Multiple moving lines: state the rule you use
There is no single reading for multiple moving lines. In the three-coin method each line takes 6, 7, 8 or 9; six lines run bottom to top, and 6 and 9 are the changing lines that flip to form the resulting hexagram. That part is deterministic and can be recalculated. How to use several changing lines, however, belongs to interpretation: traditions differ, and the tool shows every changing line rather than naming one rule as the only standard. So the order is: record the six values, the changing positions, the original and resulting hexagrams; state which convention you adopt; only then discuss meaning. If someone claims a line is a classical quotation, ask for the passage and line reference instead of treating a modern prompt as a classical text.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
- Changing positions follow from the values and are recalculable; the selection rule is a traditional choice that must be stated.
- Write the six raw values and changing positions first, then the original and resulting hexagrams, and only then interpretation.
- Traditions weight multiple changing lines differently; you need not unify them, but label the source and scope.
- Keep modern reflection prompts apart from classical text, and require a passage and line reference for any quotation.
A reading flow for multiple changing lines
- 01Record six values
Write the six tosses bottom to top, keeping the raw 6, 7, 8 and 9 rather than only drawing yin and yang.
- 02Mark changing lines
Mark only 6 and 9 as changing, and check that their count matches how often those values appear.
- 03Flip to the result
Flip only the changing positions, leave the other lines untouched, and look up both hexagram names and numbers.
- 04Declare the rule
State which tradition or reason you follow for multiple changes, and note that it is an interpretive choice, not a calculation.
- 05Then discuss meaning
Only after structure and rule are written, record associations and separate modern prompts from classical text.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
Why declare a rule before reading multiple changes
The mechanical part of a three-coin cast is clear: each line takes 6, 7, 8 or 9, six lines run bottom to top, and 6 and 9 are the changing lines that flip to form the resulting hexagram, with names following the King Wen sequence. This part is deterministic; anyone who recalculates from the same six numbers gets the same original hexagram, changing positions and result. So when two or more lines change, the first task is not to hunt for a sentence of meaning but to write the six numbers and changing positions down clearly.
The real disagreement comes next: with several changing lines, do you focus on one line, read both hexagrams together, or work through each change? That belongs to interpretive tradition, not calculation. The tool shows every changing line rather than naming one rule as the only standard. A reader who wants a discussable conclusion should therefore state which convention they use and why, so others can see which reading they are following instead of mistaking one school's habit for a universal rule.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
Fix the structure first: six values, changing positions, two names
Before any discussion of selection, fix the structure. Write the six tosses in bottom-to-top order as six rows and keep the raw values rather than only drawing solid and broken lines; a value records two things at once, since yin or yang sets the current shape and young or old decides whether it changes. Copy only the shapes and you can no longer tell which rows should flip. Then mark every 6 and 9, and flip only those positions to obtain the resulting hexagram.
The value of this step is that it can be checked. If the number of changing lines does not match how often 6 and 9 appear, the problem lies in the record, not the interpretation. If a stable line is altered during the flip, the name will be wrong. Keeping all of this on one sheet before looking up names and theme prompts lets an error be traced to a specific row rather than leaving a vague sense of not understanding. Once the structure passes, discussing a selection rule becomes meaningful.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
A comparison table: how traditions handle multiple changes
The table below sets common approaches side by side, not to rank them but to make the differences visible. The focus column describes what each habit tends to emphasise; it is a traditional and editorial summary, not a paraphrase of unread classical passages. The tool itself does not name a single standard and simply displays all changing lines. Readers can choose one approach and say so, or explain a mixed reading and its reasons.
Note that none of these approaches changes the structure already calculated. Whichever you choose, the six values, changing positions, original and resulting hexagrams stay the same; only your attention and the way you organise the explanation shift. Writing the rule before the reading leaves a checkable interface for yourself and others: they may disagree with your selection, but at least they can see which rule produced the conclusion.
Wenbu · calculation conventions ↗Wenbu · three-coin method ↗
Separate structural checks from meaning
A structural check answers what the hexagram is, which lines change and what it becomes; it has one answer and can be recalculated. Interpretation answers what it means for you; it depends on tradition, context and the real situation you supply, and has no single answer. Mixing the two invites the common error of using interpretation to cover a recording mistake, or replacing numbers that should be checked with a sentence that merely sounds deep.
The hexagram theme prompts in this tool are written by Wenbu and are not quotations from a classical edition. That matters: a theme prompt is a starting point for reflection, not a classical text and not validation of an outcome. If someone claims a sentence comes from a particular hexagram and line of the Zhou Yi, ask for the passage and line reference; without one, treat it as modern commentary rather than traditional authority. Keeping that boundary stops the discussion of multiple changing lines from sliding into claims that cannot be tested.
