# Poker Video: No Limit Hold'Em by sthief09 (Micro/Small Stakes)

## Applied Math: Episode Three

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### Applied Math: Episode Three by sthief09

This episode contains several parts: answer for episode 2's quiz, a very brief lesson basic poker combinatorics, Bayesian range construction using weights, and concludes with an OOC lesson in Goal Seek and a quiz for episode 3. Episode 3 finally contains a NLHE example, which will be expanded upon in episode 4.

You know the numbers behind poker are important, but don't know where to start. Or maybe you know the basics of poker math but aren't able to apply them to improve your game. If either of these describes you, you're in the right place. For this series, sthief09 will teach you the basics and help you transform them into a way to test theories, try out alternative lines, and get a better understanding of the numbers that are the driving force behind poker.

### Video Details

• Game:
• Stakes: Micro/Small Stakes
• 90 minutes long
• Posted about 2 years ago

## Comments for Applied Math: Episode Three

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#### AlephOne

9 posts
Joined 02/2009

Small error here - there are only 2 ATs since two combos are eliminated by the black Aces.

#### sthief09

2342 posts
Joined 07/2007

Small error here - there are only 2 ATs since two combos are eliminated by the black Aces.

d'oh. I spend so much time staring at the #s that I wind up making the silly mistakes

#### soleztis

DC Dalai Lama
1019 posts
Joined 09/2010

I can't reiterate enough how great this format is with the downloadable workbooks and work along structure of the video. I haven't been this into poker math maybe ever.

#### soleztis

DC Dalai Lama
1019 posts
Joined 09/2010

This might be nit picking but instead of paste special formula twice we can just drag the corner of the cell and it will do the same thing. Just a little bit faster and can save some time if you are doing a lot of these

#### soleztis

DC Dalai Lama
1019 posts
Joined 09/2010

As I fill out my tables tables I am imagining taking these type of discussions to forums or study groups to analyze hands and the obvious feedback being "Too much guessing" or "How do you know?" What is the response to that?

#### cpau33

2340 posts
Joined 11/2009

As I fill out my tables tables I am imagining taking these type of discussions to forums or study groups to analyze hands and the obvious feedback being "Too much guessing" or "How do you know?" What is the response to that?

yeah I agree.

#### sthief09

2342 posts
Joined 07/2007

As I fill out my tables tables I am imagining taking these type of discussions to forums or study groups to analyze hands and the obvious feedback being "Too much guessing" or "How do you know?" What is the response to that?

I've had this discussion before. Everything we do in poker is based around assumptions of our opponent's ranges. Not only that, but we make assumptions of what the best play is based on what are assumptions of our opponents' ranges are. At least the math takes care of that first assumption, what the best play is, given villain's range. We make assumptions every single hand we play (ie I think this guy fastplays his set almost always, or I think this guy c-bet bluffs almost his entire range). We may not know unequivocally what the best play is by crunching the numbers, but at least we knock out some of the guesswork.

Beyond that, the math lets us play around with opponent ranges and get an idea of what types of plays are profitable against what types of opponents. Through episode 5, we'll create sort of a dashboard that enables us to play around with these assumptions so we know just how loose, tight, passive, or aggressive villain has to be for certain plays to be profitable.

You could even try crowdsourcing on forums. You can ask questions like "how often does villain 3-bet sets when we c/r on this flop" and through the 'wisdom of the crowds' you can get a more accurate estimation of a range. From there you can share the results. Sounds like a nifty idea to me actually.

#### soleztis

DC Dalai Lama
1019 posts
Joined 09/2010

Thanks for that answer. I am not at all questioning the method, just making sure I could articulate a proper response when the question is inevitably brought up.

I love the crowdsourcing idea. While we can run filters in our own HEM, this data may be limited or cover very specific games. Polling forums could give us an idea of the differences in play at various stakes, or even enlighten us to how our own HEM stats might not be a large enough sample size, and due to variance are experience very different responses to certain bets.

2 posts
Joined 04/2010

#### Ass Get to Jigglin

4273 posts
Joined 10/2010

Josh- I think I'm still a bit unclear on why our equity would be 75% instead of 80% in this hand. On the Wikipedia page, they say:

"Put in terms of BayesÂ´ theorem, the probability of a student being a girl is 40/100, the probability that any given girl will wear trousers is 1/2. The product of these two is 20/100, but we know the student is wearing trousers, so one deducts the 20 students not wearing trousers"

So what would be the equivalent of this 20 student deduction in this poker example? What's the difference between "Eff. Equity" and "New Equity," and why are they different?

I've only gotten as far as the timestamp so far, so if this is explained/illustrated later in the video, I apologize.

