Yarrow Stalk Algorithms Compared: Five Steps, Different Odds
Yarrow stalk algorithms compared: how five casting steps shift line odds, which numbers to record, and what to check before buying a book, course, or app.
Answer First
Yarrow stalk algorithms compared step by step show that five procedural choices — the set-aside, the left-right division, the remainders, the bundles removed, and the 6-7-8-9 mapping — determine your line odds. Most books, courses, and apps teach one variant silently; recording which one you used keeps your consultation log honest.
Definition: The yarrow stalk method is the I Ching divination procedure in which fifty yarrow stalks are handled through three divisions to produce one hexagram line numbered 6, 7, 8, or 9. An algorithm here is simply the exact rule set: which stalks are set aside first, how the remaining stalks are split into two heaps, how remainders are counted by fours, which bundles are removed, and how the final count is mapped to a line number.
Why: Small procedural differences change the probability of each line type. Before you trust the odds printed in a book or app, and before you interpret a moving line, you should know which variant produced it.
Example: Under the standard model, the classic procedure yields 6 (old yin) 1/16 of the time, 7 (young yang) 5/16, 8 (young yin) 7/16, and 9 (old yang) 3/16. A simplified variant that skips the held stalk changes those totals, and a coin procedure equivalent to the yarrow method — the one Edward A. Hacker presented in 1980 — reproduces the same odds with coins instead of stalks.
Key Facts
This yarrow stalk algorithms compared keeps documented facts separate from interpretive tradition.
Before the tables, one framing helps: yarrow stalk algorithms compared this way are arithmetic, not prophecy — the odds follow from the counting rules.
- The classic procedure starts with 50 stalks, sets one aside, and works with 49.
- Three divisions produce one line; six lines produce one hexagram.
- After three divisions the stalks in hand total 24, 28, 32, or 36, mapped to 6, 7, 8, and 9.
- Lines 6 and 9 are moving (changing) lines; 7 and 8 are stable.
- The classic distribution under the standard model: 6 at 1/16, 7 at 5/16, 8 at 7/16, 9 at 3/16; a changing line appears one time in four.
- The three-coin method gives 1/8, 3/8, 3/8, 1/8; a two-coin variant circulated in some modern manuals gives each line one time in four.
- Predictive interpretations are culturally meaningful but not validated by scientific testing as reliable forecasts.
Table 1. The five steps, the classic rule, and what changes the odds
| Step | Classic rule | Common deviation | Effect on the odds |
|---|---|---|---|
| 1. Initial set-aside | 50 stalks; set one aside; cast with 49 | Begin with 49 directly, or change the total | First-division totals stop being 5 and 9; every downstream probability shifts |
| 2. Left-right division | Split the 49 into two heaps; hold one stalk from the right heap between your fingers | Take the held stalk from the left heap, or skip it | The 5/9 (first) and 4/8 (later) totals no longer hold |
| 3. Remainder count | Count each heap by fours; a full bundle of four counts as remainder 4 | Count a full bundle as 0 | First-division totals become 4 and 8; the odds change |
| 4. Bundles removed | Set aside the held stalk plus both remainders each division | Remove only the remainders | A different count remains in hand; the line numbers change |
| 5. Numerical mapping | 24→6, 28→7, 32→8, 36→9 | Assign the numbers differently | Same stalks, different line labels; the changing-line rate changes |
Table 2. Line probabilities by method
| Method | 6 (old yin) | 7 (young yang) | 8 (young yin) | 9 (old yang) | Changing line |
|---|---|---|---|---|---|
| Yarrow stalk, standard model | 1/16 | 5/16 | 7/16 | 3/16 | 1/4 |
| Coin equivalent to yarrow (Hacker, 1980) | 1/16 | 5/16 | 7/16 | 3/16 | 1/4 |
| Three-coin method | 1/8 | 3/8 | 3/8 | 1/8 | 1/4 |
| Two-coin variant | 1/4 | 1/4 | 1/4 | 1/4 | 1/2 |
Expert Explanation
The first thing to notice when yarrow stalk algorithms compared is that every variant shares the same five-step skeleton. What differs is the rule chosen inside each step, and each choice moves the odds.
