Abingdon and Witney redux

[Douglas]

A study of bridge club deals from these two UK towns was published in the UK many years ago, and some years later in the ACBL Bulletin. This study purported to demonstrate that a little more systematic care in shuffling bridge deal cards would result in noticeably better bridge deals.

When evaluated with Pearson's 1900 Chi-square formula, the Abingdon deals result in an approaching zero result. The Witney deals evaluate to a close to one value, indicating unusual, but not extraordinary, closeness to expected values. These differences are ascribed to the different shuffling treatment used by the Witney club members.

However, based on the same observed outcomes, but using actual probability (p-value) measuring evaluation, a rather more distinct statistical result view appears.

First, the Chi-square evaluation does not produce a p-value. Never has, never will. Its evaluation result does lie in the same zero to one range that p-values lie in, but it is better described in traditional statistics terms as a correlation value (not a coefficient). Correlation measurement is vaguer than proper p-value measurement.

The study reports how many of each of the ten most common hand-types there are for both clubs. Since there are 39 total hand-types, the other 29 total results can be calculated by subtracting from total hand-types (1,336) to create an eleventh other category.

For Abingdon, only the first category (4432), and our eleventh category have obvious significant meaning after determining each category's p-value. The odds against the first category occurring fairly are 56,150:1 (4.13 mean standard deviations). For the eleventh category, 78:1 (-2.24 mean standard deviations).

However, if we assume there was a transcription error of 20 (+/-5) too much in category one, then both p-values fall right into line with what can be expected from this kind of hand-dealt bridge deals evaluation.

The real surprise to me is the Witney results. It is not even remotely possible they where hand-dealt. They are so close to expected values for each category that they exhibit not very good pseudo-randomness, and most likely were dealt by computer with one of those early limited-period pseudo-random number generators.

Douglas

[t***@att.net]

Chi-Square values do not lie between 0 and 1 but between 0 and infinity. The associated p-value does like between 0 and 1.

Neither of these observations validates the reported Abingdon and Witney result.

[p***@infi.net]

Post by Douglas
A study of bridge club deals from these two UK towns was published in the UK many years ago, and some years later in the ACBL Bulletin. This study purported to demonstrate that a little more systematic care in shuffling bridge deal cards would result in noticeably better bridge deals.
When evaluated with Pearson's 1900 Chi-square formula, the Abingdon deals result in an approaching zero result. The Witney deals evaluate to a close to one value, indicating unusual, but not extraordinary, closeness to expected values. These differences are ascribed to the different shuffling treatment used by the Witney club members.
However, based on the same observed outcomes, but using actual probability (p-value) measuring evaluation, a rather more distinct statistical result view appears.
First, the Chi-square evaluation does not produce a p-value. Never has, never will. Its evaluation result does lie in the same zero to one range that p-values lie in, but it is better described in traditional statistics terms as a correlation value (not a coefficient). Correlation measurement is vaguer than proper p-value measurement.
The study reports how many of each of the ten most common hand-types there are for both clubs. Since there are 39 total hand-types, the other 29 total results can be calculated by subtracting from total hand-types (1,336) to create an eleventh other category.
For Abingdon, only the first category (4432), and our eleventh category have obvious significant meaning after determining each category's p-value. The odds against the first category occurring fairly are 56,150:1 (4.13 mean standard deviations). For the eleventh category, 78:1 (-2.24 mean standard deviations).
However, if we assume there was a transcription error of 20 (+/-5) too much in category one, then both p-values fall right into line with what can be expected from this kind of hand-dealt bridge deals evaluation.
The real surprise to me is the Witney results. It is not even remotely possible they where hand-dealt. They are so close to expected values for each category that they exhibit not very good pseudo-randomness, and most likely were dealt by computer with one of those early limited-period pseudo-random number generators.
Douglas

The stats courses I have tutored over the years don't always cover Chi-square tests, so I am less familiar with those than hypothesis testing on a mean or proportion. If I understand correctly, a goodness-of-fit test would involve estimating how many of each hand pattern you could expect out of so many deals from the theoretical probabilities. You would then compute (Observed - Expected)^2 divided by Expected, and sum across each hand type.This sum is the Chi-quare statistic, which has a known distribution. If the test statistic is fairly large, you reject the hypothesis that the deals are consistent with the theoretical probabilities. I don't know why this cannot be expressed as a p-value, that is, the probability that the test statistic could be so large if the null hypothesis were true. The Wikipedia article uses the term p-value; do you know of an online reference for what you call "correlation value" ?

As for your analysis of the reported results, I take it that the null was reported as rejectable for the Abingdon deals (p or c value close to zero) but non-rejecteable for the Witney deals (p or c value near 1.) (The difference IIRC was that in Witney they asked everyone to mildly shuffle their hands after the last round, as one usually does before passing to the next table.) I am not clear why you assume a transcription error on the Abingdon deals. On the Witney deals, you say the fit was too perfect. Is the data available online?

As with most studies, it seems no one attempted to reproduce these results, so a flawed analysis may have been taken as truth. Really, any single result should be treated with scepticism.

[jogs]

χ²?? I can't relate to χ². I understand variance. I understand standard deviation. Isn't degrees of freedom related to sample size? Those numbers just have no meaning to me.

jogs
------------
Are any of you getting garbage from χ²(X²)?

[p***@infi.net]

Post by jogs
χ²?? I can't relate to χ². I understand variance. I understand standard deviation. Isn't degrees of freedom related to sample size? Those numbers just have no meaning to me.
jogs
------------
Are any of you getting garbage from χ²(X²)?

The symbol is showing up fine for me, using Google Groups.

As for what chi-square means, consider this: 4333 distribution should occur 10.5% of all hands. If you recorded 100 deals, you'd expect about 42 of the 400 hands to be perfectly flat. Suppose you counted 80 such hands -- you'd think that was odd, right? Computing a chi-square test statistic allows you to quantify how unusual such a result would be.

[Douglas]

Post by p***@infi.net
As for what chi-square means, consider this: 4333 distribution should occur 10.5% of all hands. If you recorded 100 deals, you'd expect about 42 of the 400 hands to be perfectly flat. Suppose you counted 80 such hands -- you'd think that was odd, right?

The odds against you having such an outcome are 67,537,326:1. Coming close to lotto odds! How realistic do you want that to be in your intellectual universe?

However, that is not a large enough sampling of deals. How large should it be?

I did this kind of calculation for many years, and only achieved frustration. I would guess that if I had a database of 100,000 fair hand-dealt deals, I would achieve an observable statistical distinction between them, and computer dealt pseudo-random deals measuring the frequency of only 4333 hands. I do not believe such a database exists, or even has a chance of existing in my lifetime.

The distinction would occur because the variates would continue accumulating beyond the 70,000 deal point where they stop accumulating in the very best pseudo-random generator I have tested to date. I think this is something like what the stat community refers to when they discuss size effect.

Also, the 4333 hand is near the middle of the probability space when considering all 39 hand types. Use instead the two most common hand types (4432, 5332), and this cumulative distinction would happen much, much sooner. But even then, you would need more than 100 deals. There is a certain minimum critical mass necessary in any valid random sampling.

