# Poker Video: Misc/Other by bellatrix (Micro/Small Stakes)

## Math Attacks: Episode One

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### Math Attacks: Episode One by bellatrix

Chapter 1 - The topic is meaning of +EV, or making decisions and probability related to them. The homework file for this week is here.

Bellatrix takes you on a journey through The Mathematics of Poker by Bill Chen and Jerrod Ankenman, breaking down each chapter one at at time. Warning - if you haven't figured it out by now, there will be math!

### Video Details

• Game:
• Stakes: Micro/Small Stakes
• 37 minutes long
• Posted over 2 years ago

## Comments for Math Attacks: Episode One

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138 posts
Joined 05/2010

If you want some help with that I'll be glad to share what I know.
But I basically learned sigma notation(that's that greek E looking thing) from khan academy

however I'll give a warning because I think he basically gives you the proof for the equation that bellatrix is asking for.

#### Slowjoe

1116 posts
Joined 01/2010

Ok, I just re-read Chapter One, and I'm pretty sure that NOWHERE in it, does it bother to explain that monstrousity in your bonus question! Nor do they bother defining/explaining the terms used in other similar math formulas in their own book! This REALLY frustrates me to no end!! So, I take it you have to have a degree in math to be in the know here, or else research all the arcane symbols as best you can, and try to make sense of them! WHY would they not include these definitions in their book? Like a glossary, perhaps? I mean, if you are going to TEACH something, then TEACH it! Grrr....!!

Edit: So, I can't possibly "prove" it, since I can't even decipher what it effing MEANS!

I think it's a fun extra credit question for the math geeks who already understand the probability/ev material. It's totally un-needed for the rest of the book, if that makes any difference.

<spoiler>The easiest way to prove it is to work from right to left using proof by induction.</spoiler>

#### huntse

1432 posts
Joined 11/2010

Ok, I just re-read Chapter One, and I'm pretty sure that NOWHERE in it, does it bother to explain that monstrousity in your bonus question! Nor do they bother defining/explaining the terms used in other similar math formulas in their own book! This REALLY frustrates me to no end!! So, I take it you have to have a degree in math to be in the know here, or else research all the arcane symbols as best you can, and try to make sense of them! WHY would they not include these definitions in their book? Like a glossary, perhaps? I mean, if you are going to TEACH something, then TEACH it! Grrr....!!

Edit: So, I can't possibly "prove" it, since I can't even decipher what it effing MEANS!

I sympathise with your frustration, but imagine if every poker book started by explaining what a deck of cards was, what suits and ranks were in it, what dealing meant etc. You'd never get anything advanced done if you tried to explain everything from the beginning every time.

In the same way, mathematicians often don't try to define everything in their work as this would take too long and distract from the main points they're trying to make. So they'll often only provide references and definitions for things which they consider to be outside of the mainstream canon of whatever field they're working in, and if you don't know what they're talking about, it's up to you to flesh out the basic definitions.

One good place to find a glossary of definitions of math terms is "Mathworld", so for example if you want to know what a combination is, you go to http://mathworld.wolfram.com/Combination.html and you'll find a lot of links you can traverse through to various related concepts.

#### huntse

1432 posts
Joined 11/2010

Gbucks is about hand vs range, but in the gbucks article he talks about the EV of the opponent's play using their actual hole cards versus our possible range given our actions, not our hand vs their range.

#### bellatrix

826 posts
Joined 12/2007

Gbucks is about hand vs range, but in the gbucks article he talks about the EV of the opponent's play using their actual hole cards versus our possible range given our actions, not our hand vs their range.

Well, yeah, just as the Fundamental Theorem of Poker goes both ways, so does Galfond's version.

#### micropoker

1 posts
Joined 02/2009

Thanks for the series, it looks like some very interesting topics. I haven't read the book yet, but I'm always welcome for some more in-depth mathematics.

Some constructive criticism early on: It seems like you didn't prepare too well for presenting the information. Following and understanding all the ideas would be easier for us if you prepared what you were going to say for each slide ahead of time and practiced it. It's difficult to follow your train of thought when you're correcting yourself and getting your words and numbers jumbled...feels like you improvised it.

With regard to the Gambler's Fallacy, would the assumption that ones - EV will be balanced out in successive all-in situations be more correct as the sample siZe of hands played approached infinity? And is the main reason it's a fallacy due to the fact that the gambler is in a very finite number of situations? I ask this because, looking at the p(k) vs (k) distribution graph on the probability slide, it would appear that the number of (k) values above and below the average weigh each other out. Looks like if you had so many '12' values you could expect, eventually, to have about as many '8' values and so on.

I appreciate all the work you put into it and I look forward to the next episodes!

