Casting the I Ching

What it is

The procedure for generating a hexagram: six lines, each determined one at a time from the bottom up, each turning out to be one of four values.

The four line types are the whole system, and they matter more than the labels suggest:

Value	Name	Line	Behaviour
6	old yin	broken	changing — becomes yang
7	young yang	solid	stable
8	young yin	broken	stable
9	old yang	solid	changing — becomes yin

A changing line transforms into its opposite, producing a second hexagram. The reading is the movement from the first to the second — which is why the book is called the Changes.

Where it came from

The yarrow stalk method is the older and is described in the Ten Wings commentaries. It uses fifty dried milfoil stalks.

The three-coin method appears much later, and is generally understood as a simplification for practitioners without stalks, time or patience.

How it is done

Yarrow. One stalk is set aside and takes no further part. The remaining forty-nine are divided at random into two heaps; one stalk is taken from the right heap and held; each heap is then counted off in fours, and the remainders are set aside. The residue is gathered and the whole operation repeated twice more. What remains after three operations determines one line. Eighteen operations produce a hexagram, and the whole thing takes perhaps twenty minutes.

Three coins. Throw three coins. Heads count three, tails two, by the usual modern convention. Sum them: 6, 7, 8 or 9, which is the line. Six throws produce a hexagram, in about a minute.

What we can and cannot say

We can say the two methods are not equivalent, and this is arithmetic rather than opinion.

The coin method is symmetric. Each line is the sum of three independent two-value throws, giving:

• 6 (changing yin) — 1 in 8
• 7 (young yang) — 3 in 8
• 8 (young yin) — 3 in 8
• 9 (changing yang) — 1 in 8

The yarrow procedure is not symmetric, because the counting-off of remainders does not weight the outcomes evenly:

• 6 (changing yin) — 1 in 16
• 7 (young yang) — 5 in 16
• 8 (young yin) — 7 in 16
• 9 (changing yang) — 3 in 16

Both give the same total probability of a changing line — a quarter. But they distribute it differently. Under yarrow, a changing yang line is three times as likely as a changing yin line. Under coins they are equally likely. Old yin, the most dramatic transformation in the system, is twice as rare with stalks as with coins.

So the same question, asked with the same sincerity on the same day, has measurably different odds of producing a given answer depending on which implement is to hand.

We can say the tradition has noticed and has not settled it. Traditionalists argue the yarrow asymmetry is meaningful — that yin is stable and slow to change, and the procedure encodes something true. Others treat the coin method as an acceptable approximation whose designers simply got the arithmetic wrong. Nobody can adjudicate, because there is no outcome to check against.

This is the same structural problem as the house systems in houses and aspects, and it is worth naming as a pattern: incompatible methods, materially different outputs, sincere practitioners on each side, and no procedure for discovering which is wrong.

We can say the modern proliferation makes it worse. Dice, random number generators, apps and web pages all cast hexagrams, mostly on the coin distribution, some on the yarrow one, and almost none tell the user which.

We can say the ritual conditions — ask once, ask sincerely, do not repeat the question hoping for a better answer — are unfalsifiable but not pointless. A rule against re-asking is a rule against shopping for the answer you wanted, which is a real discipline whatever it is grounded in.

We cannot say either method is right. What can be said is that a tradition holding that the method of consultation matters has made a testable internal claim, and that after two thousand years it remains untested.

Further reading

• The Ten Wings' account of the yarrow procedure, in Wilhelm/Baynes or any full edition.
• Analyses of the yarrow probability distribution are widely available; the arithmetic is straightforward and worth doing once yourself.