|
|
|||||||
| View Poll Results: If you voted Rep, was your reason.... | |||
| Family Values - Religion |
   
|
3 | 12.00% |
| Dem Scandals - Individ. character |
  
|
0 | 0% |
| Military - Iraq |
  
|
5 | 20.00% |
| Branding - loyalty |
  
|
0 | 0% |
| Economy - taxes |
  
|
12 | 48.00% |
| Poker |
  
|
5 | 20.00% |
| Voters: 25. You may not vote on this poll | |||
 |
|
|
Thread Tools | Display Modes |
|
#61
10-28-2007, 09:51 AM
|
|||
|
|||
Re: Something I\'ve been thinking about
Rainclouds,
I calculated the variance of the distribution of the villians equity. The equities are the outcomes of his hand distributions that make up that equity. I guess thats what your getting at? Your point is confusing to me because your language is slightly incorrect. 
|
|
#62
10-28-2007, 09:56 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
Your and many others here are making the misstake of thinking that you can win a fraction of the pot. You always win 100% or 0% so the variance is the same. And I have no idea why are you are referring to population variance and sample varince when we obviously know everything about the distribution. [/ QUOTE ] ummm.... to your first point ?? I'm calculating the variances of the data set of numbers. It tells us about the distribution. Which is what you want to know. Preferably, you'd like to calculate the skewness to figure out which sample is the best. Because you want one that is right skewed. To answer the second point. There's two different formula's for the variance of a sample or the variance of a population. edit: The fact we know "everything about the population" means that we're calculating the variance of a population.
|
|
#63
10-28-2007, 10:05 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
Rainclouds, I calculated the variance of the distribution of the villians equity. The equities are the outcomes of his hand distributions that make up that equity. I guess thats what your getting at? Your point is confusing to me because your language is slightly incorrect. [/ QUOTE ] My point is: 1) you calculated the variance of the distribution of the villains equity 2) I calculated the variance of the outcome of the hand 3) Poker players are interested in (2) and don't care about (1) 4) the variance of the distribution of the villains equity has no influence on the variance of the outcome of the hand. I pointed that out with point 1 to 4 in a previous post of mine
|
|
#64
10-28-2007, 10:05 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
ummm.... to your first point ?? I'm calculating the variances of the data set of numbers. It tells us about the distribution. Which is what you want to know. Preferably, you'd like to calculate the skewness to figure out which sample is the best. Because you want one that is right skewed. [/ QUOTE ] I don't understand what you are trying to say, but you are wrong about the variance [ QUOTE ] To answer the second point. There's two different formula's for the variance of a sample or the variance of a population. edit: The fact we know "everything about the population" means that we're calculating the variance of a population. [/ QUOTE ] Population variance and sample variance is something you use when you want to estimate the real variance. In this case we know the variance, so please do not refer to these.
|
|
#65
10-28-2007, 10:13 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
Rain,
I see what your saying now. We make the same amount of money on all of the situations because our equity is 50%. So really in the long run it doesn't matter which sample we choose. We make the same amount of cash on each situation. However, in the short run you'd prefer one that is right skewed, because there is a better chance of catching one of the higher equities as opposed to the lower. For example, the first sample you have a 50/50 shot of making it or not. In the next, 2/3 of the time you have a good chance, 1/3 of the time you have a bad. Think of deal or no deal, clearly you'd rather three cases with two cases having large numbers, as opposed to two cases of 0 and the amount. Oct, Umm....using the sample formula for calculating the population is used for calculating the real variance of the population when that variance is not known. In the above example the variance of each equity was not given, neither was the population variance....but the population variance can be calculated. Thats what I did.....
|
|
#66
10-28-2007, 10:21 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
Ringmaster is spot on and he has answered all questions which can be asked about this situation, imo. To summarize once again: 1) our equity vs villains range is 50% in all situations (we all agreed on that) 2) therefore, our chance of winning the pot is 50% (ORLY) 3) if you lose the pot, you lose all, if you win the pot, you win the whole pot (ORLY) 4) therefore, no matter what the distribution of villains range is, we have 50% chance of winning the whole pot, and 50% chance of losing the whole pot (YA RLY). 5) variance is the mean square deviation of values from their arithmetic mean 6) the arithmetic mean is 0.5 7) if we win, we win 1. The deviation from the arithmetic mean is 0.5. The square deviation is 0.5*0.5=0.25 8) if we lose, we win 0. The deviation from the arithmetic mean is -0.5. The square deviation is -0.5*-0.5=0.25 9) The variance is the mean of 0.25 and 0.25, which is 0.25 (ORLY) 10) From (1) to (9) follows that the variance is the same for all situations. It's mathematically proven so there's not really anything to argue about. And now I must go to sleep. [/ QUOTE ] ahhh this is your calculation. It took me a while to find this. Do you have a source? No offence or anything, but I've never seen standard deviation calculated like that ever. edit: Oh you build a yes ladder very clearly in this post. By that I mean you make clearly true statements at the start, which people will answer yes to. So by the time you get to the end its very aggreeable because your in an agreeing frame frame of mind. The reader is so used to saying yes that they just by habit answer yes. This is a conversation trick that can be used for winning arguements or getting your way. Stop using that trick. It makes you very convincing.
