Casting Methods & Fidelity: Coins, Yarrow, Reproducibility

The coin method (Liu Yao): how to toss

Toss three coins at once: heads counts 3, tails 2. Sums: 6 (three heads) is old yang — moving; 7 (two heads) young yang; 8 (one head) young yin; 9 (three tails) old yin — moving. Six tosses stack into the hexagram, then the Najia chart is assembled by rule.

The per-line probabilities follow the binomial distribution: old yang 1/8, young yang 3/8, young yin 3/8, old yin 1/8. This site records every toss of yours; once the cast is complete, the chart is assembled and read by rule — the system never invents a hexagram for you.

The yarrow-stalk method (classical): how to divide

From the Great Commentary: "The number of the great expansion is fifty, of which forty-nine are used." Forty-nine stalks are divided, one hung aside, counted by fours, the remainder set back — three rounds form one line, eighteen rounds the hexagram.

Working out that process gives the per-line probabilities: old yang 3/16, young yang 5/16, young yin 7/16, old yin 1/16. Compared with coins, the total probability of a moving line is the same 25%, but old yang and old yin are no longer symmetric (3/16 vs 1/16) — a real mathematical difference between the methods, not mystical rhetoric.

Per-line probability comparison

Both methods yield moving lines 25% of the time; the difference is the shape of the four outcomes.

In other words: yarrow casts old yang (moving toward yang) more readily and old yin almost never; coins are symmetric between the moving poles. Tradition holds yarrow to be the more solemn form — half of that is simply that it is slow: half an hour of eighteen changes is itself the act of thinking one question through.

Selecting texts with multiple moving lines

Zhu Xi's rules, from the Yixue Qimeng:

• One line movesRead the moving line's text of this hexagram as primary
• Two lines moveRead both moving lines' texts, the upper one takes precedence
• Three lines moveCombine the Judgments of this hexagram and the changed one (ben as zhen, changed as hui)
• Four lines moveRead the two unmoved lines' texts of the changed hexagram, the lower takes precedence
• Five lines moveRead the single unmoved line's text of the changed hexagram
• Six lines moveQian and Kun use their special 'Yong' texts; other hexagrams read the changed hexagram's Judgment

Reproducibility: same input, same hexagram

Number casting (Mei Hua): the two numbers you give uniquely determine the upper and lower trigrams and the moving line; any system applying the same formula reaches the same result.

Time casting (Mei Hua): upper trigram = year-branch number + lunar month + lunar day; lower = that sum + hour-branch number; moving line = the total mod 6. The formula is public — you can verify it yourself.

Coin casting (Liu Yao): the hexagram is determined solely by your six tosses; the site assembles and reads the Najia chart by rule and keeps every toss on record for review.

How the daily hexagram is derived

The hexagram on /iching/today is cast by Shao Yong's time method fixed at the noon hour: year-branch number + lunar month + lunar day gives the upper trigram; adding the noon-branch number (7) gives the lower trigram and moving line. The computation is deterministic — the same date recalculated by anyone yields the same hexagram; the page updates once a day.

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