#21
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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] |
#22
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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 |
#23
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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] |
#24
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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? |
#25
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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. |
#26
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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? |
#27
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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]
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#28
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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> |
#29
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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? |
#30
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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 ] They definitely should write more books for the narrow audience. I could easily read a whole book about valuebetting the river or somesuch topic. |
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