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

Time Link to 00:11:58

You meant we multiply it by 2, since order is Not important; if it was we wouldn't

Time Link to 00:14:46

Could you elaborate what the number from the formula represent? (The probability of getting dealt 2 suited cards one) I mean id do the 12/51 for that, but with this one,
the 52 choose 2 is all the ways we get 2 cards
but how you get 4*(13 choose 2) ?

Could you elaborate what the number from the formula represent? (The probability of getting dealt 2 suited cards one) I mean id do the 12/51 for that, but with this one,
the 52 choose 2 is all the ways we get 2 cards
but how you get 4*(13 choose 2) ?

4 because of 4 suits
13 choose 2. The number of combinations within 13 cards (all of one suit).
Now we have to divide by the number of all probabilities of having 2 cards (52 choose 2).

I agree that for just one suited cards it seems like much easier to write 12/51, but it might be easier to get youself used to the combinatorics. Especially, when you start counting combinations later to put people on a range (e.g. is it more likely that he has a flush draw or that he has a TP+ on the turn...).

Except for the math bits, i really enjoyed this video!

Time Link to 00:09:08

why is "A given B" the same as "A without B"?

I just started reading this book a couple weeks ago so excited that your doing this series!!! Thanks for doing it

why is "A given B" the same as "A without B"?

A more clear definition of A|B is the probability of A occurring given that B occurred


edit: mixed them up

I personally was thrilled to watch this series and i have to admit after watching it i really liked it alot, cant wait to see the next episode about the variance

@Bellatrix: You talked at the end of the video about homework, i noticed you talked also about it in your preview about it. What is your idea with that?

A more clear definition of A|B is the probability of A occurring given that B occurred


edit: mixed them up

yeah I understand that, I just don't understand why "A without B" is the same thing.

Time Link to 00:23:45

This is not what pot odds means! Your pot odds here are 5.00 to 1 (20/100) and your chances of hitting are 4.75:1 (8/38). Pot odds is the price you're getting laid, not the chance of winning the pot.

Yeah, in the future, "A | B" means "A given B", any other explanation is confusing, I agree.

I personally was thrilled to watch this series and i have to admit after watching it i really liked it alot, cant wait to see the next episode about the variance

@Bellatrix: You talked at the end of the video about homework, i noticed you talked also about it in your preview about it. What is your idea with that?

You can download the homework posted with this video, work through it and send it to my e-mail at DC (bellatrix@deucescracked.com). If you send something in, you get the solutions for you to compare, no grading. Please send in LaTeX files or scanned pages, no text formulas.

The homework will help you practice the stuff or at least internalize the concepts better than just listening to a video. It is 100% voluntary

Not really what i was expecting tbh. I literally just got Mathematics of Poker today in the post and read the first chapter followed by this video. I think without having read the first chapter in the book i would be lost and have come away with very little from this video. I dont expect you to follow the book exactly , however i thought you could of done a bit better at explaining some of it. I got the feeling 'probability' to you is pretty simple and you just briefly touched on it and breezed through it all rather quickly. I liked your explanation of dependent and independent events using the idea of a bowl of marbles. It was this different approach and actually hearing you discuss it that helped add to my understanding of what the book told me.

I looked at your homework , question 1 looks good.
Question 2 a) looks thought provoking - i like it
2 b) ive never played roulette , wouldnt know where to start.
Question 3 ' A team is favored to win a game (moneyline) at -250 (-180, -110, +300)' i have no idea what that means. I dont know what 'no juice' means either.

Not every poker player is from Las Vegas and a gambler in all forms.

Hope this post helps

I don't quite understand, you wouldn't have understood the video without reading the first chapter, but would like me to stay close to the book more? Like when I talked about G-bucks and Sklansky-bucks I veered off the book quite a lot. Do you feel I should just stick to the book?

For the homework terminology, google is your friend (e.g. rules of roulette, payout structures etc.). Note that these terms get thrown away all the time at the poker table (in live games), so you should probably familiarize yourself with gambling terms, but as always, nothing is absolutely necessary to win at poker, just every little bit helps.