Post by p***@infi.net
Computing a chi-square test statistic allows you to quantify how unusual such a result would be.

So let us do the Chi-square goodness-of-fit test for comparison from your given facts:

80 - 42 = -38. When we square -38, the minus sign goes away, and returns (programmer speak) 1,444. Now we div1de by expected value 42 = 34.38. Now double that = 68.76. This is our Chi-square sum. I plug it into my trusty Excel 2016 chisq.dist.rt() function with one degree of freedom, and the scientific notation of 1.11098E-16 returns. That means it is a really tiny amount. When I convert it to odds against, this is what I get: 9,001,047,129,234,239:1.

Only one of these two values can be a p-value. The other has to be something else. In other words, simple one-dimensional facts like this are not allowed two distinctly different valid p-values. My money is on the binomial derived value being the valid p-value in every like set of facts.

Douglas

[p***@infi.net]

Post by Douglas

Post by p***@infi.net
As for what chi-square means, consider this: 4333 distribution should occur 10.5% of all hands. If you recorded 100 deals, you'd expect about 42 of the 400 hands to be perfectly flat. Suppose you counted 80 such hands -- you'd think that was odd, right?

The odds against you having such an outcome are 67,537,326:1. Coming close to lotto odds! How realistic do you want that to be in your intellectual universe?
However, that is not a large enough sampling of deals. How large should it be?
I did this kind of calculation for many years, and only achieved frustration. I would guess that if I had a database of 100,000 fair hand-dealt deals, I would achieve an observable statistical distinction between them, and computer dealt pseudo-random deals measuring the frequency of only 4333 hands. I do not believe such a database exists, or even has a chance of existing in my lifetime.
The distinction would occur because the variates would continue accumulating beyond the 70,000 deal point where they stop accumulating in the very best pseudo-random generator I have tested to date. I think this is something like what the stat community refers to when they discuss size effect.
Also, the 4333 hand is near the middle of the probability space when considering all 39 hand types. Use instead the two most common hand types (4432, 5332), and this cumulative distinction would happen much, much sooner. But even then, you would need more than 100 deals. There is a certain minimum critical mass necessary in any valid random sampling.

Post by p***@infi.net
Computing a chi-square test statistic allows you to quantify how unusual such a result would be.

80 - 42 = -38. When we square -38, the minus sign goes away, and returns (programmer speak) 1,444. Now we div1de by expected value 42 = 34.38. Now double that = 68.76. This is our Chi-square sum. I plug it into my trusty Excel 2016 chisq.dist.rt() function with one degree of freedom, and the scientific notation of 1.11098E-16 returns. That means it is a really tiny amount. When I convert it to odds against, this is what I get: 9,001,047,129,234,239:1.
Only one of these two values can be a p-value. The other has to be something else. In other words, simple one-dimensional facts like this are not allowed two distinctly different valid p-values. My money is on the binomial derived value being the valid p-value in every like set of facts.
Douglas

I think I made a mistake setting up the example by discussing all four hands, since they are not independent. But I could have had said you noticed South's hand was flat on 80 out of 400 deals, rather than the expected 42.

I am unable to follow most of the rest of what you said but I gather your first "odds against" was using the binomial distribution and that the chi-square approximation gave a markedly different result, though both were highly unlikely. I raised the question one time in, I think, a Stats discussion group as to why we used the normal approximation rather than the binomial when hypothesis testing on a proportion, and was told that to use the binomial required a "continuity correction." But now I think that's nonsense -- given a specific sample size, the results are discrete, not continuous, so why not use the binomial? And I gather that chi-square is a similar fudge, not needed given modern computing power.

[jogs]

Post by p***@infi.net
I think I made a mistake setting up the example by discussing all four hands, since they are not independent. But I could have had said you noticed South's hand was flat on 80 out of 400 deals, rather than the expected 42.

Your example was 100 deals of 4 hands each. The 4 hands are interdependent. When one hand is 4333, it increases the chances of the other three hands being 4333.

Althou there are 39 possible combinations, many of those combinations occur infrequently. Therefore the sample size would need to be in the millions to test if your sample mirrored the true distribution. χ² was developed at least 50 years before the computer. I wouldn't use χ².

[t***@att.net]

Chi-Sq with k degrees of freedom is the distribution function of the sum of k independent standard normal variables. It has lots of uses in statistics. One could start with a Wiki page and iterate the bibliography operator.

[Steve Willner]

Post by Douglas
These differences are ascribed to the different shuffling treatment
used by the Witney club members.

I've mentioned before that I've collected shapes on something like 2000
hands dealt in the ACBL. Only about half are entered in my spreadsheet,
but so far there's no evidence against randomness.

Chi-square seems the obvious way to do the analysis, and I don't
understand Douglas' comments at all. Chi-square is "frequentist" and
not "Bayesian," so one has to be careful when stating the results, but
that's a standard criticism of all frequentist methods.

If there's a better way to do the analysis, I'd love to hear what it is.

[jogs]

Post by Steve Willner
Chi-square seems the obvious way to do the analysis, and I don't
understand Douglas' comments at all.

I can't relate to χ². I like the normal approximation to all physical phenomenon. Find a sample of 1000+ boards. Test for the frequency of 10+ cards in a suit. Test 0, 1, 2,....,9. See if these number of occurrances are close to expected.

[t***@att.net]

ChiSq is the L2 distance (normalized) between two empirical distributions. Knuth (I think in Volume II) has a derivation of the ChiSq statistic. Also see https://en.wikipedia.org/wiki/Chi-squared_distribution Thus the ChiSq does relate the approximation of most physical measurements (actually the errors or deviations thereof) by a normal distribution. Not every statistical quantity of interest is normally distribution though. The distribution of a sample of N items from a normal distribution when approximating the underlying distributions variance by the observed sample variance is not a normal distribution (it's a t-distribution.)

There are lots of distances between statistical distributions. ChiSq has the advantage of being simple to compute and also of it being simple to compute its p-values. One could use an L_1 or L_inf instead of the L_2 distance. There are others.

[Douglas]

I've mentioned before that I've collected shapes on something like 2000 hands dealt in the ACBL. Only about half are entered in my spreadsheet, but so far there's no evidence against randomness.

Interesting turn of phrase "no evidence against randomness." I have never thought about it in that way before.

Chi-square seems the obvious way to do the analysis, and I don't

understand Douglas' comments at all.

I spent many years operating under the belief that Pearson's Chi-square formulation was the only way to determine randomness, much less distinguish between possibly different kinds.

I wonder if you can see that it is fundamentally an averaging formula, independent of specific placement of the data used in it, and restricted to the absolute values of its variates. In the A & W study with its 11 categories of frequency results, a variate of, say, 9, or -9, in any of the 11 categories creates the same exact effect on the final evaluation result. Whereas, specific p-value determined for each category allows for nearly unlimited basic distinctions.

If there's a better way to do the analysis, I'd love to hear what it is.

I can suggest the simplest way to do a useful testing of your ACBL data which I discovered along the way to where I am now.

For each deal, merely count the most commonly expected three hand-types; 4432, 5332, and 5431. Count them as one lump sum each deal. So if a particular deal has one 4432 hand, and one 5332 hand, it would count 2 for that deal. By now, it takes me longer to record that number than to determine it.

