# Coin Toss Probabilities and the I Ching

The I Ching often provides some interesting synchronicities when used as a method of divination or contemplation. Having recorded and analysed the results of Tarot readings for some time with the notion of trying to find statistical biases in the planetary and zodiacal themes of my results, I recently started to do the same thing with the I Ching to see if anything significant became apparent.

Since April 4th of this year, a total of 40 I Ching consultations have been recorded, resulting in the creation of a total of 68 Hexagrams (this includes those created from Changing Lines). These 40 readings led to the formation of 240 (as 40 x 6 = 240) lines, of which 122 (50.83%) were Yin lines and 118 (49.17%) were Yang. The proximity of these figures show the expected probability of 50/50 being very closely approximated.

The same can be said for the actual numbers of heads and tails thrown in these castings, in which three coins are thrown and given scores to produce the necessary Trigrams and Hexagrams. The scoring system works like this:

Changing Yin: 3 Tails = 6.
Yang: 2 Tails and 1 Head = 7
Yin: 2 Heads and 1 Tail = 8
Changing Yang: 3 Heads = 9.

With a Hexagram requiring 18 separate coins to be tossed (in batches of three), 40 different initial Hexagrams required a total of 720 coins being flipped. In my results, 378 (52.5%) of these coins came in as Heads and 342 (47.5%) came in as tails. While this varies a small amount from the expected 50/50 ratio, it’s still too close to be recognised as a skewed result.

Things become a little more complicated when analysing the probabilities of producing Changing and Unchanging Yin and Yang lines, but the expected probabilities for each of these expressed as fractions is:

6. Changing Yin: 1/8th.
7. Yang: 3/8ths.
8. Yin: 3/8ths.
9. Changing Yang: 1/8th.

With 240 lines being produced over those 40 readings, the expected count for each kind of Yin and Yang line would be:

6. Changing Yin: 30.
7. Yang: 90.
8. Yin: 90.
9. Changing Yang: 30.

(i.e. 30 + 90 + 90 + 30 = 240)

What was actually produced however, was:

Changing Yin: 20.
Yang: 90.
Yin: 102.
Changing Yang: 28.

This reveals that although the balance between Yin and Yang in total is about what it should be (see the second paragraph above), an imbalance of probabilities is notable around the Yin lines, with the Changing Yin Line appearing 33% less than it should and the Unchanging Yin Line appearing 13.3% more than it should. In total, Changing Lines should appear 25% of the time (as 1/8th + 1/8th = 1/4 = 25%), but in these results, due to the particularly large skew in results relating to the Changing Yin, the Changing Lines appear exactly 5% less than expected.

Is this significant, though? Well, almost. A skew of 5% is on the very cusp of what you could call significant in statistical terms so this doesn’t clearly represent what could be called ‘interference’ from the magical mechanisms that are supposed to lie behind such divinatory methods. I believe it would take at least 1,000 readings to reach what could be called a truly significant set of statistical results, but as this would probably take several years to complete, I can’t present anything solid and ‘scientific’ being expressed thus far.

However, at this early stage, the fact that most of the apparent skewing comes around both the Changing and Unchanging Yin lines can lead to a hypothesis being drawn about a possible synchronistic ‘interference’ (at least as far as my own results are concerned) coming from the Yin, the feminine aspect of the Tao.