The Mathematics of poker by Bill Chen & some dude...
 

anyone read this book? whats the word yo?

Re: The Mathematics of poker by Bill Chen & some dude...
 

It is excellent. You want to post this in "Books and Publications." Or better yet, search Books and Publications, there is plenty on it.

Re: The Mathematics of poker by Bill Chen & some dude...
 

theres a lot of math in it so if you like math its cool

Re: The Mathematics of poker by Bill Chen & some dude...
 

there's also a lot of poker in it.
I consider it to be a very correctly titled book....yo.

Re: The Mathematics of poker by Bill Chen & some dude...
 

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there's also a lot of poker in it.
I consider it to be a very correctly titled book....yo.

[/ QUOTE ]

i agree with this review

Re: The Mathematics of poker by Bill Chen & some dude...
 

sorry i didnt know about this forum or that there was a 20 page post on it already

Re: The Mathematics of poker by Bill Chen & some dude...
 

Can someone who's "not so hot" on the math side of things still get something out of this book? Will it be worth a read even though I would have to skip the majority of the mathamatical text which looks like japanese to me [img]/images/graemlins/confused.gif[/img].

Re: The Mathematics of poker by Bill Chen & some dude...
 

I'm enjoying it a lot and don't consider myself to be very good at math nor do I pay much attention to the specific calculations. I also feel they might as well have printed some of that stuff in a different language as far as I'm concerned. But there's more than enough simple meat in there to still make it worthwhile and they mostly just throw in the equattions and calculations for those who care and for completeness.
You don't even need to bother trying to figure out the calculations since the text usually gets the general point across anyway.

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
Can someone who's "not so hot" on the math side of things still get something out of this book? Will it be worth a read even though I would have to skip the majority of the mathamatical text which looks like japanese to me [img]/images/graemlins/confused.gif[/img].

[/ QUOTE ]
all the maths is explained very well. there is no prior knowledge needed.. probability is like the easiest branch of maths- its really not that hard to pick up..

Re: The Mathematics of poker by Bill Chen & some dude...
 

It's like reading a textbook. Lots of pages containing really small text.

No thanks. Probably a good book, but I'm not interested in it.

Re: The Mathematics of poker by Bill Chen & some dude...
 

If you never take advantage of the book, just copy down the hu jamming chart. It is useful book for thinking about playing against tough players and playing balanced poker. It is NOT a how to book.

Re: The Mathematics of poker by Bill Chen & some dude...
 

I've only had the book a few days and haven't had a chance to go through it properly yet. I know about ROR formula already but the very useful looking RoRU(risk of ruin with uncertain win rate) formula I can't figure out yet. Anyone have some practical example(s) using pt based data?

Re: The Mathematics of poker by Bill Chen & some dude...
 

I just started reading this book. I consider myself above average at "poker math" -- specifically EV calc type stuff. I graduated with a comp sci degree so i'm not too foreign to formal math...

I think it's hilarious how many greek symbols and equations they have in first section marked "Basics". I'm understanding the book so far, although I had to re-read a few pages when i got momentarily lost, but I can't imagine how joe-average poker player could possibly understand the concepts starting off in the "Basics" section.

They should have done a better job dumbing it down and/or removing many of the equations/greek symbols/math lingo until at least later in the book. I know being math guys they feel the need to build the "foundation" of ideas so they can build on it later, but if you want to reach a wide audience it's simply not a good strategy to keep people interested. I have one friend who tried to read this book and threw it out 2 chapters in because of all the graphs/equations/and "foreign letters" that people w/o a math background don't understand.

That said I'm looking forward to reading the rest of the book for myself so I can translate it to others.

WoT

Re: The Mathematics of poker by Bill Chen & some dude...
 

"if you want to reach a wide audience"


I never got the impression they wanted to reach a wide audience.

Re: The Mathematics of poker by Bill Chen & some dude...
 

It is probably a great book but unless you have a strong math background you will find it frustrating. I know I was not able to get much out of it at all. I think the guys who are saying that it's "fairly basic" are much stronger in math than they realize. Also, I would add that I don't think understanding the complex material in that book is necessary to be a winning poker player, I'm sure it wouldn't hurt and could only help but certainly is not necessary.

Re: The Mathematics of poker by Bill Chen & some dude...
 

From what I have seen of if so far it is defintely a book that is very daunting for the non mathematically minded. I have a mathematics and statistics degree - from a long time ago now and I am rusty, but even for someone like me I think it will need very careful reading and involve some relearning to grasp the equations. At the minute I'm still trying to work out the RoRU equation. I wish Chen had given some examples of it in this book [img]/images/graemlins/frown.gif[/img]
Early days yet as have only looked at a small bit of the book but I think an even slightly gentler introduiction and lengthier explanations and examples of formulas would have been a good idea. I get the impression that they have made the mistake of many intelligent math people of not adequately explaining the math assuming too readily that the reader is soaking it up, whereas in reality even people like me are having to do double takes to understand the stuff.