#### Ass Get to Jigglin

4273 posts
Joined 10/2010

Josh- I think I'm still a bit unclear on why our equity would be 75% instead of 80% in this hand. On the Wikipedia page, they say:

"Put in terms of BayesÂ´ theorem, the probability of a student being a girl is 40/100, the probability that any given girl will wear trousers is 1/2. The product of these two is 20/100, but we know the student is wearing trousers, so one deducts the 20 students not wearing trousers"

So what would be the equivalent of this 20 student deduction in this poker example? What's the difference between "Eff. Equity" and "New Equity," and why are they different?

I've only gotten as far as the timestamp so far, so if this is explained/illustrated later in the video, I apologize.

Any word on this?

138 posts
Joined 05/2010

Any word on this?

I just started watching this now and stopped to check this thread for this exact reason.
What I think is going on is that we are asking "what are the chances that villain won the pot". So we are observing that someone won a pot and we don't know who is who but we can figure out the probability based on our knowledge of the probabilities of both ranges.
It isn't exactly explained well in the video, but we are neither the hero or the villain but an observer. The question should be "what are the chances that the person that won the pot is the villain?"

does that make sense?
It's a little more clear in the book Mathematics of Poker with the medical false positive problem.

#### Ass Get to Jigglin

4273 posts
Joined 10/2010

I just started watching this now and stopped to check this thread for this exact reason.
What I think is going on is that we are asking "what are the chances that villain won the pot". So we are observing that someone won a pot and we don't know who is who but we can figure out the probability based on our knowledge of the probabilities of both ranges.
It isn't exactly explained well in the video, but we are neither the hero or the villain but an observer. The question should be "what are the chances that the person that won the pot is the villain?"

does that make sense?
It's a little more clear in the book Mathematics of Poker with the medical false positive problem.

yeah, that's starting to make a bit more sense I think. But if the villain has 20% equity (50% against 40% of hero's range), then how is "the chance that the person that won the pot is the villain" equal to 25%? In the trousers example, not every student has to be wearing trousers, but in this example, someone has to win the pot. I just feel like I'm missing something crucial.

#### sthief09

2342 posts
Joined 07/2007

yeah, that's starting to make a bit more sense I think. But if the villain has 20% equity (50% against 40% of hero's range), then how is "the chance that the person that won the pot is the villain" equal to 25%? In the trousers example, not every student has to be wearing trousers, but in this example, someone has to win the pot. I just feel like I'm missing something crucial.

yeah, that's starting to make a bit more sense I think. But if the villain has 20% equity (50% against 40% of hero's range), then how is "the chance that the person that won the pot is the villain" equal to 25%? In the trousers example, not every student has to be wearing trousers, but in this example, someone has to win the pot. I just feel like I'm missing something crucial.

I think this is my fault. The example is not EXACTLY the same in wiki vs. poker and that's why it's causing confusion. Let's change around the wiki example to have it make more sense:

Instead of the question being "GIVEN that a student is wearing trousers, what are the chances it's a girl" let's change it to "what % of ALL students wear skirts?"

I find the easiest way to attack a problem like this is to put it into numbers. To rehash the problem, 60% of the overall students are boys. All boys wear trousers. Half the girls wear trousers.

Say there are 100 students. 60 boys and 40 girls. 0 boys wear skirts and 20 girls wear skirts. 20% of the students wear skirts.

In poker terms, let's say:
- It's the flop
- We bet and villain shoves
- We have AK on Kh7s6s2d
- We put villain either on a set or a combo draw

60% of the time villain has a set (we don't exactly have 0% equity but it's close to it)
40% of the time villain has a combo draw
We estimate we have 50% against the combo draw

So if we run this example 100 times:
Villain will have a set 60 times (we win 0)
Villain will have a combo draw 40 times (we win 20)

So we win 20 out of 100 = 20% equity

So it's just that the 2 problems were asking slightly different questions.

Sorry for the delay. The first time I saw this I tried to answer this, I did it on paper and got flustered and failed to revisit it.

#### musashi

2 posts
Joined 06/2010

Hi,

Is there any other way to get all the spreadsheet? I don't know why, but I don't have access to the server ...

#### Ass Get to Jigglin

4273 posts
Joined 10/2010

I think this is my fault. The example is not EXACTLY the same in wiki vs. poker and that's why it's causing confusion. Let's change around the wiki example to have it make more sense:

Instead of the question being "GIVEN that a student is wearing trousers, what are the chances it's a girl" let's change it to "what % of ALL students wear skirts?"

I find the easiest way to attack a problem like this is to put it into numbers. To rehash the problem, 60% of the overall students are boys. All boys wear trousers. Half the girls wear trousers.

Say there are 100 students. 60 boys and 40 girls. 0 boys wear skirts and 20 girls wear skirts. 20% of the students wear skirts.

In poker terms, let's say:
- It's the flop
- We bet and villain shoves
- We have AK on Kh7s6s2d
- We put villain either on a set or a combo draw

60% of the time villain has a set (we don't exactly have 0% equity but it's close to it)
40% of the time villain has a combo draw
We estimate we have 50% against the combo draw

So if we run this example 100 times:
Villain will have a set 60 times (we win 0)
Villain will have a combo draw 40 times (we win 20)

So we win 20 out of 100 = 20% equity

So it's just that the 2 problems were asking slightly different questions.