At the end of each 25 deals, calculate the accumulated count minus expected value to determine the accumulated variate. In Excel, I turn on the number format feature which makes negative variates appear red. So when I have a column of variate results, I can readily see the negative and positive variate pattern.

500 deals should give you a useful result. You should have a column of 20 variate amounts to look at, and the final variate amount can be evaluated for its most accurate and precise p-value known in current stat knowledge.

A question that might come to your mind at this point is, what is the meaning of these too-simple appearing final numbers? How do they relate to relative deal randomness? And, possibly, it cannot be this simple, can it?

What you likely do not realize now is that you are doing a coin-tossing experiment. You are recording the results slightly differently than anyone has suggested before, but it is coin-tossing. Because it is, the stat world currently believes they know everything there is to know about its p-values. So that part should not be an issue.

What will be the issue, I think, is how do your particular variate results relate to determining pseudo-randomness vs. naturally occurring equiprobable randomness (i.e. Hand-dealt bridge dealing).

Provide us with a set of your deal outcomes, and we can then move on to discussing their meaning.

Douglas

[Steve Willner]

Post by Douglas
Interesting turn of phrase "no evidence against randomness."

Standard frequentist terminology. We are asking whether the null
hypothesis should be rejected, i.e., whether there is evidence against
the null hypothesis.

Post by Douglas
I wonder if you can see that it is fundamentally an averaging
formula,

I'm afraid I don't see that, and I don't understand the rest of what you
wrote at all.

Post by Douglas
For each deal, merely count the most commonly expected three
hand-types; 4432, 5332, and 5431.

This seems less sensitive than the analysis I am doing, but it should
work if you have enough deals.

My data are different, though. I record the pattern of the hand I was
dealt. Expected probabilities of those distributions are known, and
"big" deviations would suggest non-random dealing. The problem is to
quantify "big" and turn it into a p value. I don't see why chi-square
isn't good enough for the purpose, though it might not be optimum.

I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

[Douglas]

Post by Steve Willner
I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

I summed your individual totals several times, and came to 999 each time. So I added 1 to the last (11th) category, and am pleased to see a total of 250 deals. I have exactly comparable data.

Here are the comparable result matrices reduced to the three most important outcomes:

Actual 419 500 81
p 0.999 0.005 0.195
SDem 3.11 2.57 0.86

Willner 397 544 59
p 0.954 0.585 0.000
SDem 1.68 0.21 3.48

SDem is Standard Deviation from expected mean.

What do these results mean?

The first category is the most important. It is the 4432 and 5332 hands combined. Greater SDem means greater variability. While the p values do not appear much different, note the substantial difference in SDem. Yours is very similar to my results from BigDeal 1.2.

The last category is next in importance. Your deals are very short of the wilder hands. Abnormally so.

The middle category is the eight hand-types from 5431 through to 4441 in ascending expected values. Again greater SDem means greater variability. It is that consistent variability which separates natural randomness from machine produced randomness currently. Starkly so when measured by this particular metric in valid p-value fashion.

Douglas

[p***@infi.net]

Post by Douglas

Post by Steve Willner
I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

I summed your individual totals several times, and came to 999 each time. So I added 1 to the last (11th) category, and am pleased to see a total of 250 deals. I have exactly comparable data.
Actual 419 500 81
p 0.999 0.005 0.195
SDem 3.11 2.57 0.86
Willner 397 544 59
p 0.954 0.585 0.000
SDem 1.68 0.21 3.48
SDem is Standard Deviation from expected mean.
What do these results mean?
The first category is the most important. It is the 4432 and 5332 hands combined. Greater SDem means greater variability. While the p values do not appear much different, note the substantial difference in SDem. Yours is very similar to my results from BigDeal 1.2.
The last category is next in importance. Your deals are very short of the wilder hands. Abnormally so.
The middle category is the eight hand-types from 5431 through to 4441 in ascending expected values. Again greater SDem means greater variability. It is that consistent variability which separates natural randomness from machine produced randomness currently. Starkly so when measured by this particular metric in valid p-value fashion.
Douglas

I understood Steve to say that he had 1038 hands, so you must place 38 or so hands in an extra category.

[p***@infi.net]

Post by Steve Willner

Post by Douglas
Interesting turn of phrase "no evidence against randomness."

Standard frequentist terminology. We are asking whether the null
hypothesis should be rejected, i.e., whether there is evidence against
the null hypothesis.

Post by Douglas
I wonder if you can see that it is fundamentally an averaging
formula,

I'm afraid I don't see that, and I don't understand the rest of what you
wrote at all.

Post by Douglas
For each deal, merely count the most commonly expected three
hand-types; 4432, 5332, and 5431.

This seems less sensitive than the analysis I am doing, but it should
work if you have enough deals.
My data are different, though. I record the pattern of the hand I was
dealt. Expected probabilities of those distributions are known, and
"big" deviations would suggest non-random dealing. The problem is to
quantify "big" and turn it into a p value. I don't see why chi-square
isn't good enough for the purpose, though it might not be optimum.
I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

I just performed a Chi-square test using your data, assuming 39 deals with 7 card or longer suits, and that you meant 6610 rather than 5510. Comparing to the probabilities in the Bridge Encyclopedia, I get a Chi-Square test statistic of 11.2, which with 16 degrees of freedom yields a p-value of .78. So we cannot reject the null hypothesis that these deals were generated with proper randomness. Looking at each category, nothing seems out of line -- the observed counts line up well with the expected.

One caveat: does your data include all four hands from each deal? That would appear to violate the independence assumption; one should record South's distribution, only (or North, or dealer, or the recorder's hand, or something.) But 1038 isn't divisible by four.

[Douglas]

Post by p***@infi.net
I just performed a Chi-square test using your data, assuming 39 deals with 7 card or longer suits, and that you meant 6610 rather than 5510. Comparing to the probabilities in the Bridge Encyclopedia, I get a Chi-Square test statistic of 11.2, which with 16 degrees of freedom yields a p-value of .78. So we cannot reject the null hypothesis that these deals were generated with proper randomness. Looking at each category, nothing seems out of line -- the observed counts line up well with the expected.
One caveat: does your data include all four hands from each deal? That would appear to violate the independence assumption; one should record South's distribution, only (or North, or dealer, or the recorder's hand, or something.) But 1038 isn't divisible by four.

So I think I'm straight now. This is 1038 deals where one hand was recorded from each deal. For whatever reason, I did not grasp that the first time. I sincerely hope the same directional hand was selected each time.

Willner's revised result matrix:

397 544 97 num
0.954 0.585 0.665 cum p
1.68 0.21 0.43 SDem

My opinion is these deals are from BigDeal 1.2. They are very close to my 250 BigDeal 1.2 results, and distinctly different from my Reno results, as well as my other accumulated pseudo-random generated results.

I ran an experiment concerning your Chi-square result.

First, I tucked that single 5510 (6610) occurrence into my other category, making it 40. It is not considered good form by most authorities to have less than 5 in any category. So my Chi-square evaluation is one less category, and therefor one less df. My result is 0.741. Yours is 0.78. That is quite a change for 1 occurrence out of 1034 don't you think?

