{
  "schemaVersion": "wenbu-knowledge-v1",
  "id": "guide-iching-three-coins",
  "slug": "iching-three-coins",
  "language": "en",
  "title": "How three coins become an I Ching hexagram",
  "description": "A clear guide to 6, 7, 8 and 9, bottom-to-top line order, changing lines and the difference between a cast and an interpretation.",
  "sections": [
    {
      "heading": "Choose a convention before casting",
      "paragraphs": [
        "Assign 2 to one side of a coin and 3 to the other. Toss three coins and add their values: the total is 6, 7, 8 or 9. Which side receives which value matters less than keeping the convention consistent.",
        "Repeat six times. The first line belongs at the bottom of the hexagram; later lines are placed above it. Reversing this order changes the hexagram, so label a manual record clearly."
      ]
    },
    {
      "heading": "Four numbers, two line shapes",
      "paragraphs": [
        "Seven is young yang, a solid line. Eight is young yin, a broken line. Nine is old yang: solid, changing to broken. Six is old yin: broken, changing to solid. Six and nine are changing lines.",
        "Three fair coins have eight equally likely combinations. The probabilities of 6, 7, 8 and 9 are 1/8, 3/8, 3/8 and 1/8. The traditional yarrow procedure has a different changing-line distribution and should not be presented as the same method."
      ]
    },
    {
      "heading": "The original and resulting hexagrams",
      "paragraphs": [
        "Draw the original hexagram from the six line values. Flip only the changing lines to construct the resulting hexagram. If none change, the two are identical. This transformation is deterministic and can be checked independently of an AI interpretation.",
        "Wenbu simulates coin outcomes with cryptographic randomness and also accepts physical coin results. The six values, changing positions and King Wen numbers remain visible for review."
      ]
    },
    {
      "heading": "Where to begin when several lines change",
      "paragraphs": [
        "Traditions differ on how to read multiple changing lines. Wenbu shows every changing position rather than claiming a universal selection rule. The short themes are original reflection prompts, not quotations from a classical edition.",
        "Begin with an open, concrete question. Record what the imagery brings to mind and revisit the note later. What you overlooked and what you actually did can be more useful than repeatedly casting until an answer feels comfortable."
      ]
    },
    {
      "heading": "Check the process with six numbers",
      "paragraphs": [
        "Write 6, 7, 8, 9, 7, 8 in bottom-to-top order. Lines one and four change: the first changes from yin to yang, the fourth from yang to yin. The other four stay as they are.",
        "Enter these as manual coin results in Wenbu and check the changing positions before reading the names. This is a worked example of the transformation, not a cast for a real-life question."
      ]
    }
  ],
  "updated": "2026-09-30",
  "authorship": "Wenbu · AI-assisted editorial; no independent expert review claimed",
  "evidenceType": "editorial",
  "links": {
    "html": "https://wenbu.app/en/learn/iching-three-coins/",
    "markdown": "https://wenbu.app/knowledge/en/iching-three-coins.md",
    "json": "https://wenbu.app/knowledge/en/iching-three-coins.json"
  },
  "outline": [
    {
      "id": "quick-answer",
      "title": "The short answer"
    },
    {
      "id": "section-0",
      "title": "Choose a convention before casting"
    },
    {
      "id": "section-1",
      "title": "Four numbers, two line shapes"
    },
    {
      "id": "reference-table",
      "title": "From a coin total to a line"
    },
    {
      "id": "section-2",
      "title": "The original and resulting hexagrams"
    },
    {
      "id": "section-3",
      "title": "Where to begin when several lines change"
    },
    {
      "id": "section-4",
      "title": "Check the process with six numbers"
    },
    {
      "id": "worked-example",
      "title": "Check the whole transformation: 47 to 60"
    },
    {
      "id": "glossary",
      "title": "Key terms"
    },
    {
      "id": "questions",
      "title": "Common questions"
    },
    {
      "id": "sources",
      "title": "Sources and their scope"
    }
  ],
  "answer": "In the three-coin method, one toss of three coins produces one line. Six tosses build the figure from bottom to top. Totals of 6 and 8 begin as yin; 7 and 9 begin as yang. Only 6 and 9 change. Keep all six numbers so another reader can reconstruct both hexagrams.",
  "takeaways": [
    "Each number records both a line’s shape and whether it changes. Copying only solid and broken lines loses part of the cast.",
    "The first toss is the bottom line. A compound name such as Lake over Water names the upper trigram first; that is a different order from the casting record.",
    "The four totals are not equally likely. Wenbu adds three independent fair binary outcomes, preserving the 1:3:3:1 distribution for 6, 7, 8 and 9."
