Discussion:
Simplifying bridge deal stats
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Douglas
2017-02-22 03:18:25 UTC
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In prior postings to this group I showed you some 11 category statistical analyses of contract bridge hand types. It probably caused some eyes to glaze over.

I simplified those 11 categories into two somewhat logical (to me) categories of interest. I began with the bridge book theoretically expected probabilities for 4432 and 5332 bridge hands of about 21.5% and 15.5%. They are the most commonly expected hands when playing bridge. I think most bridge players experience them that way. Arguments are usually about whether they are too common, or not, when hand dealt, or computer dealt. I combined those two hand types into my first category because they are close to the first third of total expected book probability. They sum to about 37%.

I then created my second category by lumping all the lest common hand types together that came close to the last third of the total expected book probability. It turned out to be the last 34 out of the total 39 possible hand types. They ended summing to about 29%.

That leaves the 5431, 5422, and 4333 bridge hands to be my leftovers at about the middles 34% book probability. They have a neutral analysis effect, and I therefore ignore.

There is an Internet site "playbridge.com" with a tab "Shuffle Project" which displays the most extensive data set of bridge hand-type distributions I am aware of to date. More than 22.5 billion hands accumulated since summer 2011.

This is now early evening Feb 21, 2017 Pacific coast U.S.A. time, and their total hands are listed as 22,523,319,200. I need to fix that number because they add hands at unspecified times.

Here are my two accumulated category totals from the column "Total Hands."

Cat 1: 8,348,895,202
Cat 2: 6,505,902,781

Here are my expected hands calculated using their "ACBL Percentage" values.

Cat 1: 8,348,943,961
Cat 2: 6,505,973,368

The statistical distance, measured in standard normal deviations, between the two Cat 1 amounts, and the two Cat 2 amounts, if correctly significant, determines true non-deterministic random bridge dealing. Period.

I give those of you who think you know basic statistics a few days time to come up with an accurate evaluation of this given categorical number data. I think you will find it an unexpected challenge.

Douglas
p***@infi.net
2017-02-22 15:57:21 UTC
Permalink
Post by Douglas
In prior postings to this group I showed you some 11 category statistical analyses of contract bridge hand types. It probably caused some eyes to glaze over.
I simplified those 11 categories into two somewhat logical (to me) categories of interest. I began with the bridge book theoretically expected probabilities for 4432 and 5332 bridge hands of about 21.5% and 15.5%. They are the most commonly expected hands when playing bridge. I think most bridge players experience them that way. Arguments are usually about whether they are too common, or not, when hand dealt, or computer dealt. I combined those two hand types into my first category because they are close to the first third of total expected book probability. They sum to about 37%.
I then created my second category by lumping all the lest common hand types together that came close to the last third of the total expected book probability. It turned out to be the last 34 out of the total 39 possible hand types. They ended summing to about 29%.
That leaves the 5431, 5422, and 4333 bridge hands to be my leftovers at about the middles 34% book probability. They have a neutral analysis effect, and I therefore ignore.
There is an Internet site "playbridge.com" with a tab "Shuffle Project" which displays the most extensive data set of bridge hand-type distributions I am aware of to date. More than 22.5 billion hands accumulated since summer 2011.
This is now early evening Feb 21, 2017 Pacific coast U.S.A. time, and their total hands are listed as 22,523,319,200. I need to fix that number because they add hands at unspecified times.
Here are my two accumulated category totals from the column "Total Hands."
Cat 1: 8,348,895,202
Cat 2: 6,505,902,781
Here are my expected hands calculated using their "ACBL Percentage" values.
Cat 1: 8,348,943,961
Cat 2: 6,505,973,368
The statistical distance, measured in standard normal deviations, between the two Cat 1 amounts, and the two Cat 2 amounts, if correctly significant, determines true non-deterministic random bridge dealing. Period.
I give those of you who think you know basic statistics a few days time to come up with an accurate evaluation of this given categorical number data. I think you will find it an unexpected challenge.
Douglas
We can get an approximate 95% margin of error for the expected number of hands in each category as sqrt(n) (1/sqrt(n)*n). For a sample size of 22.5 billion, we expect the totals to be within 150,000 of the theoretical values. They are. We cannot reject the null hypothesis that the hands conform to the theoretical probablities.
Douglas
2017-02-23 07:31:03 UTC
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Post by p***@infi.net
We can get an approximate 95% margin of error for the expected number of hands in each category as sqrt(n) (1/sqrt(n)*n). For a sample size of 22.5 billion, we expect the totals to be within 150,000 of the theoretical values. They are. We cannot reject the null hypothesis that the hands conform to the theoretical probablities.
Interesting approximation. I make it about 35,550 too much interval for category 1, and about 45,100 too much interval for Category 2. Of course, I am working with one-sided stats, and I am pretty certain you are assuming two-sided. Even so, this seems a bit much.

