II
has been covered in other poker books.
The advance group can go straight to part III.

Well, I know Chen was critisized a few times on 2+2 for botching up chapter III when trying to get into Bayesian Inference. So with that ado, I'm really looking forward to see how it SHOULD have been written.

The study group will work whatever way we all use it. For me, I plan to post as I read, as questions come to mind.

I think a quick set of points might be a good idea; unfortunately I can't help yet, as it's my first time reading it, and I suspect it is for BryanC as well. If anyone else wants to post a list, please feel free.

I'm sure we'll get off to a bit of a slow start the first couple of days, as we've just posted a schedule and people are starting to read; I hope we'll start to gain momentum over the next few days.

Well, that's the kind of suggestion we probably could have used in the "interest" thread, before we started this one. If someone cares to post a link in that forum sending them over here, that would be great...I don't have time now as I'm heading out, but I'll post one later if no one else has.

I think that is a critical point as far as the lack of participation so far. I wasn't sure when the schedule was going to be set, so didn't have time to get into it. I think we have to give people a reasonable amount of time to read and go over the material before we can have meaningful contributions.
I'll be going over the material tonight and will probably have some points in.

Once a few days have passed and people are going over the material, the floodgates will open due to the nature of difficulty of the book.


THE HUN.

I'm still working on how to get quotes in properly.

THE HUN.

I would just like to chime in and say that I'm currently reading chapter one and I will post a general overview of the content shortly.

Heres a link to the interest thread:

http://forumserver.twoplustwo.com/sh...ad.php?t=93899

Would be cool if people could keep the more general stuff on there and save this thread for discussing the book and its content.

Or you could always PM me or bobo if you prefer.

deleted

I've got your back.

Treat this like law school. You should have already read the complete part I of this book. Then ask questions.

Alright, let's start this off. In looking at this group and what my goals are at least, I want to be able to use the math in an intuitive sense at the tables. That is, when you look at some of the formulas in the books, they get fairly hairy, and I don't think anyone really has the time in the 30 seconds time limit to make a move to do calculations with exponentials and such.

The first couple of chapters give a nice primer in probability/statistics. The concepts of mean, variance, and expectation are fairly straightforward. Bayes Theory is what I would like to discuss here.

Over and over it states the usefullness of Bayes Theory in making decisions at the table and helping out with opponent hand distributions. These two tools (Bayes Theory and figuring out hand distributions) are key to me because that is what I need the most help with. I typically find myself lost in hands, and it would help to have this kind of a tool, at the very least, give me some form of probabilistic roadmap.

I would like to start a discussion on Bayes Theory at the beginning. That is, it's derivation. On page, 36, it goes over the derivation of the formula. For me, if I intuitively understand the formula, it would make the concept that mufch more easier to apply.

Can someon intuitively explain, why this formula makes sense?

I went over the derivation, and even through the steps, did not understand how the numerator nor the denominator was derived. If someone could fill in those steps that would be great.

THE HUN.

You mean Eq. 3.2?

Nominator:
P(A and B) <=> P(B and A), then you get
P(B and A) = P(A|B) * P(B)

Denominator:
It is P(A) = P(A|B)*P(B) + P(A|~B)*P(~B).
It is a binary decision if B occurs or not, and the probability
of A is the sum of the probability of both possibilities.

Hence, Eq. 3.2.

I hope it's right, but i can't give you an intuitive description.

Actually, it is more intuitive to me, now that I see it.

With the numerator: My thinking was landlocked into p(A and B), not intuitively realizing, that it is the same as p(B and A), so that now makes complete sense.

With the denominator: It now makes sense thinking about it in a binary way from the perspective of its relation to B happening.

Thank you for your help, this make a lot more sense to me.

The next question is on Bayes Theory and its relation to distributions, but that will be a little more detailed and will come later as I am at work now.

Take care,

THE HUN.

I was skipping ahead, so I'll wait for my Bayes Theory question for distributions for the next section.

THE HUN.

I wrote a post about Bayes theorum and handreading a while back.

It explains it the way I intuitively understand it.

OK so I finally got time to make a start on this today and got through part1 without too much difficulty. I found the probability equations particularly interesting, I have to admit that this stuff was mostly new to me .

When I first started learning the game I kinda learned these things by rote, like the flush draw example for instance I knew that the probability of flopping a flush draw is around about 11% and the probability of flopping a made flush is <1% but I had never really taken the time to do the maths for myself I just kinda memorized these figures without really questioning them atall.

So now that I have these equations its got me thinking that I'd like to take the time to apply them to some other types of hands to gain a greater understanding of the maths behind those as well. For example I know you will flop a set approx. 10% of the time when you hold a pocket pair and that any non paired starting hand will flop a pair around 30% of the time etc. etc. but Ive never actually done the maths for myself. The problem I'm having though is that I don't fully understand which equations to apply to which particular types of hands. In particular which equation would I apply to figure out the probability of flopping a set when I have a pocket pair? which one to use for working out the probability of flopping a pair, a gutshot when I have connectors, an open ender etc

So basically It would be cool if somebody could help me to match up these different types of hands to the correct equations. I'm just a little bit confused with regards the definitions of mutually exclusive events, independent events and dependent events as they relate to different types of poker hands on the flop.