#### bellatrix

826 posts
Joined 12/2007

Wow, joined over 2 years ago to get your first post here, I feel honored

Some constructive criticism early on: It seems like you didn't prepare too well for presenting the information. Following and understanding all the ideas would be easier for us if you prepared what you were going to say for each slide ahead of time and practiced it. It's difficult to follow your train of thought when you're correcting yourself and getting your words and numbers jumbled...feels like you improvised it.

That's always how I give my talks. The slides are well prepared, I know what I'm gonna say, but I don't have any notes written down, as to not sound robotic. I makes it sound much more natural as i get some ribs in I hadn't thought of. For example the "well, because we're not Russ Hamilton" was a thing that just came up on the fly.

I do acknowledge that I might have some extra difficulties "winging it" as I am not a natural english speaker, so I first have to organize my train of thought from german -> english. If I were to do dry runs and too many notes it would just take too much time for me and at some point I have to draw the line. Time is money, too, unfortunately.

With regard to the Gambler's Fallacy, would the assumption that ones - EV will be balanced out in successive all-in situations be more correct as the sample siZe of hands played approached infinity? And is the main reason it's a fallacy due to the fact that the gambler is in a very finite number of situations? I ask this because, looking at the p(k) vs (k) distribution graph on the probability slide, it would appear that the number of (k) values above and below the average weigh each other out. Looks like if you had so many '12' values you could expect, eventually, to have about as many '8' values and so on.

Yes, in the long run the samples even out. If you look out over the events as a whole over a significant sample you will see them even out. However, there is no predictability over what the next experiment (hand, even hand sample) is gonna bring. Even if you know all parameters and probabilities. The fact that you JUST had a winning or losing hand has no bearing on what the next hand is gonna bring. Global view versus "next hand" view.

However, when predicting parameters based on an observed sample, there is such thing as "regression to the mean" IF the first observed values are extreme in relation to the underlying true distribution: http://en.wikipedia.org/wiki/Regression_toward_the_mean

That is a bit counterintuitive, but it just states that the observed distribution is probably wrong and you will go back to the actual distribution quite quickly.

As an example, say you lose at a clip of 30bb/100 the first 1000 hands you ever play. That losing rate is extreme and yes, you may expect not to lose at that clip for the next 1000 hands. It will not even out the next 1000 hands, though ;-).

I appreciate all the work you put into it and I look forward to the next episodes!

Thanks and thanks again for the constructive criticism.

#### Ms.Bungle

827 posts
Joined 06/2008

If you want some help with that I'll be glad to share what I know.
But I basically learned sigma notation(that's that greek E looking thing) from khan academy

however I'll give a warning because I think he basically gives you the proof for the equation that bellatrix is asking for.

Hey, iseedeadmoney! Thanks a TON for the link!! Sadly, I think I will need to watch a FEW videos on this site, to bring me up to speed! Sigh...I'll get to it all eventually! But thanks, this could help out alot with the math course I'm taking too! Sweet!

#### Nssaev

194 posts
Joined 10/2010

This first episode has a lot of content in it. The presenting style is great, although I little more light could be thrown in probabilities and especially handing with combos etc ( there was only one example with any two suited), but otherwise great. I do understand your point that players should starting getting used to combos for EV calcs.

#### bellatrix

826 posts
Joined 12/2007

This first episode has a lot of content in it. The presenting style is great, although I little more light could be thrown in probabilities and especially handing with combos etc ( there was only one example with any two suited), but otherwise great. I do understand your point that players should starting getting used to combos for EV calcs.

Totally understand your point about it being packed. If you have a little bit of time, perhaps go through "Mathematics of NL Hold'em"? A lot of the concepts are explained much more in depth there.
The reason I did not present many more examples is that
a) it is beginning material, so a lot of it can be skimmed over. Sort of like in a live play video you suddenly won't explain your starting hand chart down to the greatest detail.
b) You have many more examples to work on in the homework
c) I have referred you to other material that can complement your learning on the subject. For example, you can get a lot of the concepts in Chapter 2 in threads13 video series "Tolerance".

Heh, now this post seems like I'm being lazy and the video is just a series of links towards stuff that explains in better, but my main point on the series in general is to get you in that *mindset* of seeing a hand analytically.

#### Nssaev

194 posts
Joined 10/2010

Yeah the homework is great, I started doing it, have to finish the EV part of it and will send it to you. I am really interested if I am right or wrong with my calculations.

#### SanderDeclerck

90 posts
Joined 09/2009

How do you use pokerstove on a mac?

#### bellatrix

826 posts
Joined 12/2007

How do you use pokerstove on a mac?

I use Wine/Winebottler. If you search around on 2p2 there should be a few threads about it. It took me forever to find the output pokerstove.txt file, but once I did, I could just create an alias to it. No more rebooting to Windows for me while responding to sa simple forum post.

#### Cangurino

3 posts
Joined 02/2011

The equation on the right holds for independent events as well; in this case, P(B|A) = P(B).

3 posts
Joined 02/2011