Today's Hexagramone I Ching casting with three coins

Three coins are tossed together. Heads count 3 and tails count 2, so each toss totals 6, 7, 8 or 9. Seven (young yang) and eight (young yin) are stable lines; nine (old yang) and six (old yin) are changing lines. Six tosses build the hexagram from the bottom line up. Turning each changing line into its opposite gives a second figure, the relating hexagram (之卦).

With coins, 6 and 9 each come up one time in eight and 7 and 8 three times in eight. The yarrow-stalk method of the Great Commentary (繫辭傳), with fifty stalks, gives 6 one time in sixteen, 7 five, 8 seven and 9 three. Either way a line is yang half the time, so all 64 hexagrams are equally likely. The difference is which lines change: with yarrow a yang line is three times as likely to change as a yin line, with coins the two are equal.

A line changes one time in four, so the number of changing lines is 0 in 17.8% of castings, 1 in 35.6%, 2 in 29.7%, 3 in 13.2%, 4 in 3.3%, 5 in 0.4% and 6 in 0.02%. About eight castings in ten have at least one changing line. No early source we found says which face of the coin counts 3, so the page follows the common convention of heads = 3. The tosses use the browser's cryptographic random generator (crypto.getRandomValues).

Which text to read follows the section Kao bian zhan (考變占) of the Yixue qimeng (易學啓蒙) by Zhu Xi and Cai Yuanding. It covers every case from no changing line to six.

"Judgment" here is what the rules call the tuanci (彖辭), the text under each hexagram. For three changing lines Zhu Xi says the first ten figures take the primary hexagram as main and the last ten the relating one (前十卦主貞，後十卦主悔). In the Yixue qimeng's chart of changing figures the first ten are exactly the cases where the first line changes, so this page uses that test. These rules are one 12th-century method; other traditions read every changing line.

In line names, nine (九) and six (六) only mark a yang or a yin line, not a changing one. Zhu Xi notes under the use of nines that every yang line is called nine rather than seven by convention.

The judgment of Hexagram 4, Meng, says: the first casting is answered; a second or third is disrespectful, and disrespect gets no answer (初筮告，再三瀆，瀆則不告). Zhu Xi adds that the one who asks should gather a single-minded sincerity before knocking (致其精一而扣之). The text sets no rule for websites, but this page follows its spirit and allows one casting a day, counted to midnight on this device.

The Chinese text is Zhu Xi's Yuanben Zhouyi benyi (原本周易本義) in the Siku Quanshu Wenyuange copy, as transcribed by the Kanseki Repository (KR1a0031). Errors from the transcription, including missing characters and mislabeled lines, were corrected against Zhu Xi's commentary and the received text (list below), and variant characters were normalized. The punctuation was added by K-magpie following Zhu Xi's sentence breaks.

The English translation and explanations were written by AI (Claude) from Zhu Xi's commentary and checked against the text and commentary. No modern translation is quoted. Where Zhu Xi says a meaning is unclear (未詳), the explanation says so too. For a classic public-domain English version, see James Legge, The Yî King (Sacred Books of the East, vol. 16, 1882).

The page never asks for your question. The coins are tossed in your browser, and the result is kept only in this device's browser storage as the date and six digits (for example 987678). Nothing is sent anywhere, and a result link carries only the six digits.