I next reduced my categories from 16 to 13 by consolidating several of the smaller categories. Now my smallest is 25 occurrences. My result now is 0.638. Hum.

Finally, I reduced my categories to 8. It happens that the smaller categories rather neatly consolidate to near 100 each. My result is now 0.951. Double hum.

I hardly call this a test with any sort of consistency. I already demonstrated to you that its results bear no resemblance to p-values.

Douglas

[p***@infi.net]

Post by Douglas

Post by p***@infi.net
I just performed a Chi-square test using your data, assuming 39 deals with 7 card or longer suits, and that you meant 6610 rather than 5510. Comparing to the probabilities in the Bridge Encyclopedia, I get a Chi-Square test statistic of 11.2, which with 16 degrees of freedom yields a p-value of .78. So we cannot reject the null hypothesis that these deals were generated with proper randomness. Looking at each category, nothing seems out of line -- the observed counts line up well with the expected.
One caveat: does your data include all four hands from each deal? That would appear to violate the independence assumption; one should record South's distribution, only (or North, or dealer, or the recorder's hand, or something.) But 1038 isn't divisible by four.

So I think I'm straight now. This is 1038 deals where one hand was recorded from each deal. For whatever reason, I did not grasp that the first time. I sincerely hope the same directional hand was selected each time.
397 544 97 num
0.954 0.585 0.665 cum p
1.68 0.21 0.43 SDem
My opinion is these deals are from BigDeal 1.2. They are very close to my 250 BigDeal 1.2 results, and distinctly different from my Reno results, as well as my other accumulated pseudo-random generated results.
I ran an experiment concerning your Chi-square result.
First, I tucked that single 5510 (6610) occurrence into my other category, making it 40. It is not considered good form by most authorities to have less than 5 in any category. So my Chi-square evaluation is one less category, and therefor one less df. My result is 0.741. Yours is 0.78. That is quite a change for 1 occurrence out of 1034 don't you think?
I next reduced my categories from 16 to 13 by consolidating several of the smaller categories. Now my smallest is 25 occurrences. My result now is 0.638. Hum.
Finally, I reduced my categories to 8. It happens that the smaller categories rather neatly consolidate to near 100 each. My result is now 0.951. Double hum.
I hardly call this a test with any sort of consistency. I already demonstrated to you that its results bear no resemblance to p-values.
Douglas

Thanks for the tips, as I said I have not used chi-square much. The p-values should be "1-minus" what we reported, i.e., Excel's chidist function gives the left-tail and we want the right. So the correct p-value for 16 categories (placing the single 6610 hand in with the long suits) is .25.I got .35 for 13 categories, which includes 5530 and 5440 together, and 6430, 6511 and 6610 together, with 7+ as the final category. So it looks like we did the same compression.

[Douglas]

To circle back to this thread's beginning, and complete the circle, how do the Abingdon and Witney bridge deals rate using the simple coin-toss test statistic?

Using the published numbers for 4432, 5332, and 5431 hands, the Abingdon deals produce a cumulative binomial result of 0.9999... . I would say that is approaching one. The Witney deals produce 0.467... .

Abingdon deals are ordinary hand-dealt with a probable transcription error. The Witney deals are pseudo-random, and I am not aware of anyone being able to do that by hand up to this point in time. Maybe when the robots take over!

Paul, I searched for the published statistics, but was only able to find two dead links in the original UK bridge magazine article.

Douglas

[Dave Flower]

Post by Douglas
To circle back to this thread's beginning, and complete the circle, how do the Abingdon and Witney bridge deals rate using the simple coin-toss test statistic?
Using the published numbers for 4432, 5332, and 5431 hands, the Abingdon deals produce a cumulative binomial result of 0.9999... . I would say that is approaching one. The Witney deals produce 0.467... .
Abingdon deals are ordinary hand-dealt with a probable transcription error. The Witney deals are pseudo-random, and I am not aware of anyone being able to do that by hand up to this point in time. Maybe when the robots take over!
Paul, I searched for the published statistics, but was only able to find two dead links in the original UK bridge magazine article.
Douglas

I have a PDF of the original article. If anyone wants a copy, please e-mail me

David Flower

(***@BTINTERNET.COM

[Steve Willner]

Post by p***@infi.net
I just performed a Chi-square test using your data, assuming 39 deals
with 7 card or longer suits, and that you meant 6610 rather than
5510.

Both correct; sorry about the silly typo '5510'. It's just a label and
doesn't affect the counts.

Post by p***@infi.net
Comparing to the probabilities in the Bridge Encyclopedia, I
get a Chi-Square test statistic of 11.2, which with 16 degrees of
freedom yields a p-value of .78.

Looks about right, though I didn't check the calculation. I've been
meaning to do it myself but haven't had time.

Post by p***@infi.net
One caveat: does your data include all four hands from each deal?

No, only the single hand dealt to me. All patterns are based on hand-
shuffled deals I played. To prevent bias, I excluded hands from deals I
shuffled myself. (I believe in thorough shuffling; the question is
whether typical ACBL members do as well.) Also when (rarely) I failed
to record any hand in a set, I excluded all hands in that set because
the hand I forgot might be more likely to be a flat one.

"Douglas" seems to have misunderstood what the numbers show, and I
understand hardly any of what he has written in this thread.

[Douglas]

Post by p***@infi.net
Comparing to the probabilities in the Bridge Encyclopedia, I
get a Chi-Square test statistic of 11.2, which with 16 degrees of
freedom yields a p-value of .78.

Looks about right, though I didn't check the calculation. I've been

meaning to do it myself but haven't had time.

Looks about right, huh? I have done thousands of Chi-square evaluations by now, and do not remember visualizing the probable result ahead of time once. Is it possible you are a Chi-square savant?

Post by p***@infi.net
One caveat: does your data include all four hands from each deal?

No, only the single hand dealt to me. All patterns are based on hand-shuffled deals I played. To prevent bias, I excluded hands from deals I shuffled myself. (I believe in thorough shuffling; the question is whether typical ACBL members do as well.) Also when (rarely) I failed to record any hand in a set, I excluded all hands in that set because the hand I forgot might be more likely to be a flat one.
"Douglas" seems to have misunderstood what the numbers show, and I

understand hardly any of what he has written in this thread.

Congratulations, you are the very first human who has received pseudo-random distributed hand-dealt hands from a wide variety of other players (per your above statement). Amazing. Simply amazing.

I'm sorry. The author of the Witney study did also. Silly me. There are two of you to keep each other company. Maybe others will step forward with a like kind of story to tell.

I have nothing further to offer you. I have no desire to add to your confusion.

Douglas

[Douglas]

In my experience this is a diverse interest group, able to be looked in on from most of earth. So why not take advantage of that to disprove what I am telling you in this thread.

If where you play bridge still hand deals, accumulate 250 deal records, and do the simple counting of the total 4432, 5332, and 5431 hands in those 250 deals. If you get less than 533 total, share that info with this group.

For the places that use computer deals, do the same counting, and see whether you reach anywhere near 533. In very short order you could collectively refute me.

Or we could simply ignore the subject; or better yet, talk it to death. I leave it up to you.

