Week 3

Chapter 3: Using All the Information: Estimating Parameters and Bayes' Theorem

Ok, here it is the last chapter on the basics. Bayes' Theorem is quite advanced actually, but it is what we will need later for exploitative play. After just a few trials, samples regress to the mean so quickly that you can use this against your opponent quickly. Gathering tendencies of your opponents and being certain of them to a degree will make you play optimally against them.

Anyway, here are a few topics to discuss:
1) I hope you have read or heard about the Monty Hall problem. That is the holy grail to understanding Bayes' theorem. If you don't know about it, read about it, understand it!
2) I found a kind of interesting article on Bolt's supposed steroid use on 2+2 invoking Bayes' theorem. I thought it was interesting application (Scientific American article).

Anyway, if something is way off the mean, first start doubting the test that assigns that value, then the value itself. Do you think that could be a nice summary of Bayes' applicable to poker?

Oh, and week 3 assignments are here.

Week 2

Chapter 2: Predicting the Future: Variance and Sample Outcome

Hey peeps, very late, but finally here, a disussion on Chapter 2 of the book. The assignment for this week can be found here
Some discussion obviously I want to hear your opinion on it for my 1k post :)

Do you think the distribution of poker winrates follows the central limit theorem? After all, they are not really random.

How do you deal with having periods where you play on tilt affect your WR/variance, or do you think that is part of your poker distribution and that it all "evens out"?

Comment on Week 1

Hypergeometric Distribution:

Wiki page

Just a little comment on probability distributions in poker. This is the most important one when working out stuff in poker, because you can't just put cards in the deck, once they are gone or used, they're gone and all probabilities are worked out considering that.

A couple of weeks ago we had a post dealing with "flushdrawitis" and people being very scared that when there was a "flush draw" on the board. Is that MUBS. Well, we can work out the probability of getting a flush draw, basically getting a 4 suited in a 5 card draw.

f(4;52,13,5) = (13 choose 4) (39 choose 1) / (52 choose 5) = ~10.73%

Don't get distracted by which suit, it's not important here. So if you are up against one opponent (assume you have some random cards), he will have a flush draw about 11% of the time -> not scary, but agains 4 opponents... well, you be the judge.

Solutions for week 1 have been sent out. I'm working on week 2 assignments right now. Should be up tonight. You can still, at any time send in assignments for previous weeks. There is no "late" here.

Week 1

Chapter 1 - Decisions under Risk: Probability and Expectation

So, this is it. The first week of the study group. For this week I would like you to read Chapter 1 of the book. It is really a simple introduction to probabilities and in games of chance in general.

I have a couple of discussion points, please feel free to add to the discussion or keep the discussion going too, by replying to this post. Also, any questions you might have about Chapter 1 should be attached under "comments" in this post.

1. The authors say that right now the decision with highest expected value will be the best one. As in many things in life, making the most money now, is not necessarily the best for making the most money in the future. For example a company might increase their profits in the short term by dumping poison into some lake, but the negative PR that comes with that would greatly offset their short term gains. Is it not the same with poker? Don't you think just focusing on one hand is narrow-minded and will not yield you the highest expectation in the long run?
2. Do you think any game of chance with complete known information between two players is solvable?

I can't think of any more right now, so I'll leave it at that. Oh, a really nice website about probability and gambling is The wizard of odds. That guy goes deep in just about any gambling game and side bet there is.

Anyway, I warned you that this is not an easy book and there will be homework, so the first assignment is here. It is a PDF file, 20.5KB. Please send the completed homework to my e-mail address bellatrix78 at yahoo.com (replace the "at" with @). I don't care in which format you send it (Word, LaTeX or handwritten scanned), but please try to write out all formulas correctly with an editor (it gets really tedious looking at text formulae, e.g 10^5/2*3). I will go over any homework at any time, but if you want to keep up with the course, send it to me by Monday July 21st, which is when the next Chapter will be discussed and the next homework will be posted.

What is this page for?

Hello everybody!

I wanted to create this webpage as a sort of study group to go together through the book "Mathematics of Poker" by Bill Chen and Jerrod Ankenman. By creating this study group, not only will I feel pressured to keep up with reading this book, but also the discussion will help everybody tackle the more difficult subjects in this book.

I have a strong mathematical background. My main problem with this book is laziness, I have no problem grasping the technicalities on this subject. So what does a professor usually do, if he/she wants to go into a new subject field? That's right, teach a course on that field. So that's what this study group is about. While it is a lot of discussions, I think there also should be assignments on different chapters. I will also try to present the further stuff on each chapter on this page, so that everybody can join into this discussion.

If you are only reading this after the study group has already started, that's ok. Submit your assignments and get on with the studying. You can always catch up or start new. This is an interesting matter and math is timeless. Sure, computing power gets better, but the techniques behind solving a problem mostly remain the same.

So the most important thing you need for this course is the book "Mathematics of Poker". I've attached a link through my Amazon affiliate page. If you could buy it under this link (The Mathematics of Poker), I would be very thankful. :)