# 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 almost 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

2131 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

2131 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

2131 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.

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