Douglas

[p***@infi.net]

Post by Douglas
In my experience this is a diverse interest group, able to be looked in on from most of earth. So why not take advantage of that to disprove what I am telling you in this thread.
If where you play bridge still hand deals, accumulate 250 deal records, and do the simple counting of the total 4432, 5332, and 5431 hands in those 250 deals. If you get less than 533 total, share that info with this group.
For the places that use computer deals, do the same counting, and see whether you reach anywhere near 533. In very short order you could collectively refute me.
Or we could simply ignore the subject; or better yet, talk it to death. I leave it up to you.
Douglas

You are still advocating counting four hands from one deal. Is it not obvious that once you have counted the first three hands, the fourth is deterministic, not random? Nor are the second and third independent from the first? All will tend to correspond to the expected patterns (whether expected for hand dealt or pseudo-random probabilities) but you cannot act as if you have 1000 hands worth of data from 250 deals.

[Douglas]

Post by p***@infi.net

Post by Douglas
In my experience this is a diverse interest group, able to be looked in on from most of earth. So why not take advantage of that to disprove what I am telling you in this thread.
If where you play bridge still hand deals, accumulate 250 deal records, and do the simple counting of the total 4432, 5332, and 5431 hands in those 250 deals. If you get less than 533 total, share that info with this group.
For the places that use computer deals, do the same counting, and see whether you reach anywhere near 533. In very short order you could collectively refute me.
Or we could simply ignore the subject; or better yet, talk it to death. I leave it up to you.
Douglas

You are still advocating counting four hands from one deal. Is it not obvious that once you have counted the first three hands, the fourth is deterministic, not random? Nor are the second and third independent from the first? All will tend to correspond to the expected patterns (whether expected for hand dealt or pseudo-random probabilities) but you cannot act as if you have 1000 hands worth of data from 250 deals.

Yes. How about for once you let the data speak for itself. If I am refuted by widespread facts, then you can cheerfully say "I told you so because..."

Douglas

[p***@infi.net]

Post by Douglas

Post by p***@infi.net

Post by Douglas
In my experience this is a diverse interest group, able to be looked in on from most of earth. So why not take advantage of that to disprove what I am telling you in this thread.
If where you play bridge still hand deals, accumulate 250 deal records, and do the simple counting of the total 4432, 5332, and 5431 hands in those 250 deals. If you get less than 533 total, share that info with this group.
For the places that use computer deals, do the same counting, and see whether you reach anywhere near 533. In very short order you could collectively refute me.
Or we could simply ignore the subject; or better yet, talk it to death. I leave it up to you.
Douglas

You are still advocating counting four hands from one deal. Is it not obvious that once you have counted the first three hands, the fourth is deterministic, not random? Nor are the second and third independent from the first? All will tend to correspond to the expected patterns (whether expected for hand dealt or pseudo-random probabilities) but you cannot act as if you have 1000 hands worth of data from 250 deals.

Yes. How about for once you let the data speak for itself. If I am refuted by widespread facts, then you can cheerfully say "I told you so because..."
Douglas

Steve provided 1038 hands worth of data and your response was sarcastic, as far as I can tell. When do you let the data "speak for itself?" Everything you've posted seems to involve your selecting things, rejecting things, assuming things not in evidence. I have been interested in what you have to say, but you have yet to build a convincing case about anything.

[jogs]

Post by Douglas

Post by p***@infi.net
You are still advocating counting four hands from one deal. Is it not obvious that once you have counted the first three hands, the fourth is deterministic, not random? Nor are the second and third independent from the first? All will tend to correspond to the expected patterns (whether expected for hand dealt or pseudo-random probabilities) but you cannot act as if you have 1000 hands worth of data from 250 deals.

Yes. How about for once you let the data speak for itself. If I am refuted by widespread facts, then you can cheerfully say "I told you so because..."
Douglas

Douglas, you completely missed Paul's point. Each deal is one and only one independent observation.
Of course, we don't really need any study to deduce that club players(average age of 72) will not be able to deal random hands.

[jogs]

Post by Steve Willner
I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

There are 39 possible patterns. 8 of them occur less than once every 10,000 deals. 4 more of them occur less than once every 1,000 deals.
Don't approach this test by testing patterns. Requires too large a dataset.

Test the frequency of voids, singletons, doubletons, etc.

[Douglas]

Post by Steve Willner

Post by Douglas
For each deal, merely count the most commonly expected three
hand-types; 4432, 5332, and 5431.

This seems less sensitive than the analysis I am doing, but it should
work if you have enough deals.
My data are different, though. I record the pattern of the hand I was
dealt. Expected probabilities of those distributions are known, and
"big" deviations would suggest non-random dealing. The problem is to
quantify "big" and turn it into a p value. I don't see why chi-square
isn't good enough for the purpose, though it might not be optimum.
I don't have all my deals entered yet, but for 1038 deals, I have

Post by Douglas
N 4432 4333 5332 4441 5422 5431 5521 5530 5440 6322 6331 6421 6511 6520 6430 5510
1038 229 103 168 33 122 116 30 10 16 68 31 41 10 5 16 1

(This omits all patterns with 7c or longer suits, but you can see how
many of them there will be.) Feel free to do any analysis you like.

I previously gave you advice about a simple way to test your accumulated bridge deals. Then you provided me with all that breakdown of your 1038 hands. I forgot to tell you how to do that quick determination of whether your deals are naturally random, or merely pseudo-random.

All You have to do is sum the occurrences for the the three most common hand-types: 4432, 5332, and 5431. From your data that is 229 + 168 + 116 = 513. Expected value (EV) = 1/2 of 1038 = 519.

This test has a single ruthless purpose. Are the test deals naturally random, or not. It does not envision any sort of statement about any bridge deals population parameter.

If, in at least 250 deals, there are more than the EV combined number of our three target hand-types which evaluate to a cumulative binomial p-value approaching one, those at least 250 deals are naturally occurring, or an exact emulation of such.

If, instead, we have a result like in this instance of something approaching 1/2, then the deals are pseudo-random. This distinction is starkly distinctive. It is primarily due to a previously unremarked upon characteristic of hand-type probability distribution.

I hope you can see that here the total occurrences are 6 less than EV, and therefor your 1038 deals are definitely pseudo-random. In my experience, rather ordinary pseudo-random.

It is just this simple.

Douglas

[KWSchneider]

If, instead, we have a result like in this instance of something approachin=
g 1/2, then the deals are pseudo-random. This distinction is starkly distin=
ctive. It is primarily due to a previously unremarked upon characteristic o=
f hand-type probability distribution.

Naturally random? Not sure I've ever heard that term.

ALL computer deals are pseudo-random - it's just a matter of degree. Even a 256 bit seed will not generate random deals since 52 does not divide evenly into 2^256 (Or any binary seed). While all deals can be produced, some deals are SLIGHTLY more likely than others.

If you are suggesting that hand-dealt deals are pseudo-random as well, I would agree - I could never accept that any deal from a deck that was shuffled a few times from a starting deck containing some degree of sorted cards (4 hands with suits, or suited tricks) could be anything but pseudo-random. This is evidenced in the tendency for hand-dealt deals to be flatter.

