{
  "name": "Cast probabilities by method",
  "description": "Exact line, changing-line and relating-hexagram probabilities for the yarrow-weighted and three-coin methods, worked out by enumerating all 4,096 line combinations.",
  "license": "CC BY 4.0",
  "license_url": "https://creativecommons.org/licenses/by/4.0/",
  "attribution": "The Free I Ching, https://thefreeiching.com/data",
  "source": "https://thefreeiching.com",
  "updated": "2026-10-07",
  "notice": "The I Ching is a tool for reflection, not a prediction. Nothing here forecasts events or replaces professional advice.",
  "line_value_key": "6 = old yin (changing), 7 = young yang, 8 = young yin, 9 = old yang (changing)",
  "hexagram_index_note": "Arrays for hexagram probabilities are indexed by King Wen number minus one.",
  "methods": {
    "yarrow": {
      "line_probabilities": {
        "old_yin_6": 0.0625,
        "young_yang_7": 0.3125,
        "young_yin_8": 0.4375,
        "old_yang_9": 0.1875
      },
      "probability_line_is_changing": 0.25,
      "probability_no_changing_lines": 0.177978515625,
      "probability_of_k_changing_lines": [
        0.177978515625,
        0.35595703125,
        0.296630859375,
        0.1318359375,
        0.032958984375,
        0.00439453125,
        0.000244140625
      ],
      "expected_changing_lines": 1.5,
      "primary_hexagram_probability": [
        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625,
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        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625
      ],
      "relating_hexagram_probability": [
        0.0018495917320251465,
        0.05259221792221069,
        0.017879903316497803,
        0.017879903316497803,
        0.005899369716644287,
        0.005899369716644287,
        0.030753910541534424,
        0.030753910541534424,
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      ]
    },
    "coin": {
      "line_probabilities": {
        "old_yin_6": 0.125,
        "young_yang_7": 0.375,
        "young_yin_8": 0.375,
        "old_yang_9": 0.125
      },
      "probability_line_is_changing": 0.25,
      "probability_no_changing_lines": 0.177978515625,
      "probability_of_k_changing_lines": [
        0.177978515625,
        0.35595703125,
        0.296630859375,
        0.1318359375,
        0.032958984375,
        0.00439453125,
        0.000244140625
      ],
      "expected_changing_lines": 1.5,
      "primary_hexagram_probability": [
        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625,
        0.015625,
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      ],
      "relating_hexagram_probability": [
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  }
}