Step 1: The initial set-aside
The traditional account begins with fifty stalks, of which one is set aside, leaving forty-nine for the divination. The “Yarrow Stalk Method” chapter in Chinese Leadership Wisdom from the Book of Change (Chinese University of Hong Kong Press, 2020) presents this procedure within the Book of Change tradition on pages 443–448. The number matters arithmetically: 49 is one more than a multiple of four, which is what makes the first division’s totals come out as 5 or 9 and the later divisions’ totals as 4 or 8. A variant that starts with a different count, or skips the set-aside, breaks that pattern and produces a different distribution.
Step 2: The left-right division and the held stalk
The 49 stalks are divided into two heaps — traditionally a left heap and a right heap — and one stalk is taken from the right heap and held between the fingers. This held stalk is not discarded; it becomes part of the removed bundle at the end of the division. Variants differ on which heap the stalk comes from, whether it is taken before or after the split, and whether it is taken at all. The held stalk is what shifts the first-division totals from 4/8 to 5/9.
Step 3: The remainder count
Each heap is counted out in bundles of four. The leftover is 1, 2, 3, or 4 — never 0: a heap that divides evenly counts as a remainder of 4. The held stalk plus the two remainders then totals 5 or 9 on the first division and 4 or 8 on the second and third. This remainder convention is the step where implementations most often drift, because treating a clean division as 0 instead of 4 quietly rewrites the odds.
Step 4: The bundles removed
At the end of each division, the held stalk and both remainders are set aside together. After three divisions the removed stalks total between 13 and 25, so the number still in hand is 24, 28, 32, or 36. Only these four totals can survive three passes through the counting rule; anything else means one of the earlier steps was changed.
Step 5: The numerical mapping
The final count is mapped to a line number: 24 → 6 (old yin, moving), 28 → 7 (young yang), 32 → 8 (young yin), 36 → 9 (old yang, moving). Our guide to I Ching line notation shows how the numbers 6, 7, 8, and 9 become yin, yang, and moving lines. This mapping is remarkably stable across traditions — almost every published version agrees on it. The disagreement lives in the earlier steps, not here.
Where the odds come from
This is where yarrow stalk algorithms compared on paper start to diverge from what some apps actually implement: the odds depend on how the split is modeled. The standard calculation treats the sixteen possible (left-remainder, right-remainder) pairs as equally likely. On the first division, the pairs that sum to 4 — (1,3), (2,2), (3,1) — remove 5 stalks, and the single pair (4,4) removes 9, so 5 occurs three quarters of the time and 9 one quarter. On the second and third divisions, the pairs summing to 3 — (1,2), (2,1) — remove 4, and the pairs summing to 7 — (3,4), (4,3) — remove 8, so each occurs half the time. Multiplying across the three divisions gives 36 (5+4+4) → 9 at (3/4)(1/2)(1/2) = 3/16, 24 (9+8+8) → 6 at (1/4)(1/2)(1/2) = 1/16, 28 → 7 at 5/16, and 32 → 8 at 7/16.
That “equally likely remainder pairs” assumption is a modeling choice, not a physical law: a hand splits a heap of stalks, and different assumptions about how that split behaves give slightly different first-division odds. Probability-based treatments exist precisely to make this explicit. A. G. Clarke’s “Probability Theory Applied to the I Ching” (1987) is an early English-language example of deriving line odds from the counting procedure itself, and Chappel Brown’s “Inner Truth and the Origin of the Yarrow Stalk Oracle” (1982) examines what the early yarrow stalk procedures were meant to express. If a book, course, or app prints different odds, the difference usually traces back to this modeling assumption, not to a mystical calibration.
What changes when a variant deviates
- Skipping the set-aside changes the starting total and breaks the 5/9 pattern.
- Skipping the held stalk turns the first-division totals into 4 or 8 and flattens the distribution.
- Counting a full bundle as 0 instead of 4 does the same thing from the other direction.
- Removing extra stalks pushes the final count outside {24, 28, 32, 36}, so the mapping fails altogether.
Edward A. Hacker’s 1980 note is a useful test case here: it presents a coin procedure that is exactly equivalent to the yarrow stalk method, meaning a tool that uses coins can still produce the yarrow distribution — or not. If a resource claims the yarrow odds but its own worked example produces three-coin odds, its algorithm differs from its description.
