Vampyr, on 2017-April-03, 15:25, said:
Well, this hand
9♠, T98765432♥, Q3♦, 9♣
is no more or less improbable than any other hand, but anyway there is no reason to suspect that the other hands will have unusual distribution. You have been told this already.
Should I have used the term expected frequency?
The following mathematical tables may/can/are used to determine the percentages of various distribution patterns, both for hand patterns and suit patterns.
The numbers are expressed in percentage of hands. The percentage expectation of a particular pattern with the suits identified is expressed in the last column
Probable Percentage Frequency of Distribution Patterns
Pattern Total Specific
4-4-3-2 21.5512 1.796
4-3-3-3 10.5361 2.634
4-4-4-1 2.9932 0.748
5-3-3-2 15.5168 1.293
5-4-3-2 12.9307 0.539
5-4-2-2 10.5797 0.882
5-5-2-1 3.1739 0.264
5-4-4-0 1.2433 0.104
5-5-3-0 0.8952 0.075
6-3-2-2 5.6425 0.470
6-4-2-1 4.7021 0.196
6-3-3-1 3.4482 0.287
6-4-3-0 1.3262 0.055
6-5-1-1 0.7053 0.059
6-5-2-0 0.6511 0.027
6-6-1-0 0.0723 0.006
7-3-2-1 1.8808 0.078
7-2-2-2 0.5129 0.128
7-4-1-1 0.3918 0.033
7-4-2-0 0.3617 0.015
7-3-3-0 0.2652 0.022
7-5-1-0 0.1085 0.005
7-6-0-0 0.0056 0.0005
8-2-2-1 0.1924 0.016
8-3-1-1 0.1176 0.010
8-3-2-0 0.1085 0.005
8-4-1-0 0.052 0.002
8-5-0-0 0.0031 0.0003
9-2-1-1 0.0178 0.001
9-3-1-0 0.0100 0.0004
9-2-2-0 0.0082 0.0007
9-4-0-0 0.0010 0.00008
10-2-1-0 0.0011 0.00004
10-1-1-1 0.0004 0.0001
10-3-0-0 0.00015 0.00001
11-1-1-0 0.00002 0.000002
11-2-0-0 0.00001 0.000001
12-1-0-0 0.0000003 0.00000003
13-0-0-0 0.0000000006 0.0000000002
RedSpawn asked what is the probability of getting the following hand. Vampyr said and I quote, "Well, this hand [9♠, T98765432♥, Q3♦, 9♣] is no more or less improbable than any other hand."
I see ....each hand is its own unique occurrence out of the total bridge population. The total number of possible Bridge hands is 635,013,559,600 so that hand is 1/635,013,559,600 combinations. . . .that is slick because that is not what I really meant.
I should have said, "What is the expected frequency for a 9-2-1-1 shape hand". That is a more pointed and exacting question which still involves math but stops the unnecessary choreography we are performing over semantics.
As can be seen in the table above the expected frequency of getting a 9-2-1-1 hand pattern is .001% of total hand patterns available. Just for fun, the expected frequency of getting a 13-0-0-0 is 0.0000000002% of total hand patterns available. Also, the table supports the understanding that 4-3-3-3 and 4-4-3-2 are the most frequently occurring hand patterns in the total # of bridge hands available.
Therefore, each hand pattern has different expected frequencies because the # of hand patterns available to fit the requested hand pattern criteria decreases as the suit in question gets longer.
Math! Go figure. We have distilled this discussion to semantics -- "expected frequency" versus "probability"
For your reading pleasure, I have also included a similar table discussing mathematical expected frequencies of hand patterns.
Hand Patterns Frequencies