Yes, calculating probabilities is just a first step and should come as second nature to you. If you feel lost in the first chapter, I would probably recommend "Mathematics of NL Hold'em" by Wilt on Tilt. He goes through that stuff much more slowly and in depth, because if I explain every step, the series would be just too long. I understand the best with examples, which is why I tried to sprinkle examples all throughout the video. We will come back to probability over and over again, so just keep at it and practice makes perfect.

Bellatrix,

PLEASE don't drop the additions like G-bucks and Sklansky bucks. The fact that some may struggle with them doesn't work for me: the fact is, under that argument, you simply wouldn't do the course.

It's unreasonable to expect Bella to answer every single question that comes up. If that were the case, she is likely to find this series equivalent to a fulltime job, and unlikely to complete it. I would suggest that people step forward act as teaching assistants. In fact, we should probably start a SecretHQ group.

I won't start it, since I don't have questions yet, but I'll join and assist if someone else does.

But it might be worthwhile if Bella could do a Tooltime video of installing Auctex and producing a simple Latex file. The average DC member probably won't have heard about Latex.

I won't start it, since I don't have questions yet, but I'll join and assist if someone else does.

Scratch that. I had a question, so the SecretHQ group is at http://www.deucescracked.com/forums/28-Secret-HQ/topics/365481-Maths-Attacks-Study-Group

Don't know what to say about someone that doesn't feel comfortable talking probabilities. Sort of shocking, but hey we all have our strengths and weaknesses. Sounds like the use of EXAMPLES was a big winner and deviating from the book or not was less of the issue.

Statistics is pretty simple once you're able to relate the concepts to something meaningful to you. I would definitely start youtubing some statistics stuff or googling terminology if I didn't have a grasp of basic stuff already... I can't fathom playing poker seriously without having this understanding. I'm sure there's even full courses online available for free about statistics.

For question 2b... how many green spaces are on the wheel? I've heard this isn't always standard

For question 2b... how many green spaces are on the wheel? I've heard this isn't always standard

European roulette has one zero, American roulette has two (zero and double zero).

You should probably assume American.

I'll send you solutions for both

Time Link to 00:22:42

It should be 8/44 because we can exclude two cards which the villain holds

It should be 8/44 because we can exclude two cards which the villain holds

Argh, I don't remember exactly what I said now.

I think at some point I said "you knew" he had an overpair. In that case - sure. But if you just "know" that hitting your draw will make you win the pot, then you can't do that, since one of the 8 cards could well be in opponent's hand.

Bellatrix.. I have a question about the example of pot odds where we had an open ended str8 draw.

We are on the turn obviously,(46 cards left unseen) Opponent goes all in for $20 into an all ready $100 pot. Wouldn't this actually make out pot odds 6 to 1 ? 120 into 20 = 6/1

Then you go on to say something about 38/8. This is where I'm confused.

there are 8 cards in the deck that can make our str8 and there are 46 cards unseen. This would make it 46/8 or 5.75% to 1. Is this not correct? So where does the 38/8 come into play. We cannot subtract our 8 outs from the 46 to figure are correct chances of hitting our draw can we?

So if my calculations are correct. We are being offered 6 to 1 pot odds. Our odds of hitting our str8 are 5.75 to 1. So this makes a call profitable. Correct ?

Yes, as Soepgroente pointed out, I didn't word myself correctly (even if he was wrong on his odds ;-) )

We are getting 6 to 1 odds. 120 to 20. Those are the pot odds.
For the call to be profitable we need better than 38 to 8 or 4.75 to 1 odds (not 5.75).

If the pot before was 80$ instead of 100$ in our example, the pot odds would be 5:1 and a call would still be profitable. The expected value of that call is still positive, even though it's much smaller than in the example (~87cents).

Bellatrix.. I have a question about the example of pot odds where we had an open ended str8 draw.

