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.