Wenbu · calculation conventions ↗Wenbu · three-coin method ↗
| Approach | Focus | What to state | Boundary note |
|---|---|---|---|
| Read original and result together | The direction of change across both hexagrams | Original, result and changing positions | An interpretive choice; it does not alter the calculation |
| Focus on one changing line | The meaning of a single position | Which line, and by which rule | Traditions differ; cite the source |
| Work through each change | Each changing line's prompt in turn | All changing positions and their order | Lots of material; risks becoming a list |
| Read only the resulting hexagram | The hexagram after change | Result name and number | Still keep the original and changing record |
| Record without selecting | Keep the structure for later review | Six values and both names | Useful for gathering before discussing meaning |
Wenbu · calculation conventions ↗Wenbu · three-coin method ↗
Hypothetical practice: writing the rule for two changing lines
The data below are a hypothetical teaching example, not a cast for any real question and not a randomly drawn result. Suppose a three-coin cast gives the bottom-to-top values 6, 7, 8, 9, 7, 8. We first check the structure only, then show how to declare a selection rule.
- Step one, write six rows: line 1 is 6, line 2 is 7, line 3 is 8, line 4 is 9, line 5 is 7, line 6 is 8. Keep the raw numbers, not just shapes.
- Step two, mark changes: only 6 and 9 change, so lines 1 and 4 change, two in total. Confirm the count matches how often 6 and 9 appear.
- Step three, draw the original: 6 and 8 are yin, 7 and 9 are yang; Kan below and Dui above give Lake over Water, Kun 困, number 47.
- Step four, flip only lines 1 and 4: line 1 turns from yin to yang and line 4 from yang to yin, while the other four stay, giving Water over Lake, Jie 节, number 60.
- Step five, declare the rule: for example, write that this reading uses the original and resulting hexagrams together and does not single out one changing line, noting that this is an interpretive choice, not a calculation.
- Step six, then discuss meaning: record associations beside the record, marking which are modern reflection prompts and which would need a passage and line reference to count as classical text.
The observable result is fixed: the six values, changing lines at positions 1 and 4, original Kun 47 and resulting Jie 60. Whether to focus on one line or read the pair together depends on the rule you wrote, not on the numbers. Putting the rule first lets others check your reasoning instead of seeing only a conclusion.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
Questions you may have
With two or more changing lines, must I pick a leading line?
Not necessarily. Traditions differ on how to use multiple changing lines, and the tool shows every changing line rather than naming one rule as the only standard. You may read both hexagrams together, work through each change, or focus on one line, but state the rule and its basis and note that it is an interpretive choice, not a calculation.
Wenbu · calculation conventions ↗Wenbu · three-coin method ↗
If someone's reading cites different changing positions, what do I check first?
Go back to the raw values. Changing lines can only be 6 and 9, and their count must equal how often those values appear; then check that the six lines run bottom to top and that only changing lines were flipped. Only after the structure passes should you discuss differences in selection rules and meaning.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
Can a hexagram theme prompt be quoted as classical text?
No. The hexagram theme prompts in this tool are written by Wenbu and are not quotations from a classical edition. If you want to attribute a sentence to the classic, give the passage and line reference; without one, treat it as a modern reflection prompt kept separate from classical text.
Wenbu · calculation conventions ↗Wenbu · three-coin method ↗
Terms in this guide
- Changing line
- A line valued 6 or 9 in the three-coin method; it flips when constructing the resulting hexagram while the other lines stay as they are.
Wenbu · three-coin method ↗Wenbu · calculation conventions ↗
- Resulting hexagram
- The figure after every changing line flips, often called the relating hexagram or zhi gua; together with the original it forms the two states of one cast.
- Selection rule
- An interpretive convention for deciding which changing line or hexagram to emphasise when several lines change; it does not alter the calculated structure.
See the claim and source notes
In the three-coin method each line takes 6, 7, 8 or 9; six lines run bottom to top, and 6 and 9 are the changing lines that flip to form the resulting hexagram.
6 与 9 是动爻
Traditions differ on how to use multiple changing lines; the tool displays all changing lines rather than naming one rule as the only standard.
本工具展示全部动爻
The existing guide already gives the full 6, 7, 8, 9, 7, 8 transformation from Kun 47 to Jie 60, which serves as an answer key for structural checks.
Kun 困, number 47
Sources and review scope
Wenbu drafted and checked this article in Codex. The source list records the scope of the review.
- Wenbu · three-coin method ↗Existing editorial and worked calculation · 2026-11-07 · Read excerpt
- Wenbu · calculation conventions ↗First-party implementation; not evidence of predictive accuracy · 2026-11-07 · Fetched text
Enter six values manually and check the changing positions
Before debating a selection rule, enter the six values manually in the tool and confirm that the changing positions, original and resulting hexagrams match your record; once the structure is right, write down the multiple-changing-line rule you use.
