Coins vs Yarrow
Compare the three-coin and conventional yarrow-stalk procedures, their 6–9 probability distributions, and the limits of what either method can claim.
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Two procedures, four line values
Both procedures build six lines from bottom to top and return one of four values each time: 6 is moving yin, 7 is stable yang, 8 is stable yin, and 9 is moving yang. The procedures differ in their actions and distributions, not in the line vocabulary or the six-line structure they produce.
The three-coin procedure
Assign one face of each coin the value 2 and the other the value 3, then keep that assignment fixed. Toss all three coins, add the values, and record the total as the next line. Repeat six times from the bottom line upward. Under the fair, independent coin model, the totals 6, 7, 8, and 9 have probabilities 1/8, 3/8, 3/8, and 1/8.
The conventional yarrow procedure
Begin with 50 stalks, set one aside, and work with 49. Divide the working stalks, count in fours, and set aside the prescribed remainders. Three changes determine one line; six lines require eighteen changes. This executable form was reconstructed and systematized by Zhu Xi in the twelfth century from the fragmentary account in the Xici. That history does not establish every operational detail as unchanged from antiquity.
Eighteen changes does not mean eighteen moving lines
The word change names two different things here. In the stalk procedure, three counting operations complete one line, so eighteen complete the six-line figure. After that, the resulting values tell you which of the six positions move: only a 6 or a 9 changes polarity. A full stalk procedure can therefore produce a cast with no moving lines at all. Zhu Xi’s account discusses the construction procedure and the subsequent choice of reading text separately.
The conventional distributions
The coin model distributes 6, 7, 8, and 9 as 1/8, 3/8, 3/8, and 1/8. The conventional yarrow model distributes them as 1/16, 5/16, 7/16, and 3/16. These are exact results of the stated mathematical models. Physical coins or hand divisions can depart from those fractions; a finite set of casts is not expected to reproduce them exactly.
- 6Moving yinCoins12.5%Yarrow6.25%
- 7Stable yangCoins37.5%Yarrow31.25%
- 8Stable yinCoins37.5%Yarrow43.75%
- 9Moving yangCoins12.5%Yarrow18.75%
What actually differs
In both models, yin and yang each total 1/2 and a moving line totals 1/4. The difference is directional: coins make moving yin and moving yang equally likely, while the conventional yarrow model makes moving yang three times as likely as moving yin. That changes how often the four line values occur. It does not make either method truer or more authoritative.
Choose by fit, not authority
Coins require less time and equipment; the physical yarrow procedure has more steps. More steps do not make a reading more accurate, more spiritual, or better for decisions. The current public IChingAsk flow uses the coin profile. The core also contains a direct yarrow probability-profile sampler, but it does not simulate 49 stalks, hand divisions, or eighteen changes.
Sources 5
What this guide rests on
- On Consulting the Oracle — Kenyon College course resource hosted by Joseph A. Adler. The three-coin values, six bottom-up throws, and moving-line construction.
- Introduction to the Study of the Changes (Yixue qimeng) — Zhu Xi; translated by Joseph A. Adler. The reconstructed yarrow-stalk procedure, conventional frequency model, and moving-line focus rules with their stated limits.
- Divination in Ancient China — D. Robinson, Journal of the Royal Statistical Society: Series C. The conventional 6–9 probability distributions for three coins and yarrow stalks; not evidence that every physical cast is unbiased.
- Zhouyi, Xici A9 — Received text in Zhouyi zhengyi, Chinese Wikisource witness. Primary witness for the fifty-stalk, forty-nine-used passage and abbreviated operations; not a complete executable modern procedure.
- Zhouyi benyi, with Yixue qimeng (Original Meaning and Introduction to the Study of the Changes) — Zhu Xi. Qian, Zhun, and Kan commentary, plus the Ming shi ce and Kao bian zhan sections on yarrow procedure and changing-line focus.
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