Is online poker flawed, fundamentally?
03-10-2018
, 10:27 AM
.All the best.
Edit to add (after seeing your reply) - wow, certainly did not take you long to find something in hindsight to interpret in a way that validates your obsession...
03-10-2018
, 10:53 AM
Don't worry, you will figure out a way for you to have the answer you need.
I am saying the results do not matter at all with regard to how you will misuse and misinterpret them, so you pinpointing a concern of the moment is nothing more than your standard distraction technique from the actual issue. What about two roulette wheels being spun by people of different heights, blah blah blah.
Many people who are experts in this field constantly say your approaches are invalid and your theory is invalid, and how you misinterpret data is invalid. That will continue, regardless of the actual data, because you will keep looking, in your invalid ways, until you get what you need.
If the produced data was genuinely statistically meaningful/concerning in any way you believe, then the experts would have said so. They are experts without an agenda. You are not an expert and you have an obsessive agenda.
Again, you need not worry - you will mix and match and misuse the data in a way that creates some form of bias for you to believe exists. I have said this enough times knowing it will have zero impact, so at this point I just hope how you butcher their free, vigorous work done for you is entertaining. Remember, you thought thought watching hands in a play money home game and writing notes on sticky pads would be vigorous 
.
All the best.
Many people who are experts in this field constantly say your approaches are invalid and your theory is invalid, and how you misinterpret data is invalid. That will continue, regardless of the actual data, because you will keep looking, in your invalid ways, until you get what you need.
If the produced data was genuinely statistically meaningful/concerning in any way you believe, then the experts would have said so. They are experts without an agenda. You are not an expert and you have an obsessive agenda.
.All the best.
03-10-2018
, 01:20 PM
Quote:
Surely you realize that you will be unable to give your hypothesis a legitimate test without using formal statistical tests. And these formal statistical tests will require complex formulas that will need to be programmed (or the data fed into a program designed for the purpose).
There is no way that anybody could fairly draw any conclusion, one way or the other, based upon inspecting the raw counts by eye. And nobody could, would, or should be swayed by any conclusions drawn by inspecting the raw counts by eye.
The Chi-squared test, probably the best test for the situation, is not complicated. But to someone unfamiliar with many probability and statistical concepts, it may appear to be essentially a "black box".
If you have the time, I suggest looking up the formula for the Chi-squared test of frequencies (also called the Pearson Chi-squared test). I would import the counts into a computer program/framework and calculate the Chi-squared test statistic.
Repeat this on a large number of 10,000 datasets. Or on a small number of 1,000,000 datasets.
It should become clear if the claim of "repeat value bias" is confirmed or refuted.
There is no way that anybody could fairly draw any conclusion, one way or the other, based upon inspecting the raw counts by eye. And nobody could, would, or should be swayed by any conclusions drawn by inspecting the raw counts by eye.
The Chi-squared test, probably the best test for the situation, is not complicated. But to someone unfamiliar with many probability and statistical concepts, it may appear to be essentially a "black box".
If you have the time, I suggest looking up the formula for the Chi-squared test of frequencies (also called the Pearson Chi-squared test). I would import the counts into a computer program/framework and calculate the Chi-squared test statistic.
Repeat this on a large number of 10,000 datasets. Or on a small number of 1,000,000 datasets.
It should become clear if the claim of "repeat value bias" is confirmed or refuted.
Quote:
The Pearson Chi-Squared test is in virtually every basic probability and statistic textbook.
I will try to write it down here, but interested parties should do an internet search or consult a statistics book.
Suppose we have a population which can be sub-divided into K classes. In our case, K is 52 and the classes are the 52 different playing cards As, Ah, ..., 2d, 2c.
Further suppose we are interested in testing whether all of the true underlying frequencies of each of the K classes in some specific population are equal. Call this frequency P. In our case, the population in question is the cards dealt by Pokerstars and P is 1/52.
To test this hypothesis we take a large sample of size N from this population (where large means that we get a sufficiently large number of observations in each of the K classes).
Let Si be the number of sample observations in the ith class. Clearly the sum of the Si will equal N.
Clearly, the expected number of observations in each class is simply N*P or, in our case, N/52. (If N = 10,000, N*P = 192.308.) Call this Y. So in our case Y=192.308.
Then Pearson showed that the test statistic given by:
X = Sum [i=1 to K] ((Si-Y)^2)/Y
has a Chi-squared distribution with (K-1) degrees of freedom.
You then need to compare the test value you get for X above with the appropriate critical values of the Chi-squared distribution that can be found in tables in books and on the internet.
Hope this helps and hope I didn't mess up the explanation.
I will try to write it down here, but interested parties should do an internet search or consult a statistics book.
Suppose we have a population which can be sub-divided into K classes. In our case, K is 52 and the classes are the 52 different playing cards As, Ah, ..., 2d, 2c.
Further suppose we are interested in testing whether all of the true underlying frequencies of each of the K classes in some specific population are equal. Call this frequency P. In our case, the population in question is the cards dealt by Pokerstars and P is 1/52.
To test this hypothesis we take a large sample of size N from this population (where large means that we get a sufficiently large number of observations in each of the K classes).
Let Si be the number of sample observations in the ith class. Clearly the sum of the Si will equal N.
Clearly, the expected number of observations in each class is simply N*P or, in our case, N/52. (If N = 10,000, N*P = 192.308.) Call this Y. So in our case Y=192.308.
Then Pearson showed that the test statistic given by:
X = Sum [i=1 to K] ((Si-Y)^2)/Y
has a Chi-squared distribution with (K-1) degrees of freedom.
You then need to compare the test value you get for X above with the appropriate critical values of the Chi-squared distribution that can be found in tables in books and on the internet.
Hope this helps and hope I didn't mess up the explanation.
Quote:
I'm sure you'll all be shocked to hear that a chi-squared test on the two reported samples of 1,000,000 have each come out non-significant (and not even close). At some point, PKDK, you should probably accept the fact that just spotting some "unusual" result out of 52 is simply not evidence of anything.
Simple logic will tell you that this entire exercise is pretty absurd. You have a program randomly assign a value from 1 to 52, and you are doing it a million times and counting them up. But you are doing that twice and somehow expect that one of the times is going to be different. You have admitted that you believe the randomization process used is fine - but there is something about the timing that will magically make the difference. Quite frankly, this is complete nuts.
We have now done the experiments, done statistical tests on them, and found exactly what anybody who understands what randomization means would have expected to find. Could it be time to finally put this one to bed?
Simple logic will tell you that this entire exercise is pretty absurd. You have a program randomly assign a value from 1 to 52, and you are doing it a million times and counting them up. But you are doing that twice and somehow expect that one of the times is going to be different. You have admitted that you believe the randomization process used is fine - but there is something about the timing that will magically make the difference. Quite frankly, this is complete nuts.
We have now done the experiments, done statistical tests on them, and found exactly what anybody who understands what randomization means would have expected to find. Could it be time to finally put this one to bed?
Thanks to everyone who participated in the thread to help better understand the "repeat value bias" claim regarding how Pokerstars deals its cards.
Thanks to EvilGreebo for generating twin sets of voluminous card sequences that can be analyzed to test the "repeat value bias" claim.
Thanks to VBAces for performing the Chi-squared tests on the various generated datasets to test the "repeat value bias" claim.
Drive home safely!