Enter six values manually and check the changing positions ↗A line has a one-in-four chance of moving when you use three fair coins and their outcomes are independent. Across six independent tosses, the chance of exactly two moving lines is about 29.66%. The chance of at least two is about 46.61%. To check a particular cast, keep all six recorded totals and find which positions contain 6 or 9.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
- Two of the eight coin combinations produce a moving line.
- Exactly two counts two moving positions. At least two includes three through six as well.
- Use the raw values and their positions to check a particular entry.
Three steps for checking the moving-line count
- 01Count one line
Two of the eight equally likely outcomes give 6 or 9.
- 02Place two moving lines
There are 15 pairs of positions among six lines.
- 03Check the record
Mark each 6 or 9 and check both figures with the tool.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Start with one line and count all pairs of positions
Assign one face of each coin the value 2 and the other the value 3. Three 2s make 6. Three 3s make 9. Both are moving lines. The six other combinations give 7 or 8 and stay fixed. The probability for one line is therefore one quarter moving and three quarters staying fixed.
If you specify lines one and five in advance and require the other four to stay fixed, multiply two factors of one quarter and four factors of three quarters. The result is 81/4096. Exactly two can occur in any pair of six positions. There are 15 pairs, each with the same probability, so the total is 1215/4096. Counting a pair once keeps the first and fifth lines from being counted again in the reverse order.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Use the totals to check a cast you actually recorded
At least two includes casts with three, four, five or six moving lines. You can also take the whole distribution and remove the cases with zero and one. Subtract 729/4096 and 1458/4096 from 1 to get 1909/4096. This describes six independent tosses of fair coins. A manual entry uses the six values you provide.
Suppose your record says 9, 7, 8, 8, 6, 7 from bottom to top. The 9 at line one and the 6 at line five move. The other four lines stay fixed. If the tool highlights different positions, check where you wrote the first toss and how you added the faces for each line. The probability tells you how common this count is, while the original values let you audit the cast.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
| Moving lines | Probability | Approximate share |
|---|---|---|
| 0 | 729/4096 | 17.80% |
| 1 | 1458/4096 | 35.60% |
| 2 | 1215/4096 | 29.66% |
| 3 | 540/4096 | 13.18% |
| 4 | 135/4096 | 3.30% |
| 5 | 18/4096 | 0.44% |
| 6 | 1/4096 | 0.02% |
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Enter six values and check lines one and five
This fixed exercise uses six values numbered from the bottom line to the top.
- Copy 9, 7, 8, 8, 6, 7 and circle the 9 and the 6.
- Open Enter coin results in the I Ching tool. Put each value in the corresponding position.
- The result shows moving lines one and five, with Reduction (41) changing to Dispersion (59).
- For exactly these two positions moving and the rest fixed, use 81/4096. For lines one and five both moving with the other four unrestricted, use 1/16. Keep those conditions on separate lines.
The fixed manual entry moves lines one and five. Across fair random casts, any of the 15 pairs can give a count of exactly two.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Questions you may have
Should I cast again because two lines moved?
The count alone gives you no indication of a recording error. Check the totals, the line order and the moving positions. When those match your notes, you can continue with the saved cast.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Why is the denominator 4096 rather than eight to the sixth power?
For each line we first group the eight outcomes into moving and staying fixed. Their probabilities simplify to one quarter and three quarters. The common denominator across six lines is four to the sixth power, or 4096.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Is a manually entered cast still random?
The manual tool uses the values you entered to draw the first figure and change the moving lines. The same values and order give the same figures. The probabilities describe the fair coin procedure.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
Terms in this guide
- Exactly two
- Two of the six lines move and the other four stay fixed.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
- Specified pair
- Two particular positions chosen in advance, such as lines one and five.
Current complete en canonical article ↗Wenbu · calculation conventions ↗Wenbu · three-coin method ↗Wenbu · versioned public capabilities ↗
See the claim and source notes
The three-coin guide enumerates eight equally likely outcomes under the fair, independent coin model.
Three fair coins have eight equally likely combinations.
Wenbu’s method treats 6 and 9 as moving line totals.
6 与 9 是动爻
The tool’s declared order for the six values is bottom to top.
"order": "bottom-to-top"
Sources and review scope
Wenbu drafted and checked this article in Codex. The source list records the scope of the review.
- Current complete zh canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-13 · Fetched text
- Current complete en canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-13 · Fetched text
- Wenbu · calculation conventions ↗First-party implementation; not evidence of predictive accuracy · 2026-11-13 · Fetched text
- Wenbu · three-coin method ↗Existing editorial and worked calculation · 2026-11-13 · Read excerpt
- Wenbu · versioned public capabilities ↗First-party current tool, convention and privacy contract; not external endorsement or predictive validation · 2026-11-13 · Fetched text
Enter six values and check both moving lines
Use 9, 7, 8, 8, 6, 7 in their original positions. Check that Reduction changes to Dispersion and that lines one and five are marked.
Enter six values and check both moving lines ↗