We agree about the conclusion as it happens. These particular facts do not result in critical values in either category.

I am going to wait a bit more to see if anyone else finds the challenge in doing basic stats with such lengthy numbers.

Douglas
Douglas
2017-02-24 15:04:52 UTC
Permalink
Post by Douglas
In prior postings to this group I showed you some 11 category statistical analyses of contract bridge hand types. It probably caused some eyes to glaze over.
I simplified those 11 categories into two somewhat logical (to me) categories of interest. I began with the bridge book theoretically expected probabilities for 4432 and 5332 bridge hands of about 21.5% and 15.5%. They are the most commonly expected hands when playing bridge. I think most bridge players experience them that way. Arguments are usually about whether they are too common, or not, when hand dealt, or computer dealt. I combined those two hand types into my first category because they are close to the first third of total expected book probability. They sum to about 37%.
I then created my second category by lumping all the lest common hand types together that came close to the last third of the total expected book probability. It turned out to be the last 34 out of the total 39 possible hand types. They ended summing to about 29%.
That leaves the 5431, 5422, and 4333 bridge hands to be my leftovers at about the middles 34% book probability. They have a neutral analysis effect, and I therefore ignore.
There is an Internet site "playbridge.com" with a tab "Shuffle Project" which displays the most extensive data set of bridge hand-type distributions I am aware of to date. More than 22.5 billion hands accumulated since summer 2011.
This is now early evening Feb 21, 2017 Pacific coast U.S.A. time, and their total hands are listed as 22,523,319,200. I need to fix that number because they add hands at unspecified times.
Here are my two accumulated category totals from the column "Total Hands."
Cat 1: 8,348,895,202
Cat 2: 6,505,902,781
Here are my expected hands calculated using their "ACBL Percentage" values.
Cat 1: 8,348,943,961
Cat 2: 6,505,973,368
The statistical distance, measured in standard normal deviations, between the two Cat 1 amounts, and the two Cat 2 amounts, if correctly significant, determines true non-deterministic random bridge dealing. Period.
I give those of you who think you know basic statistics a few days time to come up with an accurate evaluation of this given categorical number data. I think you will find it an unexpected challenge.
Douglas
If you look at the 22.5 million hand result table for playbridge.com, you could easily get the impression those results are very close to their expected amounts. There are very tiny percentage differences in every case. However, you might keep in mind a tiny percentage of a very large amount is usually a substantial amount in its own right.

My Cat 1 variate difference is <48,759> which evaluates to a cumulative binomial probability of about 23.0%, and that transforms to about <0.74> standard normal deviation from our expected mean (SDem). If this result where truly non-deterministic, SDem would exceed about 1.64. Because we have a minus result, and expect a positive result, we need to sum the absolute SDem's for a final statistical distance of 2.38 SD units. This is a very poor result, particularly in light of the humongous sample size.

My Cat 2 variate difference is <70,587> which evaluates to a cumulative binomial probability of about 12.7%, and that transforms to about <1.14> SDem. If this result where truly non-deterministic, SDem would be less than about <1.64>. This SDem shortage of about <0.50> at least is oriented in the correct negative direction.

This particular site fails badly as regards to 4432 and 5332 hands. It clearly uses a deficient artificial random number generator source if real-world bridge dealing emulation is its goal.