Sorry for the delay. The first time I saw this I tried to answer this, I did it on paper and got flustered and failed to revisit it.

Didn't see this until now, thanks for the reply. Though I still don't get how you arrived at 20% equity above, but in the video you say it's 25% equity. That is, I understand how you arrived at 20% equity above and how you figured out that 20% of the girls wear skirts, but I don't understand why in the video our equity comes out to 25%.

#### sthief09

2342 posts
Joined 07/2007

Didn't see this until now, thanks for the reply. Though I still don't get how you arrived at 20% equity above, but in the video you say it's 25% equity. That is, I understand how you arrived at 20% equity above and how you figured out that 20% of the girls wear skirts, but I don't understand why in the video our equity comes out to 25%.

I tried re-watching a few minutes before and after but I'm not quite sure either. Sometimes it's hard to remember exactly what I was thinking/doing and why in these math-based vids. It may not be right but maybe I just don't remember what I was showing. I know the text you quoted is correct though and that sums up using Bayes' well.

#### KisaLuuk

2 posts
Joined 12/2010

Didn't see this until now, thanks for the reply. Though I still don't get how you arrived at 20% equity above, but in the video you say it's 25% equity. That is, I understand how you arrived at 20% equity above and how you figured out that 20% of the girls wear skirts, but I don't understand why in the video our equity comes out to 25%.

when we're ahead (100% equity), we're winning 100% of the time
when we're behind( 50% equity), we're winning 0.5 the time =25% and we're losing half the time=25%
100% of all possible outcomes - 25% we're losing = 75% we're winning

hope I explained it right

#### BaseMetal

2060 posts
Joined 01/2010

I'll have a go at explaining the Bayes example from the video - I too might not get this right but I think the video was a touch misleading for this and I hope I haven't got confused and end up making this worse.

The Bayesian question being asked is "If we win how often do we start from being behind?" So us winning in this case is the equivalent of seeing the student in trousers. In a way this shows how often when we win we have come through the 'hard' start from behind path.
In the video combinatronics is used to solve it not really the Bayes formula,
P(A|B) = P(B|A)xP(A)/P(B)
in words: Prob of A given B equals Prob B given A x Prob A / Prob B,
To use it for this case, we want to find P(Start Behind | Win), in words the probability we started behind.given the event that we win.

So
P(Start Behind | Win) = P(Win | Start Behind) x P(Start Behind) / P(Win)

We can fill in the terms on the right, the only tricky one is P(Win).
P(Win | Start Behind) is the prob we win given the event we start behind = 0.5 ie we catch up 50% of the time.
P(Start Behind) = how often we start behind which is 40% we are behind = 0.4

P(Win) is the prob of us winning ie, equity, we can use an EV equation for this
P(Win) = 0.6 * 1.0 + 0.4 * 0.5 = 0.8 , ie, 60% we win 100% and 40% we win 50%. In total we win 80% of the time.
So now the Bayes formula gives us
P(Start Behind | Win) = 0.5 * 0.4 / 0.8 = 0.2/0.8 = 0.25

So knowing that we win we will have started behind 25% of the time. When we win a quarter of the time will have come from the case/path where we started behind.

Well GL to us all, stats and probs can get confusing sometimes but any pain in learning some stats should pay off in life and especially in poker and I hope this is right I am not 100% sure .

#### robstars7

8 posts
Joined 11/2012

AT 1:02:35 when tryng to get my % of range my formula keeps equaling 0.1, i dont know why what should i do ?

#### DiamondDog

122 posts
Joined 03/2008

Which '% of range' are you trying to work out
- the percentage of range represented by each individual hand,
- or the percentage of range represented by each category of hand strength?

Excel or OpenOffice?

#### sthief09

2342 posts
Joined 07/2007

AT 1:02:35 when tryng to get my % of range my formula keeps equaling 0.1, i dont know why what should i do ?

which cell(s) equal 0.1? all of them in Column G?

#### robstars7

8 posts
Joined 11/2012

yeah all in column G, i entered the forular correct in column F so i cant understand why G is like that. If i enter it manually would it ruin the table?

#### sthief09

2342 posts
Joined 07/2007

yeah all in column G, i entered the forular correct in column F so i cant understand why G is like that. If i enter it manually would it ruin the table?

it wouldn't ruin the table but that's strange that it's all coming out to the same. I can't think of a reason why. maybe you need to add more decimal places. look at a couple of different cells and make sure they are multiplying the cells they should be.

#### robstars7

8 posts
Joined 11/2012

okay ill just write them in normallly, i done the same formula calculation in column G but in a lower down cell and it was coming to 0.1 again. ill have to wrtie it in, thanks for the response.

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