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
From what I have seen of if so far it is defintely a book that is very daunting for the non mathematically minded. I have a mathematics and statistics degree - from a long time ago now and I am rusty, but even for someone like me I think it will need very careful reading and involve some relearning to grasp the equations. At the minute I'm still trying to work out the RoRU equation. I wish Chen had given some examples of it in this book [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

Example:
Suppose you have played 22,500 hands of 9-handed limit holdem, and you've won 337.5 bets, with a std deviation of
17 bets/100. So your win rate w is 1.5 bb/100, and your standard deviation s is 17.

Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

But you don't really know your true win rate, and you don't have enough of a sample to conclude that it's really super close to those numbers. Instead, we can approximate your win rate by another normal distribution. Suppose your win rate is a random variable with mean w and standard deviation that we can calculate:

s_w = 17/(sqrt(225)) = 1.1333

If we assume your win rate is distributed normally (it isn't, but it's a better approximation than assuming your win rate is exact), then we can do better by calculating your RoR for all the points in that distribution and summing them by their weights. To do this we use calculus, as in our book, and arrive at the RoRU formula:

roru = r(w,b)*(exp(2b^2(s_w^2/s^4)))(phi(w - 2b(s_w^2/s^2)) + phi(-w/s_w)

which if I've done the math right, comes out to 17.89%.

This reflects the uncertainty about our win rate -- the base RoR is our risk of ruin if we are 100% accurate on our win rate and standard deviation. But here we might have just overperformed our expectation - we're only about 1.5 standard deviations away from zero. And at w=zero, risk of ruin is 100%, while at w = 3.0 (the other side), risk of ruin only goes down by, say, 3%.

-- some dude

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]

-- some dude


[/ QUOTE ]

lol classic

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]


Example:
Suppose you have played 22,500 hands of 9-handed limit holdem, and you've won 337.5 bets, with a std deviation of
17 bets/100. So your win rate w is 1.5 bb/100, and your standard deviation s is 17.

Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

But you don't really know your true win rate, and you don't have enough of a sample to conclude that it's really super close to those numbers. Instead, we can approximate your win rate by another normal distribution. Suppose your win rate is a random variable with mean w and standard deviation that we can calculate:

s_w = 17/(sqrt(225)) = 1.1333

If we assume your win rate is distributed normally (it isn't, but it's a better approximation than assuming your win rate is exact), then we can do better by calculating your RoR for all the points in that distribution and summing them by their weights. To do this we use calculus, as in our book, and arrive at the RoRU formula:

roru = r(w,b)*(exp(2b^2(s_w^2/s^4)))(phi(w - 2b(s_w^2/s^2)) + phi(-w/s_w)

which if I've done the math right, comes out to 17.89%.

This reflects the uncertainty about our win rate -- the base RoR is our risk of ruin if we are 100% accurate on our win rate and standard deviation. But here we might have just overperformed our expectation - we're only about 1.5 standard deviations away from zero. And at w=zero, risk of ruin is 100%, while at w = 3.0 (the other side), risk of ruin only goes down by, say, 3%.

-- some dude

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lol cheers 'some dude', a pretty cool alias to have actually. I'm still at a bit of a loss for what phi is representing - I gather it's a function, do I need to look up a log table to utilise this. Any chance you can explain it further here and exactly show how you got the answer 17.89%.

btw thanks for taking the time to respond here. It's appreciated. hmm I realise I have to get busy with going through your book and maybe I won't be posing these questions then anymore.

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
[ QUOTE ]


Example:
Suppose you have played 22,500 hands of 9-handed limit holdem, and you've won 337.5 bets, with a std deviation of
17 bets/100. So your win rate w is 1.5 bb/100, and your standard deviation s is 17.

Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

But you don't really know your true win rate, and you don't have enough of a sample to conclude that it's really super close to those numbers. Instead, we can approximate your win rate by another normal distribution. Suppose your win rate is a random variable with mean w and standard deviation that we can calculate:

s_w = 17/(sqrt(225)) = 1.1333

If we assume your win rate is distributed normally (it isn't, but it's a better approximation than assuming your win rate is exact), then we can do better by calculating your RoR for all the points in that distribution and summing them by their weights. To do this we use calculus, as in our book, and arrive at the RoRU formula:

roru = r(w,b)*(exp(2b^2(s_w^2/s^4)))(phi(w - 2b(s_w^2/s^2)) + phi(-w/s_w)

which if I've done the math right, comes out to 17.89%.