Decision Framework
A practical way to keep yarrow stalk algorithms compared honestly is to write down the variant each resource teaches before you choose.
Questions to ask before you buy
- Does it name the variant? A book or course that says “the yarrow stalk method” without specifying the rule set hides the most decision-relevant information.
- What odds does it print? Compare its 6/7/8/9 probabilities against Table 2. The odds are a fingerprint of the algorithm.
- Can you see a full worked line? A good resource shows the set-aside, the held stalk, the remainders, and the removal across all three divisions.
- Can you record the method with the result? A log entry that stores “yarrow, standard model” or “three-coin” next to each line is far more useful than one storing only a hexagram name.
- Does it separate procedure from interpretation? Our comparison of I Ching coins vs yarrow stalks covers how the two families of methods differ in timing and record-keeping.
Checklist: what to record before you commit
- Starting count used (50 with one set aside, or 49 direct).
- Whether a stalk is held between the fingers, and which heap it comes from.
- Which heap is counted first in each division.
- Whether a full bundle of four counts as remainder 4.
- First-division totals actually observed (5/9 or 4/8).
- The final line numbers, and which ones were moving.
- The odds table the resource prints, if it prints one.
- The title and edition of the book, course, or app.
Key Takeaways
- Yarrow stalk algorithms compared: the five steps are the same skeleton everywhere; the rules inside them vary.
- Under the standard model, the classic distribution is 6 at 1/16, 7 at 5/16, 8 at 7/16, and 9 at 3/16, with a changing line one time in four.
- A coin method can reproduce the yarrow odds (Hacker, 1980), so “uses coins” tells you nothing about the underlying algorithm.
- The odds are a property of the procedure, not proof of accuracy: predictive interpretations are culturally meaningful but not validated by scientific testing as reliable forecasts.
- Record the variant before you interpret; the same line numbers can arise from different models with different meanings attached.
FAQ
Q: Why do guides disagree on yarrow stalk odds? A: The arithmetic gives one answer only after you fix how the heap is divided and how remainders are counted. Because the physical split is not a defined random process, authors model it differently, so published odds for the same procedure vary. Recording which variant you used matters more than memorizing a single table.
Q: What are the classic yarrow stalk probabilities for 6, 7, 8, and 9? A: Under the standard equally-likely-remainders model, the odds are 1/16 for 6 (old yin), 5/16 for 7 (young yang), 7/16 for 8 (young yin), and 3/16 for 9 (old yang). The moving lines, 6 and 9 together, appear one time in four.
Q: Is there a coin method that matches the yarrow stalk odds? A: Yes. Edward A. Hacker’s 1980 note in Philosophy East and West presents a coin procedure equivalent to the yarrow stalk method, producing the same 1/16, 5/16, 7/16, 3/16 distribution. The plain three-coin method, by contrast, gives 1/8, 3/8, 3/8, 1/8. Knowing which odds you want helps you choose a tool.
Q: Which step changes the odds most if you modify it? A: The initial set-aside and the remainder rule matter most. If you begin with 49 instead of setting one aside from 50, or treat a full bundle of four as zero rather than four, the first division no longer totals 5 or 9, and every resulting probability shifts. The numerical mapping itself is stable across traditions.
Q: Do the odds affect whether a reading is valid? A: The odds describe how often each line type appears, not whether an answer is true. Predictive interpretations of I Ching readings are culturally meaningful but not validated by scientific testing as reliable forecasts. Choose a method for what it lets you record and study, not because one algorithm seems more accurate than another.
Sources
- Yarrow Stalk Method (2020). Chapter in Chinese Leadership Wisdom from the Book of Change, pages 443–448, Chinese University of Hong Kong Press. Crossref record verified 2026-08-04; no author listed in the metadata.
- Inner Truth and the Origin of the Yarrow Stalk Oracle (1982), by Chappel Brown. Journal of Chinese Philosophy 9(2), pages 197–210.
- Probability Theory Applied to the I Ching (1987), by A. G. Clarke. Journal of Chinese Philosophy 14(1), pages 65–72.
- Brief Note on a Coin-Method Equivalent to the Yarrow-Stalk Method for Determining the Lines of a Hexagram in the I-Ching (1980), by Edward A. Hacker. Philosophy East and West 30(4), page 535.