While there are websites like Random.org that purport to generate truly random numbers, to my knowledge none of the ACBL dealing engines have a hook into one of these.

Kurt

[Dave Flower]

Post by KWSchneider

If, instead, we have a result like in this instance of something approachin=
g 1/2, then the deals are pseudo-random. This distinction is starkly distin=
ctive. It is primarily due to a previously unremarked upon characteristic o=
f hand-type probability distribution.

Naturally random? Not sure I've ever heard that term.
ALL computer deals are pseudo-random - it's just a matter of degree. Even a 256 bit seed will not generate random deals since 52 does not divide evenly into 2^256 (Or any binary seed). While all deals can be produced, some deals are SLIGHTLY more likely than others.

This problem can be avoided by rejecting the seeds that make some deals slightly more likely.

Post by KWSchneider
If you are suggesting that hand-dealt deals are pseudo-random as well, I would agree - I could never accept that any deal from a deck that was shuffled a few times from a starting deck containing some degree of sorted cards (4 hands with suits, or suited tricks) could be anything but pseudo-random. This is evidenced in the tendency for hand-dealt deals to be flatter.
While there are websites like Random.org that purport to generate truly random numbers, to my knowledge none of the ACBL dealing engines have a hook into one of these.
Kurt
--
Posted by Mimo Usenet Browser v0.2.5
http://www.mimousenet.com/mimo/post

David Flower

[KWSchneider]

ALL computer deals are pseudo-random - it's just a matter of degree. Even=

a 256 bit seed will not generate random deals since 52 does not divide eve=
nly into 2^256 (Or any binary seed). While all deals can be produced, some =
deals are SLIGHTLY more likely than others.=20
This problem can be avoided by rejecting the seeds that make some deals sli=
ghtly more likely.

How can you possibly do this without introducing more non-randomness? This is oxymoronic - "Controlled randomness"...

Kurt

[Dave Flower]

Post by KWSchneider

ALL computer deals are pseudo-random - it's just a matter of degree. Even=

a 256 bit seed will not generate random deals since 52 does not divide eve=
nly into 2^256 (Or any binary seed). While all deals can be produced, some =
deals are SLIGHTLY more likely than others.=20
This problem can be avoided by rejecting the seeds that make some deals sli=
ghtly more likely.

How can you possibly do this without introducing more non-randomness? This is oxymoronic - "Controlled randomness"...
Kurt
--
Posted by Mimo Usenet Browser v0.2.5
http://www.mimousenet.com/mimo/post

I didn't make myself clear; suppose there are 15 possible bridge hands, and the random number seed can take 16 values, 0 to 15.
Simply ignore all occurrences of 15, 0 to 14 are then equally likely.

Of course, the numbers actually involved are much bigger, but the principle is the same

Dave Flower

[jogs]

Post by Dave Flower
This problem can be avoided by rejecting the seeds that make some deals slightly more likely.

What's all this about seeds? That's why there are predictable hand sets.

It is only necessary to seed once. Leave the deck in the last shuffled state. No need to ever seed the pseudo random generator again.

[Douglas]

Post by KWSchneider
Naturally random? Not sure I've ever heard that term.

Probably not. It is short for "naturally occurring equiprobable random" which is the best description I have to date to describe the result of fair coin tossing and recording, fair die rolling and recording, fair roulette wheel twirling and recording, fair lotto number generation and recording, etc. etc. etc. Each is a natural human activity in modern life. Fair hand-dealt bridge deals are of the same class of outcomes is what I am demonstrating to you in this thread.

Post by KWSchneider
ALL computer deals are pseudo-random - ...

But, they do not have to be! There is a bridge dealing computer program which has the current ability to deal naturally random deals. All it wants is a naturally random source of input numbers. That is currently not available anywhere, because of a truly catch 22 situation right out of Joseph Heller. It requires some historical explanation, and I do not want to bore you with the somewhat lengthy explanation here.

Post by KWSchneider
If you are suggesting that hand-dealt deals are pseudo-random as well, I would agree - I could never accept that any deal from a deck that was shuffled a few times from a starting deck containing some degree of sorted cards (4 hands with suits, or suited tricks) could be anything but pseudo-random. This is evidenced in the tendency for hand-dealt deals to be flatter.

I am suggesting quite the opposite. You, I, or anyone else cannot deal pseudo-randomly on our best, or worst, day. It is somewhat like us trying to write out random number sequences. I think studies have been done on that subject.

I prefer to leave each of you with your belief about whether us old people can somehow interfere with the course of natural randomness with our apparently feeble inadequate shuffling and dealing.

Post by KWSchneider
While there are websites like Random.org that purport to generate truly random numbers, to my knowledge none of the ACBL dealing engines have a hook into one of these.

I currently categorize pseudo-random into two parts:

1. Finite length.

2. Infinite length.

I am giving serious consideration to adding a third part. "Hybrid." It would set apart BigDeal and Microsoft's current software generator which mix pseudo-random with the injection of an outside entropy source. I just do not know enough about this area yet.

My other major category, of course, is naturally occurring equiprobable random.

In which category do you suppose I place so-called "true" random number sources like Random.org? There are quite a few of them by now.

Currently, I place them into the infinite length pseudo-random category based on their performance, not their claims. Of course, until now they have had no useful way to measure their performance. They have had to rely on extensive disqualification testing (NIST, Diehard, etc.) to try to prove a positive.

Douglas

[Steve Willner]

Post by KWSchneider
ALL computer deals are pseudo-random

That depends on your definition of "random." How it should be defined
is not obvious. I think there is still debate about that even in the
community of experts (math, not bridge).

Post by KWSchneider
Even a 256 bit seed will not generate random deals since 52 does not
divide evenly into 2^256 (Or any binary seed). While all deals can be
produced, some deals are SLIGHTLY more likely than others.

This turns out not to be the case, as Dave explained.

For anyone interested in computer bridge dealing, I suggest you start by
reading the documentation for Big Deal:
https://sater.home.xs4all.nl/doc.html

And by the way, if anyone reading this is responsible for preparing
deals for play, please don't use any program that is worse than Big
Deal. Big Deal is free and compatible with dealing machines.

Post by KWSchneider
I could never accept that any deal from a deck
that was shuffled a few times from a starting deck containing some
degree of sorted cards (4 hands with suits, or suited tricks) could
be anything but pseudo-random.

And "pseudo-random" is even more in need of a definition than "random."

Post by KWSchneider
This is evidenced in the tendency for
hand-dealt deals to be flatter.

What is your evidence that hand-dealt deals tend to be flatter? By what
margin? How does that square with the data I posted?

Post by KWSchneider
While there are websites like Random.org that purport to generate
truly random numbers, to my knowledge none of the ACBL dealing
engines have a hook into one of these.

Hardware random number generators have existed for decades. (I'm told
the old 1P21 photomultiplier was initially developed as a RNG.) I
gather hardware RNGs are now quite cheap, but I don't know any dealing
programs that use them. Random.org seems to be an equivalent idea, but
again I don't know of any dealer that uses it.

The ACBL dealer is terrible (as I think we recently discussed here),
though I have heard rumors it will soon be changed to something better
(possibly Big Deal).