Douglas
p***@infi.net
2017-02-25 22:28:46 UTC
Permalink
Post by Douglas
Post by Douglas
In prior postings to this group I showed you some 11 category statistical analyses of contract bridge hand types. It probably caused some eyes to glaze over.
I simplified those 11 categories into two somewhat logical (to me) categories of interest. I began with the bridge book theoretically expected probabilities for 4432 and 5332 bridge hands of about 21.5% and 15.5%. They are the most commonly expected hands when playing bridge. I think most bridge players experience them that way. Arguments are usually about whether they are too common, or not, when hand dealt, or computer dealt. I combined those two hand types into my first category because they are close to the first third of total expected book probability. They sum to about 37%.
I then created my second category by lumping all the lest common hand types together that came close to the last third of the total expected book probability. It turned out to be the last 34 out of the total 39 possible hand types. They ended summing to about 29%.
That leaves the 5431, 5422, and 4333 bridge hands to be my leftovers at about the middles 34% book probability. They have a neutral analysis effect, and I therefore ignore.
There is an Internet site "playbridge.com" with a tab "Shuffle Project" which displays the most extensive data set of bridge hand-type distributions I am aware of to date. More than 22.5 billion hands accumulated since summer 2011.
This is now early evening Feb 21, 2017 Pacific coast U.S.A. time, and their total hands are listed as 22,523,319,200. I need to fix that number because they add hands at unspecified times.
Here are my two accumulated category totals from the column "Total Hands."
Cat 1: 8,348,895,202
Cat 2: 6,505,902,781
Here are my expected hands calculated using their "ACBL Percentage" values.
Cat 1: 8,348,943,961
Cat 2: 6,505,973,368
The statistical distance, measured in standard normal deviations, between the two Cat 1 amounts, and the two Cat 2 amounts, if correctly significant, determines true non-deterministic random bridge dealing. Period.
I give those of you who think you know basic statistics a few days time to come up with an accurate evaluation of this given categorical number data. I think you will find it an unexpected challenge.
Douglas
If you look at the 22.5 million hand result table for playbridge.com, you could easily get the impression those results are very close to their expected amounts. There are very tiny percentage differences in every case. However, you might keep in mind a tiny percentage of a very large amount is usually a substantial amount in its own right.
My Cat 1 variate difference is <48,759> which evaluates to a cumulative binomial probability of about 23.0%, and that transforms to about <0.74> standard normal deviation from our expected mean (SDem). If this result where truly non-deterministic, SDem would exceed about 1.64. Because we have a minus result, and expect a positive result, we need to sum the absolute SDem's for a final statistical distance of 2.38 SD units. This is a very poor result, particularly in light of the humongous sample size.
My Cat 2 variate difference is <70,587> which evaluates to a cumulative binomial probability of about 12.7%, and that transforms to about <1.14> SDem. If this result where truly non-deterministic, SDem would be less than about <1.64>. This SDem shortage of about <0.50> at least is oriented in the correct negative direction.
This particular site fails badly as regards to 4432 and 5332 hands. It clearly uses a deficient artificial random number generator source if real-world bridge dealing emulation is its goal.
Douglas
As with many of your posts, I don't know what you are talking about: "variate difference" "truly non-deterministic" "final statistical distance." But you repeatedly mention summing standard deviations, which simply cannot be added together in any sense I am aware of. You can sum variances, and take the square root to obtain a combined standard deviation.
jogs
2017-02-25 23:54:36 UTC
Permalink
Post by p***@infi.net
Post by Douglas
If you look at the 22.5 million hand result table for playbridge.com, you could easily get the impression those results are very close to their expected amounts. There are very tiny percentage differences in every case. However, you might keep in mind a tiny percentage of a very large amount is usually a substantial amount in its own right.
My Cat 1 variate difference is <48,759> which evaluates to a cumulative binomial probability of about 23.0%, and that transforms to about <0.74> standard normal deviation from our expected mean (SDem). If this result where truly non-deterministic, SDem would exceed about 1.64. Because we have a minus result, and expect a positive result, we need to sum the absolute SDem's for a final statistical distance of 2.38 SD units. This is a very poor result, particularly in light of the humongous sample size.
My Cat 2 variate difference is <70,587> which evaluates to a cumulative binomial probability of about 12.7%, and that transforms to about <1.14> SDem. If this result where truly non-deterministic, SDem would be less than about <1.64>. This SDem shortage of about <0.50> at least is oriented in the correct negative direction.
This particular site fails badly as regards to 4432 and 5332 hands. It clearly uses a deficient artificial random number generator source if real-world bridge dealing emulation is its goal.
Douglas
As with many of your posts, I don't know what you are talking about: "variate difference" "truly non-deterministic" "final statistical distance." But you repeatedly mention summing standard deviations, which simply cannot be added together in any sense I am aware of. You can sum variances, and take the square root to obtain a combined standard deviation.
You are correct. One can sum variances, not std dev.
I also suspect Douglas does not understand statistics.