Thanks for the link, enjoyed the read

There is no magic formula that says you have to apply this equation or that other one to a particular situation. But there's a few things that are always true, and you can use that for a few tricks.

Let's take an example: you have 33 in the big blind. It is folded to the small blind, who limps. For the sake of the example, you check. What is the chance of you hitting another 3 on the flop? You could pretend that the flop cards are turned over one by one, and ask: what is the probability of the first flop card being a 3? Well, you know your 2 hole cards, 50 cards are unknown. 2 of them are 3s, so the probability is 2 in 50, or 4%. A quick'n'dirty argument would extend that to 3 cards and say: the chance of hitting a set is roughly 12%.

You would be making a mistake there, though not a big one: the two 3s hitting the 3 flop cards are not statistically independent events. For example, the 3 being the first flop card, and the 3 being the second flop card are mutually exclusive, they cannot happen on the same flop (and if they do, someone's got some explaining to do).

Furthermore, the chance of any 3 hitting on the second flop card depends on whether the first flop card was a 3 or not. If the first card missed, there's 2 of 49 unknown cards that improve your hand, but if it hit, there's only one 3 left in the deck. So the probability of hitting on card 2 depends on card 1, these cards are statistically dependent.

To find out what the chance of any 3 hitting on the flop is, you could write down all possible ways the three cards can come with at least one 3. Ignoring suits, there's 6 of them: miss-miss-hit, miss-hit-miss, hit-miss-miss, miss-hit-hit, hit-miss-hit, and hit-hit-miss. To calculate the overall chance of hitting at least one 3, you could calculate the probability of each outcome, and then add them up. This would be correct, but cumbersome. Cumbersome, but not wrong.

Fortunately, there is a shortcut. Just as correct, but easier: you either hit at least one 3, or you don't. So the probability of hitting at least once plus the probability of missing on all three flop cards must be 100%. So p(yippie)=1-p(duh). Turns out p(duh) is vastly easier to calculate, because there is only one outcome: miss-miss-miss. So:

p(duh)=48/50 * 47/49 * 46/48 = 0.8824

p(yippie) = 1 - p(duh) = 11.75%, or 7.5-to-1.

See, there's no right way and no wrong way. But there is an easy way and a complicated way.

I had never thought about applying Bayes theorem to the question "how fast does a particular statistic converge to a meaningful value?". Are N hands enough to call someone loose? When this comes up in hand discussions, inevitably at some point someone says "N hands are not enough for a meaningful read anyway", with N, of course, arbitrarily high. You just went ahead and quantified the problem. Great post!

Excellent post, but I don't know if it answers how to intuitively understand it. Here's my shot at an intuitive understanding...

A small percentage of a large population can overwhelm a large percentage of a small population.

That is, imagine that having Gene A ensures (100%) that you will die a horrible bloody death. If you don't have Gene A, you have only a 1% chance of dying this death. Sounds like the vast majority of Americans who die this way have Gene A, right? Wrong - I forgot to tell you that only 1% of Americans have Gene A.

Of the 300 million non-A holders 1% (or 3 million) will die
Of the 3 million A holders 100% (or 3 million) will die.
Of the 6 million total bloody deaths, 3 million, or half, will be attributable to Gene A. This is because, in this case, 100% of a little = 1% of a whole lot.

(For those nits out there, I understand that this isn't exactly right as non-A would be 1% of 297m, but close enough for an intuitive understanding)

Forget the formula for a minute, and think about the medical example (p. 36). You see a positive test. What does it mean? Either the patient has the condition and the test caught it, or he doesn't and there's a false positive.

5% of the population has the condition, times 80% efficacy of the test in catching positives, is 4% with the condition. 95% of the population is healthy, times 10% false positives with the test is 9.5% without the condition.

So 13.5% of the time you test, you get a positive. Less than a third of those are true positives.

So it is not hard to see that the intrinsic statistics of the test are not the sole consideration. The main point is that the statistical distribution for whatever problem you're considering is overlayed on top of the population distribution.

This kind of logic is very important, I think, for large tournaments in the early going. How many times have you seen all-in play in the very first hand of a tourney? It should be intuitively clear that there is a population of players so impatient that they want to see a major change of fortune one way or the other within the first minute of play. If 10% of players will make a major commitment with 20% of their hands, that's comparable to 90% of players reraising the top 2% of their holdings. These maniacs fundamentally change the game balance, so that hands like JJ or even AQ come into consideration for a gamble of 100 times the blinds. In all stages of the game, it seems fairly clear that online low-stakes tourney players overvalue A-rag. How many times have you raised from early position and been called or even reraised from with A5o? This population of players raises the value of your AJ, for example. There is a population of players overly afraid of the bubble, and another class of players blissfully unaware. And so on. This goes to the heart of exploitative play, not only providing a conceptual way to think about it, but justifying action given little or no information about a specific opponent. Having that permission to act is quite important--before weaker players get weeded out.

ygunstah