|
|
#67
10-28-2007, 10:26 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
[ QUOTE ] Ringmaster is spot on and he has answered all questions which can be asked about this situation, imo. To summarize once again: 1) our equity vs villains range is 50% in all situations (we all agreed on that) 2) therefore, our chance of winning the pot is 50% (ORLY) 3) if you lose the pot, you lose all, if you win the pot, you win the whole pot (ORLY) 4) therefore, no matter what the distribution of villains range is, we have 50% chance of winning the whole pot, and 50% chance of losing the whole pot (YA RLY). 5) variance is the mean square deviation of values from their arithmetic mean 6) the arithmetic mean is 0.5 7) if we win, we win 1. The deviation from the arithmetic mean is 0.5. The square deviation is 0.5*0.5=0.25 8) if we lose, we win 0. The deviation from the arithmetic mean is -0.5. The square deviation is -0.5*-0.5=0.25 9) The variance is the mean of 0.25 and 0.25, which is 0.25 (ORLY) 10) From (1) to (9) follows that the variance is the same for all situations. It's mathematically proven so there's not really anything to argue about. And now I must go to sleep. [/ QUOTE ] ahhh this is your calculation. It took me a while to find this. Do you have a source? No offence or anything, but I've never seen standard deviation calculated like that ever. [/ QUOTE ] It's exactly your formula [ QUOTE ] variance=1/n*sum(xi-mean)^2 [/ QUOTE ] with point 1 to 4 I pointed out that for every example, there are 2 situations: 1 in which you win the pot, 1 in which you don't. Both have a 50% chance of happening in each example. xi-mean = deviation from the arithmetic mean = 0.5 and -0.5 respectively sum(xi-mean)^2 = (0.5)^2 + (-0.5)^2 variance= 1/2 * ((0.5)^2 + (-0.5)^2) = 0.25
|
|
#68
10-28-2007, 10:26 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
I calculated the variance of the distribution of the villians equity. [/ QUOTE ] Exactly. Problem is, we don't care about this, what we care about is the variance of the distribution of wins and loses. And as I and others have repeatedly shown in this thread, this distribution, and hence the variance, is the same in all 5 cases. [ QUOTE ] The equities are the outcomes of his hand distributions that make up that equity. [/ QUOTE ] The distribution of individual hand equities is irrelevant as far as calculating the variance in question. What matters is our equity vs. his range. [ QUOTE ] ummm.... to your first point ?? I'm calculating the variances of the data set of numbers. It tells us about the distribution. Which is what you want to know. [/ QUOTE ] Again, it tells us about the distribution of hands in his range. Thant's not what we want to know. We want to know about the distribution of wins and loses when we talk about variance in poker. [ QUOTE ] Preferably, you'd like to calculate the skewness to figure out which sample is the best. Because you want one that is right skewed. [/ QUOTE ] No. Skewness has nothing to do with this. If you want a better explanation than this, read the thread.
|
|
#69
10-28-2007, 10:28 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
edit: Oh you build a yes ladder very clearly in this post. By that I mean you make clearly true statements at the start, which people will answer yes to. So by the time you get to the end its very aggreeable because your in an agreeing frame frame of mind. The reader is so used to saying yes that they just by habit answer yes. This is a conversation trick that can be used for winning arguements or getting your way. Stop using that trick. It makes you very convincing. [/ QUOTE ] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] I just made a step-by-step reasoning that's easy to follow. Just spelling it out for those who are no stats-freaks. Every statement in my reasoning is true. No tricks involved. WTF?
|
|
#70
10-28-2007, 10:33 AM
|
|||
|
|||
|
Re: Something I\'ve been thinking about
[ QUOTE ]
[ QUOTE ] edit: Oh you build a yes ladder very clearly in this post. By that I mean you make clearly true statements at the start, which people will answer yes to. So by the time you get to the end its very aggreeable because your in an agreeing frame frame of mind. The reader is so used to saying yes that they just by habit answer yes. This is a conversation trick that can be used for winning arguements or getting your way. Stop using that trick. It makes you very convincing. [/ QUOTE ] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] I just made a step-by-step reasoning that's easy to follow. Just spelling it out for those who are no stats-freaks. Every statement in my reasoning is true. No tricks involved. WTF? [/ QUOTE ] Maybe he can point out which point out which step is wrong instead of dismissing it as a trick. [img]/images/graemlins/tongue.gif[/img] FWIW I thought it was a pretty good cliff's notes.
|
|
|
|
Linear Mode