We are on the turn obviously,(46 cards left unseen) Opponent goes all in for $20 into an all ready $100 pot. Wouldn't this actually make out pot odds 6 to 1 ? 120 into 20 = 6/1

Then you go on to say something about 38/8. This is where I'm confused.

there are 8 cards in the deck that can make our str8 and there are 46 cards unseen. This would make it 46/8 or 5.75% to 1. Is this not correct? So where does the 38/8 come into play. We cannot subtract our 8 outs from the 46 to figure are correct chances of hitting our draw can we?

So if my calculations are correct. We are being offered 6 to 1 pot odds. Our odds of hitting our str8 are 5.75 to 1. So this makes a call profitable. Correct ?

The expression of odds is dealt with in first couple of episodes of WiltOnTilt's Maths of No Limit Holdem series. It's clear that you aren't understanding odds, and I'd strongly recommend watching at least the early episodes of that series as background for this. It's also the case that the whole of that series is some of the best video on the site, but not all of it is directly helpful for this video.

Your question is about a notation difference. "38 losses to 8 wins" or "38 to 8" expresses the same idea as 8/46. I'm sure you simply made a typo with "5.75% to 1", but when expressing odds, you set losses against wins, so 38/8 calculates the number of losses if we want to express them "x:1".

You are correct about the 6:1 pot odds, but our odds of hitting the straight are (38/8):1 = 4.75:1.

Funny you mention the series of Mathematics of NLHE by WoT. This is a great series and I was just watching it when this same situation came up.

I now understand that when we have 8/46, we must subtract our 8 outs from the 46 remaining cards in order to make the correct ratio. Which is 8/38 or 4.75/1

Thanks to Bella and SlowJoe for your very fast responses.

Also thanks to everyone at Deuces Cracked. This is an amazing site and because of it I pretty much have a lock on every game in my home town and some casinos near by as well.

Keep the good stuff coming. Ill be a member for life!

4 because of 4 suits
13 choose 2. The number of combinations within 13 cards (all of one suit).
Now we have to divide by the number of all probabilities of having 2 cards (52 choose 2).

I agree that for just one suited cards it seems like much easier to write 12/51, but it might be easier to get youself used to the combinatorics. Especially, when you start counting combinations later to put people on a range (e.g. is it more likely that he has a flush draw or that he has a TP+ on the turn...).

I was thinking about other ways to compute this probability on my way to work today. 12 / 51 is obviously the simplest way. The 4 * (13 choose 2) / (52 choose 2) is straight by definition of the probability. How about the following (admittedly useless) way:
P(not a pocket pair) * 0.25 = (16/17) * (1/4) = 4/17, as expected.
The 0.25 is the ratio of suited to all the combos of 2 card (e.g. KQ: 4 KQs of 16 KQ total). P(not a pocket pair) = 1 - P(pocket pair) = 1 - 3/51 = 1 - 1/17 = 16/17. Alternatively, P(pocket pair) = 13 * (4 choose 2) / (52 choose 2) = 1/17. I find it interesting that for every pair that contains say 2d, there is 16 non-pair combos with 2d. Just to visualize: we could map
2d2h to the set of remaining 12 harts + 4 diamonds;
2d2c to the set of remaining 12 clubs + 4 other diamonds;
2d2s to the set of remaining 12 spades + 4 remaining diamonds

I was thinking about other ways to compute this probability on my way to work today. 12 / 51 is obviously the simplest way. The 4 * (13 choose 2) / (52 choose 2) is straight by definition of the probability. How about the following (admittedly useless) way:
P(not a pocket pair) * 0.25 = (16/17) * (1/4) = 4/17, as expected.
The 0.25 is the ratio of suited to all the combos of 2 card (e.g. KQ: 4 KQs of 16 KQ total). P(not a pocket pair) = 1 - P(pocket pair) = 1 - 3/51 = 1 - 1/17 = 16/17. Alternatively, P(pocket pair) = 13 * (4 choose 2) / (52 choose 2) = 1/17. I find it interesting that for every pair that contains say 2d, there is 16 non-pair combos with 2d. Just to visualize: we could map
2d2h to the set of remaining 12 harts + 4 diamonds;
2d2c to the set of remaining 12 clubs + 4 other diamonds;
2d2s to the set of remaining 12 spades + 4 remaining diamonds

Wow, nice. Took me a while to understand, but now that I do, I like it!
Just be careful not to crash while thinking these things if you drive yourself to work ;-)

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!

