Coins against yarrow stalks
The hidden probabilities of the oracle
Choose how many readings to simulate and compare coins against yarrow stalks bar by bar.
To consult the oracle you have to generate six lines, each in one of four states: young yang or young yin (static) and old yang or old yin (moving). The three coins give a symmetric distribution; the ancient method of the 49 yarrow stalks does not. The question: where does it show?
● = moving state · faint bar = static line
● = moving state · faint bar = static line
Where do the sixteenths of the yarrow come from? The experiment the ritual of the 49 stalks derives them step by step, with exact fractions.
| Quantity | Three coins | Yarrow (49 stalks) | Verdict |
|---|---|---|---|
| P(present line = yang) | 1/2 | 1/2 | identical |
| P(line moves) | 1/4 | 1/4 | identical |
| expected yang lines (present) | 3.00 | 3.00 | identical |
| among moving lines, share of old yang | 50% | 75% | different |
| expected yang lines (future) | 3.00 | 2.25 | ◆ different |
The present hexagram comes out identical in both methods: each line is yang with probability 1/2, so the 64 hexagrams are equiprobable. And the rate of change matches too: 1/4 per line. The yarrow only breaks the symmetry in the direction of the change: a moving line is 3 times more likely to be yang-falling-to-yin. Measurable consequence: the future hexagram leans towards yin (2.25 yang lines against 3.00).
With coins P(yang) = 1/2 on every line; with yarrow the line probabilities are 1/16, 3/16, 5/16 and 7/16. Both methods give P(yang) = 1/2, but a different proportion of old lines.
verificar_oraculoThe types of claim and the full bibliography (APA) are in Foundations.