[jogs]

Post by Steve Willner

Post by KWSchneider
ALL computer deals are pseudo-random

That depends on your definition of "random." How it should be defined
is not obvious. I think there is still debate about that even in the
community of experts (math, not bridge).

What debate? Software pseudo RNG are not random. They do have the appearance of randomness. It is an algorithm of a predetermined series. Each number generated is calculated from the previous number.

[p***@gmail.com]

Post by jogs
What debate? Software pseudo RNG are not random. They do have the appearance of randomness. It is an algorithm of a predetermined series. Each number generated is calculated from the previous number.

Holding a degree in statistics and probability, I can tell you that "random" simply means "unpredictable." It is subjective. If A can predict a sequence and B can't, then the sequence is random for B and not random for A.

Complete randomness is quite hard to achieve in everyday life. I'm sure that hand deals are not completely random. Indeed, there was a man (name forgotten) who was unbeatable in gin rummy. He could remember the sequence of cards played in the previous deal. This biased the odds of the cards that were likely to be drawn next from the deck, which gave him a big advantage.

[jogs]

Post by p***@gmail.com

Post by jogs
What debate? Software pseudo RNG are not random. They do have the appearance of randomness. It is an algorithm of a predetermined series. Each number generated is calculated from the previous number.

Holding a degree in statistics and probability, I can tell you that "random" simply means "unpredictable." It is subjective. If A can predict a sequence and B can't, then the sequence is random for B and not random for A.
Complete randomness is quite hard to achieve in everyday life. I'm sure that hand deals are not completely random. Indeed, there was a man (name forgotten) who was unbeatable in gin rummy. He could remember the sequence of cards played in the previous deal. This biased the odds of the cards that were likely to be drawn next from the deck, which gave him a big advantage.

https://en.wikipedia.org/wiki/Pseudorandom_number_generator

"also known as a deterministic random bit generator ".

[Steve Willner]

Post by p***@gmail.com
Holding a degree in statistics and probability, I can tell you that
"random" simply means "unpredictable." It is subjective. If A can
predict a sequence and B can't, then the sequence is random for B and
not random for A.

That's one possible definition. Other people would make "stochastic" a
requirement. Still others (see Kurt's article) make a distinction on
how the number was generated.

[KWSchneider]

Post by Steve Willner

Post by KWSchneider
ALL computer deals are pseudo-random

That depends on your definition of "random." How it should be defined
is not obvious. I think there is still debate about that even in the
community of experts (math, not bridge).

Random and Pseudo-Random numbers are defined very clearly and can be tested for verification. All one needs to do is read the NIST documentation I referenced earlier. There are two basic types of generators used to produce random sequences: random number generators (RNGs) and pseudorandom number generators (PRNGs).

An RNG uses a nondeterministic source (i.e., the entropy source), along with some processing function (i.e., the entropy distillation process) to produce randomness (unpredicability).

A PRNG uses one or more inputs and generates multiple ?pseudorandom? numbers. Inputs to PRNGs are called seeds. In contexts in which unpredictability is needed, the seed itself must be random and unpredictable.

HENCE - by definition, any deal based on a "seed" is pseudo-random. The goal, of course, is to create truly "random" pseudo-random numbers.

Post by Steve Willner

Post by KWSchneider
Even a 256 bit seed will not generate random deals since 52 does not
divide evenly into 2^256 (Or any binary seed). While all deals can be
produced, some deals are SLIGHTLY more likely than others.

This turns out not to be the case, as Dave explained.

My point to Dave, and to you, is that a reduction in bit length of an "overbit" seed (like Big Deal's 160 bit seed), introduces non-randomness when the seed is too "big". IMO this method of "tossing" out a non-inclusive result biases the results away from true randomness.

Post by Steve Willner
For anyone interested in computer bridge dealing, I suggest you start by
https://sater.home.xs4all.nl/doc.html
And by the way, if anyone reading this is responsible for preparing
deals for play, please don't use any program that is worse than Big
Deal. Big Deal is free and compatible with dealing machines.

Post by KWSchneider
I could never accept that any deal from a deck
that was shuffled a few times from a starting deck containing some
degree of sorted cards (4 hands with suits, or suited tricks) could
be anything but pseudo-random.

And "pseudo-random" is even more in need of a definition than "random."

See above for definition. A shuffled deck starts with a "seed" - essentially the layout of the cards before the deal - and an improperly shuffled deck after collecting tricks could converge to flatter hands. As an experiment, take a deck, deal and sort the hands into tricks. Stack the tricks, deal and repeat.

Post by Steve Willner

Post by KWSchneider
This is evidenced in the tendency for
hand-dealt deals to be flatter.

What is your evidence that hand-dealt deals tend to be flatter? By what
margin? How does that square with the data I posted?

It's been strictly anecdotal and represents my experience in the years before the advent of "computer dealing".

Post by Steve Willner

Post by KWSchneider
While there are websites like Random.org that purport to generate
truly random numbers, to my knowledge none of the ACBL dealing
engines have a hook into one of these.

Hardware random number generators have existed for decades.

No they haven't - they are "pseudo-random number generators" with a repeating pattern (not random). The only way to guarantee randomness is entropically.

Kurt

[Steve Willner]

Post by KWSchneider
Random and Pseudo-Random numbers are defined very clearly

Yes, there are clear definitions. The trouble is that are several of
them that don't agree. There are also unclear definitions. I think you
need some insight into the math world to appreciate this. I'm no
expert, but I've done a little reading and talked to experts.

Post by KWSchneider
and can be tested for verification.

You can test various statistical properties, but that can never verify
that a sequence is random. A test can prove a sequence is non-random or
at least unlikely to be random.

Post by KWSchneider
An RNG uses a nondeterministic source (i.e., the entropy source),

...

Post by KWSchneider
A PRNG uses one or more inputs and generates multiple ?pseudorandom?
numbers.

If the seed is random, isn't at least the first output of the PRNG random?

For practical generation of bridge deals, I don't see why the
distinction is important. What is important is that there are enough
bits of entropy to begin with and that the PRNG is cryptographically secure.

Post by KWSchneider
My point to Dave, and to you, is that a reduction in bit length of an
"overbit" seed (like Big Deal's 160 bit seed), introduces
non-randomness when the seed is too "big".

Please explain that. Big Deal uses a mapping from integers to bridge
deals. Why is any particular integer favored over any other?

SW> Hardware random number generators have existed for decades.

Post by KWSchneider
No they haven't

Look up the history of the 1P21, which was used in WW2. Also look up
the history of cryptography. How do you think "one time pads" were
generated?

Post by KWSchneider
- they are "pseudo-random number generators" with a
repeating pattern (not random).

The devices I mentioned do not repeat except by chance; they are true
hardware random number generators based on physical principles.

[jogs]

Post by Steve Willner
You can test various statistical properties, but that can never verify
that a sequence is random. A test can prove a sequence is non-random or
at least unlikely to be random.

The PRNG sequence is not random. It is a deterministic sequence. But it can pass a test as if it were random.

Post by Steve Willner
If the seed is random, isn't at least the first output of the PRNG random?

Stop reordering the deck. Leave the deck in a shuffled state.
Then there would be no need for a seed.