Programmers have known how to write pseudo random generators for over 50 years. Also know how to properly simulate the shuffling of a deck of cards.
There is no need to test any of this.
Douglas
2017-02-26 01:05:28 UTC
Permalink
Post by p***@infi.net
Post by Douglas
Post by Douglas
In prior postings to this group I showed you some 11 category statistical analyses of contract bridge hand types. It probably caused some eyes to glaze over.
I simplified those 11 categories into two somewhat logical (to me) categories of interest. I began with the bridge book theoretically expected probabilities for 4432 and 5332 bridge hands of about 21.5% and 15.5%. They are the most commonly expected hands when playing bridge. I think most bridge players experience them that way. Arguments are usually about whether they are too common, or not, when hand dealt, or computer dealt. I combined those two hand types into my first category because they are close to the first third of total expected book probability. They sum to about 37%.
I then created my second category by lumping all the lest common hand types together that came close to the last third of the total expected book probability. It turned out to be the last 34 out of the total 39 possible hand types. They ended summing to about 29%.
That leaves the 5431, 5422, and 4333 bridge hands to be my leftovers at about the middles 34% book probability. They have a neutral analysis effect, and I therefore ignore.
There is an Internet site "playbridge.com" with a tab "Shuffle Project" which displays the most extensive data set of bridge hand-type distributions I am aware of to date. More than 22.5 billion hands accumulated since summer 2011.
This is now early evening Feb 21, 2017 Pacific coast U.S.A. time, and their total hands are listed as 22,523,319,200. I need to fix that number because they add hands at unspecified times.
Here are my two accumulated category totals from the column "Total Hands."
Cat 1: 8,348,895,202
Cat 2: 6,505,902,781
Here are my expected hands calculated using their "ACBL Percentage" values.
Cat 1: 8,348,943,961
Cat 2: 6,505,973,368
The statistical distance, measured in standard normal deviations, between the two Cat 1 amounts, and the two Cat 2 amounts, if correctly significant, determines true non-deterministic random bridge dealing. Period.
I give those of you who think you know basic statistics a few days time to come up with an accurate evaluation of this given categorical number data. I think you will find it an unexpected challenge.
Douglas
If you look at the 22.5 million hand result table for playbridge.com, you could easily get the impression those results are very close to their expected amounts. There are very tiny percentage differences in every case. However, you might keep in mind a tiny percentage of a very large amount is usually a substantial amount in its own right.
My Cat 1 variate difference is <48,759> which evaluates to a cumulative binomial probability of about 23.0%, and that transforms to about <0.74> standard normal deviation from our expected mean (SDem). If this result where truly non-deterministic, SDem would exceed about 1.64. Because we have a minus result, and expect a positive result, we need to sum the absolute SDem's for a final statistical distance of 2.38 SD units. This is a very poor result, particularly in light of the humongous sample size.
My Cat 2 variate difference is <70,587> which evaluates to a cumulative binomial probability of about 12.7%, and that transforms to about <1.14> SDem. If this result where truly non-deterministic, SDem would be less than about <1.64>. This SDem shortage of about <0.50> at least is oriented in the correct negative direction.
This particular site fails badly as regards to 4432 and 5332 hands. It clearly uses a deficient artificial random number generator source if real-world bridge dealing emulation is its goal.
Douglas
As with many of your posts, I don't know what you are talking about: "variate difference" "truly non-deterministic" "final statistical distance." But you repeatedly mention summing standard deviations, which simply cannot be added together in any sense I am aware of. You can sum variances, and take the square root to obtain a combined standard deviation.
I am getting somewhat familiar with your arguing style by now. Here you begin by exaggerating points, and then follow by demonstrating your ignorance as proof of my incorrectness.

It is absolutely true that summing standard deviations does not makes sense. However, you do seem to realize that when you create a confidence interval, something you seem to like to do, you are also summing "standard deviations from some mean." I assume you are familiar with depictions of a normal curve. When you start at the left at <1.96> and move right to 1.96 to create an interval representing 0.95 cumulative probability, it can be proper to refer to that interval as a total 3.92 standard normal deviations from the mean (In this instance the mean being zero), and I call that a statistical distance.

Another lesser point: You who does not know the intrinsic difference between constrained numbers, and independent numbers, is in poor position to pretend not to know what "non-deterministic" is. Hint: It has something to do with the concept "independence."

Douglas

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