I'm up for this was literally just googling this book and any related resources, I might lag a little behind since I also like to read Chomsky and Finkelstein in my spare time and have finals coming up but I'll definitely be following!
First part i did on my own although go stuck when got down to TJQKA on Betting and trying to get one formula to copy down. Had to refer to you Equations a few times frustrating but fun in the end when it started to piece together
that tables assumes that those hand rankings determine the winner of the hand, which is a bit overly simplistic. but in a river situation with no chops and those hand ranking then yes its correct
lots of issues when thinking bout hand rankings like that tho,
that tables assumes that those hand rankings determine the winner of the hand, which is a bit overly simplistic. but in a river situation with no chops and those hand ranking then yes its correct
lots of issues when thinking bout hand rankings like that tho,
that tables assumes that those hand rankings determine the winner of the hand, which is a bit overly simplistic. but in a river situation with no chops and those hand ranking then yes its correct
lots of issues when thinking bout hand rankings like that tho,
was referring to the game in thread below. Was just messing with Excel and used top 13 hands instead of 2 to A and Villain only playing top5, then extended to 169 hands and villains range to approx 20%
If it's all in preflop, then you need to stove it against a calling range, if I'm not mistaken we will get a depolarised solution rather than a polarised solution, basically approximates a sb v bb check r shove game where sb always limps
If it's all in preflop, then you need to stove it against a calling range, if I'm not mistaken we will get a depolarised solution rather than a polarised solution, basically approximates a sb v bb check r shove game where sb always limps
* Its a half-street type of game, in which there are only 13 cards used: 2-T, J, Q, K, A
* Two players: Villain and Hero. They both get dealt a single random card.
Rules.
* There is already $100 in the pot. Hero and Villain have $100 in stacks left.
* Villain is first to act (OOP) and he always checks.
* Hero can either a) shove or b) check behind.
a) If Hero checked, there is a showdown and the player with the higher rank card wins the pot.
b) If Hero shoved, Villain:
- Calls with top of his range: T, J, Q, K, A
- Folds with 2-9
Yeah but...how do I say it...you just mapped those cards to other labels. Thats all, right? You could just as well even map them to...fruit names but as long as you have a ranking system (which basically says that a hand/card/fruit with a higher number always has 100% equity against any lower one) the game stays basically the same - you just have to calculate more EVs. In the jam/fold game (Chapter 12) there will be a similar ranking but because the best hand preflop does not always win, the rules will be slightly changed.
Alright, anybody has any questions about Chapter 1? We should probably move on to the next one on Saturday...
Yeah but...how do I say it...you just mapped those cards to other labels. Thats all, right? You could just as well even map them to...fruit names but as long as you have a ranking system (which basically says that a hand/card/fruit with a higher number always has 100% equity against any lower one) the game stays basically the same - you just have to calculate more EVs. In the jam/fold game (Chapter 12) there will be a similar ranking but because the best hand preflop does not always win, the rules will be slightly changed.
Alright, anybody has any questions about Chapter 1? We should probably move on to the next one on Saturday...
It did. Thats why whether you map: [A -> AA, K -> KK, Q -> QQ,...] or [A -> 100, K -> 101, Q -> 102,...] or even add 200 new cards/objects, its still the same game (or did I miss something?).
It did. Thats why whether you map: [A -> AA, K -> KK, Q -> QQ,...] or [A -> 100, K -> 101, Q -> 102,...] or even add 200 new cards/objects, its still the same game (or did I miss something?).
I just finished chapter 1. I understood the second half of the chapter more than the first. Also like the coinflip examples and how to calculate probabilities of positve/negative EV.
Still have to read the last 10 posts of this thread... Will get to that in a bit
Thx. Unfortunately, I won't probably have any decent poker-related example for Chapter 2. But! I'm planning to overcompensate it with two eek examples for Chapter 3.