  ],
  "figure": {
    "caption": "Two states of one cast: only lines 1 and 4 change",
    "description": "Read 6, 7, 8, 9, 7, 8 from bottom to top. The original is Lake over Water, Kun 困, number 47. Flipping the first and fourth lines gives Water over Lake, Jie 节, number 60. The other four lines stay unchanged."
  },
  "table": {
    "title": "From a coin total to a line",
    "columns": [
      "Total",
      "Coin combinations",
      "Original line",
      "Resulting line / probability"
    ],
    "rows": [
      [
        "6 · Old yin",
        "2 + 2 + 2; one arrangement",
        "Broken, changing",
        "Becomes solid; 1/8"
      ],
      [
        "7 · Young yang",
        "Two 2s and one 3; three arrangements",
        "Solid, stable",
        "Stays solid; 3/8"
      ],
      [
        "8 · Young yin",
        "One 2 and two 3s; three arrangements",
        "Broken, stable",
        "Stays broken; 3/8"
      ],
      [
        "9 · Old yang",
        "3 + 3 + 3; one arrangement",
        "Solid, changing",
        "Becomes broken; 1/8"
      ]
    ]
  },
  "example": {
    "title": "Check the whole transformation: 47 to 60",
    "intro": "This is a teaching example, not a random reading for you. Draw six numbered spaces with line 1 at the bottom. Enter 6, 7, 8, 9, 7, 8 in that order.",
    "steps": [
      "Draw broken lines at positions 1, 3 and 6, and solid lines at 2, 4 and 5. Leave the original numbers alongside them before reading any interpretation.",
      "Separate the figure into lower and upper groups. The bottom three form Kan, Water; the top three form Dui, Lake. The lookup is Lake over Water: Kun 困, number 47.",
      "Flip only the changing positions. The 6 at line 1 becomes solid; the 9 at line 4 becomes broken. Do not reverse the entire diagram or alter a stable line.",
      "Identify the new groups: Lake below, Water above. This is Jie 节, number 60. Save the six numbers, changing positions 1 and 4, and both hexagram names together.",
      "Ask an Agent to repeat those details before interpreting them. If it selects one changing line over another, request its reading convention. A claim to quote the classic needs a passage and line reference."
    ],
    "conclusion": "The checkable result is the structural change from 47 to 60. Reading it as “meet constraint with moderation” is a possible modern association, not a causal fact established by the numbers."
  },
  "faq": [
    {
      "question": "Should I cast again if no lines change?",
      "answer": "No. Each line has a 3/4 chance of being stable, so a six-line cast has about a 17.8% chance of having no changes. Record that outcome. The two hexagrams are identical; a second cast is not needed to make the first one valid."
    },
    {
      "question": "Are digital coins more accurate than physical coins?",
      "answer": "Wenbu uses the same numerical distribution as three fair coins. Physical outcomes may also depend on the coins and how they are tossed. Matching a probability model does not establish predictive power. Manual entry is useful when you want to keep a physical casting process."
    },
    {
      "question": "What should I give another Agent for a reproducible check?",
      "answer": "Provide the six numbers, the bottom-to-top order, the three-coin method, the original number and the changing positions. An unlabeled screenshot cannot distinguish 6 from 8 or 7 from 9, so it may not contain enough information to reconstruct the resulting hexagram."
    }
  ],
  "glossary": [
    {
      "term": "Yao 爻",
      "definition": "One line of a hexagram, numbered from the bottom upward."
    },
    {
      "term": "Changing line",
      "definition": "A line valued 6 or 9 in this coin method; it flips when constructing the resulting figure."
    },
    {
      "term": "Resulting hexagram",
      "definition": "The figure after every changing line flips, often called the relating hexagram or zhi gua 之卦."
    }
  ],
  "sources": [
    {
      "title": "Wenbu · src/lib/iching.ts",
      "url": "https://github.com/Digidai/wenbu/blob/main/src/lib/iching.ts",
      "scope": "Supports the probabilities, bottom-to-top order, changing-line algorithm and random/manual modes; the example is checked against this implementation."
    },
    {
      "title": "《周易》· 困",
      "url": "https://zh.wikisource.org/wiki/周易/困",
      "scope": "Primary text for hexagram 47 and its line texts, separate from the original reflection exercise."
    },
    {
      "title": "《周易》· 节",
      "url": "https://zh.wikisource.org/wiki/周易/節",
      "scope": "Primary text for Jie, the resulting hexagram; it is not cited as documentation for the software’s random algorithm."
    },
    {
      "title": "Chinese Text Project · Book of Changes",
      "url": "https://ctext.org/book-of-changes",
      "scope": "Further reading; not validation of real-world predictions."
    },
    {
      "title": "Book of Changes · Xi Ci I",
      "url": "https://ctext.org/book-of-changes/xi-ci-shang",
      "scope": "Further reading; not validation of real-world predictions."
    }
  ]
}