Douglas
2017-02-22 03:18:25 UTC
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
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