I think Chapter 2 is not really that important, although I might be wrong. Btw, if anyone had any problems with (proving) CLT this will help.
been pretty busy with other things lately but going through this thread makes me remember why I never finished this book in the first place(and second and third and millionth place)
been pretty busy with other things lately but going through this thread makes me remember why I never finished this book in the first place(and second and third and millionth place)
I'll post my summary for Chapter 2 on Thursday/Friday, maybe it will help clear some things up. Until then, keep in mind: 1) the most important thing is to understand general concepts/ideas presented in the book, as well as the end results of those various equations. You don't have to understand every single formula/detail2) you can still ask questions if you don't understand something (seriously, this is the last time I'm reminding you about this)
I'll post my summary for Chapter 2 on Thursday/Friday, maybe it will help clear some things up. Until then, keep in mind: 1) the most important thing is to understand general concepts/ideas presented in the book, as well as the end results of those various equations. You don't have to understand every single formula/detail2) you can still ask questions if you don't understand something (seriously, this is the last time I'm reminding you about this)
yes I struggled to make it through the whole book too, took me several tries myself, but if you are having problems continuing do what I did which is try to understand the main points. Unless you are really into math these equations will not make sense. I'm medium skill with math, finished trigonometry in high school but no calculus. Even my mind glazed over when trying to understand what every little detail meant. Just skim over and try to listen to how they are applying the equations rather than to understand every little breakdown. PS I am very much looking forward to this discussion so that I can learn in greater depth how this book applies, GREAT THREAD!!
Variance describes how far from the EV, you can expect your results to be. It is:
a) Always positive. b) Additive across n trials:
(just like EV). c) Loose, wild games produce more variance than tight, passive ones.
Standard Deviation is just a square root of Variance:
So for a given n number of hands:
whereas
Few Standard Deviations for most popular games (you can actually find those numbers in HM2, probably also in PT4):
2. Central Limit Theorem and Normal Distribution.
Central Limit Theorem - the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.
(So this actually applies perfectly to poker - we have a large number of independent events (hands) and for each one we can calculate EV and V (both are finite).)
Normal Distribution is given by a formula:
(Btw, that is a probability density function so: )
a) It doesn't contain negative values (because...probability is always >= 0):
b) The area under the curve is always equal to 1:
Its peak is located at the mean and Standard Deviation influences the width of the curve (well...because by definition Std.Dev describes how far results are from the mean).
- mean (EV)
- standard deviation
- Variance
Here is how it looks like:
To calculate the probability of a certain event falling between a and b, we need to calculate the area under the curve for that region. Unfortunately, the integral cannot be solved analytically so we need to do it numerically. Fortunately, it has already been done: formula 2.7 in MoP
I dont want to get into this stuff too much but there is this CDF function which basically answers the question: whats the probability of a certain event a being less or equal to it (so its calculating the probability of: (- infinity; a> ). So if you have 2 events: a and b, what you can do is calculate CDF(a) and CDF(b) and then substract each other and in result you will get the area (which is probability) between both events (thats what the 2.8 formula in MoP really does). In reality, you will usually just calculate a Z-score (more on this later) and then use a website such as this one:HERE to get what you need
One more thing, we could play a bit with the formula and transform it like this:
Now, the:
is the distance from a given x to the mean (EV). If we divide it by
, we get that distance in terms of standard deviations. This is actually called a Z-score:
Z-score – indicates how many standard deviations an observation is above or below the mean (EV).
Example:You are winning at $25/100 hands over a decent sample with a $350/100 Standard Deviation. Whats the Z-score of you breaking even for the next 20k hands?
This basically means that you are 1 Std.Dev below expectation (EV). You can enter that Z-score into the website, I just posted a link to, or look at the normal distribution graph to get the probability associated with -1 Std.Dev. Either way, its about 15.9%. So if you had 100 samples of 20k hands, you can expect to be break even in 16 of them
(There are some examples in MoP with those type of calculations so I dont know if I have to post more of them. Anyway, they are not really that important, so if you dont understand them (or you dont even want to) just skip them.)
3. Final notes about Variance.
a) Variance is a bi*ch. b) Variance does not justify bad play. c) Variance does not only relate to downswings. It also accounts for those upswings/heaters which recreational players love so much. d) The goal should not be to decrease Variance (???) but to increase Winrate!
(Here is an example in 10NL NLHE showing the effect of increasing WR)
was literally just googling this book and any related resources, I might lag a little behind since I also like to read Chomsky and Finkelstein in my spare time and have finals coming up but I'll definitely be following! 
