Shufflix: Statistical Validation

Assorted statistical tests are run on output from Shufflix.  The purpose is to test whether the hands generated are indeed unbiased.

General Description of the Test Method Used

• 128 bits of random data acquired from www.random.org.  This fills the role of the entropy data gathered from /dev/urandom in the on-line verison of Shufflix.
• A systematically generated tournament name.
• The date 2001-12-31.
• The timestamp of the actual run of the dealing.

The chi² test yields a single number between zero and one, which can be taken as sort of measurement of how well the observations fit with the theoretically predicted results.   Large numbers (close to 1) denote a good fit while small numbers (close to 0) denote a bad fit.  A statistical test like this is often taken to be accepted at the 95% confidence level if the chi² number is greater than 0.05.  Note, however, that the distribution of the chi² statistic follows a uniform distribution between 0 and 1, so that one true result out of 20 is expected to be less than 0.05.

The statistical tests can be criticized for using one sample to generate several different statistics, since these different observations cannot be completely independent of each other.  For the time being, that will not be helped.

Results

Test name	Test description	chi2 statistic	observations	spreadsheet
n-pat	Pattern of North's hand, e.g. 5-5-2-1, 4-4-4-1.   4-4-3-2 is most likely.	0.29	n-pat.txt	n-pat.xls
d7-patt	Taking groups of four consecutive boards, who gets the  7, e.g. NNSW, EWEW.  All patterns are equally likely.	0.84	d7-patt.txt	d7-patt.xls
hcp	How many high card points does a randomly selected hand on each board have, e.g. 16 hcp, 3 hcp.  10 hcp is the most likely outcome.	0.83	hcp.txt	hcp.xls
8-card	Number of 8-cards suits held by West per 1000 hands.  The typical value is around 4.	0.73	8-card.txt	8-card.xls
void-hst	Number of boards with a void per runs of 36 boards.  The typical value is 6 or 7.		void-hst.txt
sa-c2	Who gets the A and the 2, e.g. E-E or N-S.  All 16 combinations are about equally likely, but combinations where the same hand gets both are a little less likely than those where different hands are involved.	0.26	sa-c2.txt	sa-c2.xls
di-acekg	Who gets theA and theK?  This is basically the same kind of test as above.	0.76	di-acekg.txt	di-acekg.xls
h-akq	Who gets the K when theAQJ are on the same hand?	0.67	h-aqj.txt	h-aqj.xls
split	When NS have exactly 8 s between them, how do the remaining 5 s split?	0.20	split.txt	split.xls

The results are fine so far.  Empty chi² values are given where the spreadsheet for the calculation is not made yet.  More statistics will appear later as they get processed.