This reflects the uncertainty about our win rate -- the base RoR is our risk of ruin if we are 100% accurate on our win rate and standard deviation. But here we might have just overperformed our expectation - we're only about 1.5 standard deviations away from zero. And at w=zero, risk of ruin is 100%, while at w = 3.0 (the other side), risk of ruin only goes down by, say, 3%.

-- some dude

[/ QUOTE ]

lol cheers 'some dude', a pretty cool alias to have actually. I'm still at a bit of a loss for what phi is representing - I gather it's a function, do I need to look up a log table to utilise this. Any chance you can explain it further here and exactly show how you got the answer 17.89%.

btw thanks for taking the time to respond here. It's appreciated. hmm I realise I have to get busy with going through your book and maybe I won't be posing these questions then anymore.

[/ QUOTE ]

phi is the cumulative normal distribution function. Suppose you have a normal distribution with mean mu and standard deviation s. For any value, you can make a "z-score," which is essentially the number of standard deviations away from the mean that you are.

z(x) = (x - mu)/s

So if your distribution has a mean of 10 and a standard deviation of 5, then 2.5 has a z-score of -1.5.

Phi(z) is the probability that if you randomly select a point from your distribution, it will lie to the left of the z-score z.

So take the familiar example that 68% of points lie between +1 and -1 standard deviations. This implies that phi(-1) is 16%, phi(0) is 50%, and phi(1) is 84%.

I got 17.89% by using the following variables:

w = 1.5
s = 17
n = 225
s_w = 1.13333
b = 300

ror(w,b) = exp(-2*1.5*300/17^2) = .0444
(that's term 1 in the roru formula)

exp(2*(300^2)*(1.13333^2/1.5^4)) = 15.929
(thats the second term)

phi(1.5 - 2*300*(1.13333^2/1.5^2)) = .121673
(that's the third term)

phi(-1.5/1.13333)
(that's the fourth term)

Multiplying terms 1,2, and 3 together and adding term 4 gives 17.89%.

-- still some dude

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]


exp(2*(300^2)*(1.13333^2/1.5^4)) = 15.929


[/ QUOTE ]

Thanks again senor Jerrod.
I understand phi now thanks. And to give a little something back to 2+2 community to calculate the phi of a value in Excel use NORMSDIST function.

I'm still baffled though in at least one spot. I worked out that exp(2.768141347) = 15.929, but the figure in brackets here appears to be equal to 45668.86716, the exp(45668.867169) is massive of course. Am I reading the equation wrong or missing out on a bracket somewhere? [img]/images/graemlins/confused.gif[/img]

Re: The Mathematics of poker by Bill Chen & some dude...
 

Its a good book. I'm not far away from title it a "must read". it really helps you analyse your own hands and think diferently about situations.

btw: i spend about 2,5 month of getting the math down in the first ca. 50 pages

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]


phi is the cumulative normal distribution function. Suppose you have a normal distribution with mean mu and standard deviation s. For any value, you can make a "z-score," which is essentially the number of standard deviations away from the mean that you are.

z(x) = (x - mu)/s

So if your distribution has a mean of 10 and a standard deviation of 5, then 2.5 has a z-score of -1.5.

Phi(z) is the probability that if you randomly select a point from your distribution, it will lie to the left of the z-score z.

So take the familiar example that 68% of points lie between +1 and -1 standard deviations. This implies that phi(-1) is 16%, phi(0) is 50%, and phi(1) is 84%.

I got 17.89% by using the following variables:

w = 1.5
s = 17
n = 225
s_w = 1.13333
b = 300

ror(w,b) = exp(-2*1.5*300/17^2) = .0444
(that's term 1 in the roru formula)

exp(2*(300^2)*(1.13333^2/1.5^4)) = 15.929
(thats the second term)

phi(1.5 - 2*300*(1.13333^2/1.5^2)) = .121673
(that's the third term)

phi(-1.5/1.13333)
(that's the fourth term)

Multiplying terms 1,2, and 3 together and adding term 4 gives 17.89%.

-- still some dude

[/ QUOTE ]

Ah I spotted a little error you made that caused my confusion. It should have read exp(2*(300^2)*(1.13333^2/ 17 ^4)) = 15.929
(thats the second term)

phi(1.5 - 2*300*(1.13333^2/ 17 ^2)) = .121673
(that's the third term)

You had entered the win rate in to the formula instead of the standard deviation.Easily done. [img]/images/graemlins/wink.gif[/img]

Re: The Mathematics of poker by Bill Chen & some dude...
 