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
www.khanacademy.org

however I'll give a warning because I think he basically gives you the proof for the equation that bellatrix is asking for.
http://www.khanacademy.org./video/sequences-and-series--part-1?playlist=Calculus

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>

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.

Time Link to 00:32:01

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.

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.

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!

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.

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
www.khanacademy.org

however I'll give a warning because I think he basically gives you the proof for the equation that bellatrix is asking for.
http://www.khanacademy.org./video/sequences-and-series--part-1?playlist=Calculus

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!

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.

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.

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.

Time Link to 00:35:49

How do you use pokerstove on a mac?

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.

Time Link to 00:11:33

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

Time Link to 00:18:39

So the expected value is not a characteristic of the probability distribution but one of the random variable you implicitly define.

Time Link to 00:17:13

Let A be the event that there are two spades on the flop, B the event that a given player holds two spades. You calculated the probability P(A|B). However, in flushdrawitis we are interested in the opposite conditional probability P(B|A), namely given that the board is two-tone, what is the probability my opponents holds a flush draw.

Let A be the event that there are two spades on the flop, B the event that a given player holds two spades. You calculated the probability P(A|B). However, in flushdrawitis we are interested in the opposite conditional probability P(B|A), namely given that the board is two-tone, what is the probability my opponents holds a flush draw.

Yeah, you are correct. Somehow I went through this backwards.

Should be 11 choose 2 / 47 choose 2 if we don't have one of the suits in our hand (or 10 choose 2 / 47 choose 2 if we do)

Bad example to make that "flushdrawitis" point. But a good example on how to calculate conditional probablities, sigh.

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

That's right!
Didn't feel like I should mention it, but you are certainly correct

So the expected value is not a characteristic of the probability distribution but one of the random variable you implicitly define.

The probability distribution acts as a sort of weighting function. It still needs to be multiplied by each possible outcome.

is this series really important for poker player, because I have some problems with understanding this formulas...

is this series really important for poker player, because I have some problems with understanding this formulas...

I feel that I can't answer the question, because I am biased.
Is this series absolutely necessary to crush the games? Of course not.
But I do feel it will give you some valuable insights on how to approach the game.

Time Link to 00:01:49

Hi,
We could say that :

Probality that one event happens = Number of favorable events / All possible events

Example :
Probabilty to have 2 or 6 by launching a die is : 2 (2 favorable numbers among 6) / 6 (the numbers of the dice) = 2/6
Regards

Time Link to 00:19:13

Hi,
I dont know if already done, we have to mention that the sum of p_i is 1 = 100 %
Regards

Time Link to 00:31:24

Hi,
It will be useful to explain thru example the Slansky bucks concept
Regards

Hi,
It will be useful to explain thru example the Slansky bucks concept
Regards

I thought I did that later in the episode?

6 people in our study group... Six different answers for the Lotto question in the homework.

Go TEAM!

6 people in our study group... Six different answers for the Lotto question in the homework.

Go TEAM!

I had several answers in the beginning, too. Just send me an e-mail (bellatrix@deucescracked.com) with one of your solutions and I'll be sure to get you mine. Good luck, mates!

Cheers!

We video-conferenced and winnowed our answers down to one or two, so shouldn't be too bad.



PS on a highly unrelated note my apartment building faces north so I can see Bellatrix when I head out to work at midnight. Except I'm in the Southern Hemisphere and Orion appears upside down to me! So she's on the bottom-left, rather than the top-right.

I can see Bellatrix when I head out to work at midnight. So she's on the bottom-left, rather than the top-right.

FYP. Makes it more cryptic. ;-)