Yarrow and coin simulator
Two methods dominate the tradition: the ancient yarrow-stalk procedure and the later three-coin method. They do not produce the numbers six, seven, eight and nine with the same probabilities.
The yarrow-stalk method
The Great Commentary says: 'The number of the great expansion is fifty; forty-nine are used. Divide them in two to represent the two; hang one to represent the three; count them off by fours to represent the four seasons; return the remainder between the fingers to represent the intercalary month.' In practice: take fifty stalks and set one aside; split the forty-nine at random into two heaps; take one stalk from the right heap and hold it between the fingers; count off both heaps in fours and place the remainders between the fingers. That is one 'change'. Repeat twice with the remaining stalks; three changes give one line. The stalks left after the third change, divided by four, give six, seven, eight or nine.
The three-coin method
Toss three coins at once; heads count 3, tails 2; the sum gives six, seven, eight or nine. Common since the Tang and Song dynasties, it is quick—but its probabilities are symmetrical.
Probabilities of the two methods
| Number | Yarrow | Coins |
|---|---|---|
| 6 old yin (changing) | 1/16 = 6.25% | 1/8 = 12.5% |
| 7 young yang | 5/16 = 31.25% | 3/8 = 37.5% |
| 8 young yin | 7/16 = 43.75% | 3/8 = 37.5% |
| 9 old yang (changing) | 3/16 = 18.75% | 1/8 = 12.5% |
The difference: with yarrow, old yang (nine) is three times as likely as old yin (six), so yang lines change more readily; with coins they are equally likely. An often-overlooked detail that shows the two traditions do not understand 'change' in exactly the same way.