I substituted 400 big bets for 300 big bets in Jerrod 'Some dude' Ankenman's formula, the result for RoRU that I got were rorU = 35.53% almost twice the rate for having 300 big bets, obviously this can't be correct.

I also did a check of the example given on page 302. Implementing the formula as described by Jerrod and I got a slightly different answer of 3.566% RoRU.

Both of my calculations were done in excel with formulas that correctly worked out Jerrod's example given earlier on this thread!!

I can't see any mistake that I might have made. Is it possible that there is a problem with this formula or with the way the dude descibed it here?

Re: The Mathematics of poker by Bill Chen & some dude...
 

Oops spotted the mistake that I made with the 400 big bets [img]/images/graemlins/blush.gif[/img].

My 2nd more monor observation is right though I still think.

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

[/ QUOTE ]

On what basis do you use standard deviation to predict what will happen a future sittings at a poker table?

Re: The Mathematics of poker by Bill Chen & some dude...
 

Chen just wrote it so he would get invited to High Stakes Poker. [img]/images/graemlins/wink.gif[/img]

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
[ QUOTE ]
Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

[/ QUOTE ]

On what basis do you use standard deviation to predict what will happen a future sittings at a poker table?

[/ QUOTE ]

<montypython>It's only a model.</montypython>

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Traditional risk of ruin says, for a 300 bet bankroll:

ror = exp(-2*w*b/s^2) = exp(-2*1.5*300/289) = 4.44%

This is the risk of ruin if your TRUE win rate is 1.5 bb/100 and your TRUE standard deviation is 17 bb/100.

[/ QUOTE ]

On what basis do you use standard deviation to predict what will happen a future sittings at a poker table?

[/ QUOTE ]

<montypython>It's only a model.</montypython>

[/ QUOTE ]

How about next time you guys come up with a model you do so for poker, and not some imaginary game?

Re: The Mathematics of poker by Bill Chen & some dude...
 

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"if you want to reach a wide audience"


I never got the impression they wanted to reach a wide audience.

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They definitely should write more books for the narrow audience. I could easily read a whole book about valuebetting the river or somesuch topic.

Re: The Mathematics of poker by Bill Chen & some dude...
 

This is the most interesting book I had on the subject

Re: The Mathematics of poker by Bill Chen & some dude...
 

[ QUOTE ]
"if you want to reach a wide audience"


I never got the impression they wanted to reach a wide audience.

[/ QUOTE ]

poor assumption on my part. i thought they wanted to sell books.

Re: The Mathematics of poker by Bill Chen & some dude...
 

I consider it to be the best poker book I own (I got 30ish, mainly NL)

Re: The Mathematics of poker by Bill Chen & some dude...
 

great book ,ive probably learned more about poker in this book than most other books on holdem but i still got many many reads b4 i grasp most of the concepts ..

Re: The Mathematics of poker by Bill Chen & some dude...
 

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I just started reading this book. I consider myself above average at "poker math" -- specifically EV calc type stuff. I graduated with a comp sci degree so i'm not too foreign to formal math...

I think it's hilarious how many greek symbols and equations they have in first section marked "Basics". I'm understanding the book so far, although I had to re-read a few pages when i got momentarily lost, but I can't imagine how joe-average poker player could possibly understand the concepts starting off in the "Basics" section.

They should have done a better job dumbing it down and/or removing many of the equations/greek symbols/math lingo until at least later in the book. I know being math guys they feel the need to build the "foundation" of ideas so they can build on it later, but if you want to reach a wide audience it's simply not a good strategy to keep people interested. I have one friend who tried to read this book and threw it out 2 chapters in because of all the graphs/equations/and "foreign letters" that people w/o a math background don't understand.

That said I'm looking forward to reading the rest of the book for myself so I can translate it to others.

WoT

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i am in engineering and u said the book is mostly statistics, i cant really think how u expect to not have any of this notation, this is used in almost any statistical calculation

Re: The Mathematics of poker by Bill Chen & some dude...
 

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exp(2*(300^2)*(1.13333^2/1.5^4)) = 15.929


[/ QUOTE ]

Thanks again senor Jerrod.
I understand phi now thanks. And to give a little something back to 2+2 community to calculate the phi of a value in Excel use NORMSDIST function.

I'm still baffled though in at least one spot. I worked out that exp(2.768141347) = 15.929, but the figure in brackets here appears to be equal to 45668.86716, the exp(45668.867169) is massive of course. Am I reading the equation wrong or missing out on a bracket somewhere? [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]

he may have taken the natural log and u worded this a little weird? i dont have a calc in front of me but natural log is the inverse of exp so it would be much smaller, i'll try it on a calc later if i find mine