[KWSchneider]

A study of bridge club deals from these two UK towns was published in the U=
K many years ago, and some years later in the ACBL Bulletin. This study pur=
ported to demonstrate that a little more systematic care in shuffling bridg=
e deal cards would result in noticeably better bridge deals.
When evaluated with Pearson's 1900 Chi-square formula, the Abingdon deals r=
esult in an approaching zero result. The Witney deals evaluate to a close t=
o one value, indicating unusual, but not extraordinary, closeness to expect=
ed values. These differences are ascribed to the different shuffling treatm=
ent used by the Witney club members.
However, based on the same observed outcomes, but using actual probability =
(p-value) measuring evaluation, a rather more distinct statistical result v=
iew appears.
First, the Chi-square evaluation does not produce a p-value. Never has, nev=
er will. Its evaluation result does lie in the same zero to one range that =
p-values lie in, but it is better described in traditional statistics terms=
as a correlation value (not a coefficient). Correlation measurement is vag=
uer than proper p-value measurement.
The study reports how many of each of the ten most common hand-types there =
are for both clubs. Since there are 39 total hand-types, the other 29 total=
results can be calculated by subtracting from total hand-types (1,336) to =
create an eleventh other category.
For Abingdon, only the first category (4432), and our eleventh category hav=
e obvious significant meaning after determining each category's p-value. Th=
e odds against the first category occurring fairly are 56,150:1 (4.13 mean =
standard deviations). For the eleventh category, 78:1 (-2.24 mean standard =
deviations).=20
However, if we assume there was a transcription error of 20 (+/-5) too much=
in category one, then both p-values fall right into line with what can be =
expected from this kind of hand-dealt bridge deals evaluation.
The real surprise to me is the Witney results. It is not even remotely poss=
ible they where hand-dealt. They are so close to expected values for each c=
ategory that they exhibit not very good pseudo-randomness, and most likely =
were dealt by computer with one of those early limited-period pseudo-random=
number generators.
Douglas

NIST has a "Statistical Test Suite" (described in publication 800-22-rev1a, most recently revised APR 2010) that will provide randomness testing. As described in the paper, randomness is a probabilistic property - the properties of a random sequence can be characterized and described in terms of probability. The likely outcome of statistical tests, when applied to a truly random sequence, is known a priori and can be described in probabilistic terms.

There are an infinite number of possible statistical tests (many of which are described in the paper), each assessing the presence or absence of a ?pattern? which, if detected, would indicate that the sequence is nonrandom. But, because there are so many tests for judging whether a sequence is random or not, no specific finite set of tests is deemed ?complete.?

Consequently, any single method that you may choose to determine "randomness" is only a subset of a complete analysis, and provides in and of itself, only a statistical likelihood of randomness.

Kurt

[t***@att.net]

Even if computer-generated deals are pseudo-random, that does not preclude them being non-predictable and having the correct distribution. Trivial example: if it takes more than 1000 deals to break start predicting the next deals, the system is good enough for 999 deals.

[t***@att.net]

The statistical properties of a good pseudo-random-number-generator should not depend on the seed. It's always possible that "poor" seeds will be generated during the operation of the generator; seeds are just output values being input.

A good method of managing seeds is to use the clock time when the program starts (probably to a milli-second or the like) and other input (perhaps something entered by the used) as a seed. Of course one makes a copy of the seed used for debugging purposes. If the run is successful, that seed can be discarded.

[Douglas Newlands]

Post by t***@att.net
The statistical properties of a good pseudo-random-number-generator should not depend on the seed. It's always possible that "poor" seeds will be generated during the operation of the generator; seeds are just output values being input.
A good method of managing seeds is to use the clock time when the program starts (probably to a milli-second or the like) and other input (perhaps something entered by the used) as a seed. Of course one makes a copy of the seed used for debugging purposes. If the run is successful, that seed can be discarded.

Is it?
Let's count up day and date for milliseconds
2000 years
365 days per year
24 hours per day
3600 seconds per hour
1000 milliseconds per second
that gives you 0.6 x 10**14 starting values.
The number of bridge hands is 0.5 x 10**29 so the number
of starting points you get are 10**-15 of the space of all hands.

What are you going to add to get the number of starting points up
to the number of bridge hands?

doug
who is dipping a very cautious toe into the statistics swamp.

[Lorne Anderson]

Post by t***@att.net
The statistical properties of a good pseudo-random-number-generator
should not depend on the seed. It's always possible that "poor" seeds
will be generated during the operation of the generator; seeds are
just output values being input.
A good method of managing seeds is to use the clock time when the
program starts (probably to a milli-second or the like) and other
input (perhaps something entered by the used) as a seed. Of course
one makes a copy of the seed used for debugging purposes. If the run
is successful, that seed can be discarded.

Using the clock is an appaulingly bad way to create seeds and cannot
come close to generating bridge hands randomly. On a Windows machine a
seed generated from the clock can only generate 0.000000000000000008% of
all possible deals.

The best seed generator for Windows computers is the CryptGenRandom()
function:

https://en.wikipedia.org/wiki/CryptGenRandom

You also need to use a decent generator such as ISAAC or the Mersenne
Twister.

[t***@att.net]

The Windows seed generator is similar to what I described except that for not saving any of the original numbers. It will create the about twice number of seeds as just taking a clock time. It uses two clock streams that are somewhat independent (clock time and time since another clock started.) The purpose of the CryptGenRandom procedure is to create hidden seeds; I'm just trying to get seeds not dependent on my idea of what a seed should look like.

For these simulations, one of the Mersenne Twisters would be fine. A very long period Lehmer generator would work too. ISAAC would be poor; it's not designed for Monte Carlo stuff but rather it's an attempt to be unpredictable. The period is too short.

I'd probably generate deals using a quasi-Monte Carlo strategy. There are only 39 independent choices for dealing. (If one deals one hand at a time, the fourth hand is just the left-overs.) The deals are not independent of each other, but the cards within a deal are independent. The averages over deals converge much more rapidly than a Monte Carlo would. QMC isn't suitable for dealing hands for competition though.

If I get time, I'll look at this a bit more closely. It might be possible to just grab 52 two-bit numbers for hand assignment but there are some constraints; it's a bit like sampling an inverse-geometric distribution.

[t***@att.net]

One doesn't need a different starting number for each hand. One needs a different starting number for each simulation run. A simulation generates a sample and is valid if the proper distribution is sampled and the samples are independent.

What's necessary is a number that isn't picked by the experimenter. In debugging runs, the same starting number is obviously used for reproducibility. In real runs, one wants to remove unconscious bias. Note that were one playing a game, a seed is needed that is unpredictable. For this case, I usually use the clock time and a number put in by the player (more with several players) and something like the time between entering two numbers (which cannot be controlled to the precision of the time measurement); just have a player enter a number, wait for a prompt, then enter another number.

It's possible to get accurate results in with the same number streams but that takes us to the realm of quasi-Monte Carlo rather than simple simulations and isn't useful in playing against opponents. An entirely different type of error analysis is needed (and is often difficult to get.)

One point of this procedure is to quiet critics who may say, "You picked the seed numbers to get what you wanted."