p Statistics: Pokerhands
by JVSchmidt


General considerations
The Poker-Hands-Test (PHT) is a way to investigate the statistical behaviour of 5 digits long substrings. Therefore it completes the results from the direct digits frequence analysis.
To perform a PHT we divide all possible substrings into seven different classes which cover all possible digits combinations. The likelihood values for these combinations can be reached easily if every digit apperas with equal right.

CombinationDigit patternProbability for the combination
No two digits the sameabcde0,3024
One pairaabcd0,504
Two pairsaabbc0,108
Three of a kindaaabc0,072
Full houseaaabb0,009
Four of a kindaaaab0,0045
Five of a kindaaaaa0,0001

Analysis looks like this:
14159 - One pair
26535 - One pair
89793 - One pair
23846 - No the same
26433 - One pair
83279 - No the same
50288 - One pair
41971 - One pair
69399 - Three of a kind
37510 - No the same
etc.

Results
Number of analyzed digits: 4.2x109 digits
Number of analyzed poker hands: 840.000.000
Analysis started at digit: 1
Chi2-value for the Pokerhand statistic = 4,1849

Pokerhand
No the sameOne pair Two pairs Three of a kind Full house Four of a kind Five of a kind
Measured 254.035.567 423.350.199 90.718.132 60.476.965 7.556.107 3.779.020 84.010
Expected 254.016.000 423.360.000 90.720.000 60.480.000 7.560.000 3.780.000 84.000


The analysis of pokerhand was made in groups of 60 million hands each.
Beyond this the the starting point was moved from 1 to 6 to examine the dependance in this parameter.
More details you can find here(EXCEL-file): Download here

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