Sunday, December 25, 2005

Probabilities and percentages in yarrow stalks consultation

Probabilities on divinations by yarrow and coins are occasionally discussed in forums and since one uses the yarrow stalks most of the time to divine, one decided to check and confirm its odds. Clearing the dust off the old journals was not a problem, but collating the information seems a bit tedious therefore one stopped after taking a random sample of 192 (64 hexagrams x 3) hexagrams obtained from early 1981 to the middle of 1987. Not much point in going through the rest of the journals I thought to collate divinations for a further eighteen years to 2005, if the statistics from the sample matches the published probabilities on yarrow consultation.

For those interested, Steve Marshall has a well written article on the probabilities on yarrow and coins in his Yijing Dao website. The published probabilities (one has converted them to percentages) for the yarrow are as follows:

6 -- x -- Moving yin 1 in 16 (6.25 %)
7 ------- Static yang 5 in 16 (31.25 %)
8 --- --- Static yin 7 in 16 (43.75 %)
9 ---o--- Moving yang 3 in 16 (18.75 %)

Since one did the sampling in three batches of 64 hexagrams, each batch showed a slight difference in the probabilities for the moving yin, static yang and yin, and the moving yang as follows:

6 Moving yin /7.55 % / 5.47 % / 7.03 %
7 Static yang /30.99 % / 31.25 % / 27.34 %
8 Static yin /40.89 % / 44.53 % / 47.66 %
9 Moving yang /20.57 % / 18.75 % / 17.97 %

From the above samples, the middle batch percentages about matches the published probabilities on yarrow consultation. Although the other two batches vary, the published probabilities are acceptable as a much larger sample was used by the publisher to even out the differentials.

What is of more interest is that a divination that uses yarrow stalks provides about three times more chances of obtaining a moving yang line than obtaining a moving yin line; whereas a coin divination provides an equal 12.5 % chance of getting either a yin or yang line that moves (or changes). This bias for moving yang lines over moving yin lines from the use of yarrow has been occasionally pointed out in forum discussions. Although it is proven true, do take cognizance of the fact that there are more static yin lines to compensate for fewer moving yin lines and that the total percentages for (both static and moving) yin and yang lines equal to 50 % each in the long run (see middle batch results as an example).

While on the subject of probabilities, from the random sample of 192 hexagrams spanning over six and half years, we would like to think that we can get all 64 hexagrams of the Yi at least once?

Well, it did not quite turn out that way. Two hexagrams that of Hexagram 53 Jian / Development and Hexagram 61 Zhong Fu / Inner Truth did not appear as answers to my questions until about five years later in 1992. Was that statistics or profoundness of the Yi? One would leave it to scholars and the experts to reason that out too.

Meanwhile we wait cheerfully.

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