# Probabilities with coins and yarrow stalks

Some people have suggested that the method of consulting via coins is not as good as the yarrow rite because the yarrow's probabilities of yin and yang lines occurring is asymmetric, whereas it is symmetric in the coin ritual and therefore not representative of how it should be.

This is a fallacy, because although the original method of consulting the Yijing was by yarrow stalks the yarrow rite as we know it today is a late reconstruction (12th century) and is not necessarily performed as it was originally. The way to perform the original rite has been lost. In fact, the oldest extant method we have is the coin method. Where the yarrow rite really scores is that it is more meditative and encouraging of deeper contemplation, but as to whether yin and yang lines were originally intended to have differing chances of arising is quite unknown. To my thinking, their chances ought to be equal since they are polar opposites. In practice, of course, whatever method you use you obtain the hexagram you need. The maths of probability is a relatively late way of thinking and it is doubtful the originators of the Yijing consultation methods took it into account.

With coins, there is a one in eight chance of obtaining a moving yin or yang (i.e. they are equally likely), and a three in eight chance of obtaining a static yin or yang. Changing lines are less likely than static lines, which is why most times you get only one or two lines changing, though it is possible for all six to change.

With yarrow stalks, the probabilities are as follows, according to whether you obtain 6, 7, 8, or 9. I have put the equivalent coin probability in square brackets:

6 – moving yin: 1 in 16 [coin: 2 in 16]
7 – static yang: 5 in 16 [6 in 16]
8 – static yin: 7 in 16 [6 in 16]
9 – moving yang: 3 in 16 [2 in 16]

This is curious, because here a static yin has a slightly greater chance of occurring than a static yang, whereas a moving yang line is three times more likely to occur than a moving yin line (moving lines again being less likely than static lines). This does not seem to make as much sense as the probabilities inherent in the coin method, which at a glance look more 'evened out'. As for the original yarrow technique, it could well have had different probabilities to both of these methods. Suffice it to say, I have obtained meaningful oracles with both methods and, taking into account the fact that you are consulting an oracle, it seems misguided to get hung up over the probabilities of 'chance operations'. For further information on the reconstruction of the yarrow rite and probability, see Steve Moore's review of Stick Dice.

Tradition holds that Wang Xu, a Daoist recluse, invented the coin tossing method in the 4th century BCE. He is better known as Guiguzi, 'philosopher of the demon valley'. But there are many coin tossing methods and it's not certain that he invented the three-coin method for the Yijing particularly, more the idea of consulting by coin tossing. The three-coin method we have today is usually attributed to Ma Yi, circa 9th century CE.

The 50-stalk yarrow rite has been described many times, but the version [PDF] given in Greg Whincup's 'Rediscovering the I Ching' is the most sensible way to describe it since this makes clear how the numbers 6, 7, 8, and 9 are derived. Namely, if you ignore the stalks set aside in the three manipulations for each line and instead combine the two heaps you've been working with then the bundle will have 36, 32, 28, or 24 stalks. If you then count it off in groups of four you will lay out 9, 8, 7, or 6 small piles, directly giving you the line number (known as the xiang number, see Rutt pp 162–166, and also yaoshu).

Although yarrow divination is mentioned in the Zuozhuan, a chronicle of the period 722–468 BCE, the actual procedure is not described in that text.

### A brief note on the Zuozhuan

Legge's translation of the Zuozhuan – in 'The Chinese Classics', Vol. V, 1872 – is out of copyright and in the public domain. Much of the text pertaining to the yarrow divination stories was put on the web by Bro. Andrew Thornton for a course at Saint Anselm College. Legge's translation is somewhat turgid compared with the more recent translation of these same extracts in Zhouyi: The Book of Changes by Richard Rutt (pp 173–197). Rutt translates all 19 stories from the Zuo concerning hexagrams and in addition includes examples of Zhouyi divination found in the 5th century BCE Guoyu, the 'Discourses of the States'. Some of the Zuozhuan divination material was also translated by Kidder Smith in 'Harvard Journal of Asiatic Studies' 49 (1989): Zhouyi Interpretation from Accounts in the Zuozhuan [PDF]. See also Hellmut Wilhelm's paper from 'Journal of the American Oriental Society' 79 (1959): I-Ching Oracles in the Tso-chuan and the Kuo-yü [PDF].