TL;DR: The I Ching has four common methods of casting a hexagram: yarrow stalk divination by the great expansion method (50 stalks, using 49, three changes per line), tossing three coins, casting by numbers (Mai Hoa), and casting by time. Yarrow stalks give probabilities for the four line types of 1/16 old yin, 5/16 young yang, 7/16 young yin, and 3/16 old yang, so moving yang occurs three times as often as moving yin; tossing three coins, under the Văn Vương kim tien khoa convention (tails 3, heads 2), gives 2/16, 6/16, 6/16, and 2/16, meaning moving yin and moving yang are equal. The two methods are therefore not equivalent in probability, while casting by numbers and by time yield exactly one moving line.
Title: How to cast an I Ching hexagram: yarrow stalk divination, tossing three coins, casting by numbers and by time, and why each method gives different moving-line probabilities
What is I Ching divination and why are there many ways to cast a hexagram?
I Ching divination (bói Dịch) is a form of divination in which you toss or divide to receive one of the 64 hexagrams, each made up of six yin or yang lines stacked from the bottom up. When casting, each line is assigned one of four numbers: 6 (old yin), 7 (young yang), 8 (young yin), 9 (old yang). Old lines (6 and 9) are moving lines, which change into lines of the opposite polarity to produce a second hexagram. Different casting methods give different probabilities for the four line types, and that is precisely why the schools are not entirely equivalent when they interpret.
According to the English Wikipedia article on I Ching divination, there are two main methods for building lines: using 50 yarrow stalks or three coins. Beyond these there are methods that cast by interpreting time, direction or people instead of tossing or dividing. The yarrow stalk method is usually chosen by traditionalists for its complexity and the time it takes; the coin method suits people who need a quick result.
Historically, according to a survey by Lê Anh Minh posted on the Lý số Việt Nam forum, oracle bone divination (using turtle plastrons) dates from the Shang era, yarrow stalk divination from the Zhou era, while coin divination is of unknown origin and is regarded as a variant of yarrow stalk divination. The same article cites Phan Bội Châu and Nguyễn Hiến Lê, who held that the I Ching should be read as a philosophical book rather than a divination manual, and cites Richard Wilhelm, who held that divination lacks moral significance. These are viewpoints worth knowing before going into casting technique.
How does yarrow stalk divination by the great expansion proceed?
The yarrow method uses 50 stalks but takes only 49, setting one aside as the Supreme Ultimate. For each line, the diviner performs three changes (tam biến) to arrive at a number 6, 7, 8 or 9. The procedure consists of splitting the stalks into two bundles, taking one stalk from the right bundle and tucking it between the fingers, counting the left and right bundles in multiples of four, gathering the remainders, and repeating. After three changes, the remaining number of stalks divided by four gives the line. The six lines are built from the bottom up, line one (sơ) first, line six (thượng) last.
Yarrow stalks allow anywhere from 0 to 6 moving lines in a hexagram. According to Wikipedia, the yarrow method favours static lines over moving lines in a ratio of 3:1. This means most yarrow hexagrams will have no moving lines or only a few, and when there are moving lines, moving yang lines clearly predominate.
How does tossing three coins differ in probability?
Tossing three coins for each line gives four outcomes: three backs, three faces, two backs and one face, two faces and one back. In the Văn Vương kim tiền khóa (anonymous, traditionally attributed to King Wen; this attribution lacks historical evidence and the text belongs to a later era), a clear convention is set out as follows: three bronze coins are tossed; if only one back (the side without characters) appears it is called "đơn", marked with one dot, corresponding to a yang line; when two backs appear it is called "chiết", marked with two dots, corresponding to a yin line; when three backs appear together it is called "trùng", drawn as a circle, corresponding to a moving yang line; and if all three are the character side it is called "giao", marked with a cross, corresponding to a moving yin line. The text adds: a circle counts as one point but, being moving, is used as two points; a cross counts as two points but, being moving, is used as one point. This method yields a line in a single toss instead of three changes, so it is far quicker.
If the back side is assigned the value 3 and the character side the value 2, the sum of three coins gives exactly the four numbers 6, 7, 8, 9: three character sides (2+2+2) is 6, that is old yin; two characters and one back (2+2+3) is 7, that is young yang; one character and two backs (2+3+3) is 8, that is young yin; three backs (3+3+3) is 9, that is old yang. This is a count of the eight possibilities of three coins, each with two sides, so each outcome has a probability of 1/8, which over a denominator of 16 becomes 2/16 for old yin, 6/16 for young yang, 6/16 for young yin, and 2/16 for old yang. This means the probability of moving yin and moving yang is equal, both at 2/16. The yarrow method, by contrast, gives 1/16 old yin, 5/16 young yang, 7/16 young yin, 3/16 old yang, that is moving yang (3/16) is three times moving yin (1/16).
Because of this gap, the two methods are not probabilistically equivalent. Someone interpreting by yarrow will meet more moving yang lines, while someone interpreting by coins will meet moving yin and moving yang at equal frequency. This is the point on which the schools usually disagree: some regard yarrow as the standard for its traditional character and complexity, others choose coins for convenience and hold that probability is not the deciding factor.
Table of probabilities for the four line types
| Line type | Name | Yarrow stalks | Three coins |
|---|---|---|---|
| 6 | Old yin (moving yin) | 1/16 | 2/16 |
| 7 | Young yang (static) | 5/16 | 6/16 |
| 8 | Young yin (static) | 7/16 | 6/16 |
| 9 | Old yang (moving yang) | 3/16 | 2/16 |
The table above shows that the total probability of a moving line is 4/16 for yarrow (1/16 + 3/16) and also 4/16 for coins (2/16 + 2/16). Although the totals are equal, the distribution by yin and yang is quite different, and that directly affects the changed hexagram that is produced.
What is special about casting by numbers and by time?
Casting by numbers and by time uses neither yarrow stalks nor coins. The diviner takes numbers from the moment of the question, from a name, from a date, or from any available data, and reduces them to a hexagram. According to Wikipedia, this is the group of methods that interpret time, direction or people instead of tossing or dividing. The common feature of this group is that it gives exactly one moving line, or no moving line at all, and never allows two to six moving lines as yarrow does.
On Nhật Nguyệt, the hexagram of the day uses the LapQueTheoNgay tool, which is the site's own convention, not a classical I Ching school. This needs to be said clearly so that readers do not mistake it for a traditional method. Likewise, the GieoLucHao tool uses the three-coin toss, while LapQueMaiHoa casts by three numbers. That each tool uses a different method is deliberate, since each method suits a different interpretive system.
Comparison table of casting methods
| Casting method | Implement | Possible number of moving lines | Tool on Nhật Nguyệt |
|---|---|---|---|
| Yarrow stalks (great expansion) | 50 yarrow stalks, 49 used | 0 to 6 | No automated tool |
| Three coins | 3 coins | 0 to 6 | GieoLucHao |
| Casting by numbers | Three numbers or numerical data | Exactly 1 | LapQueMaiHoa |
| Casting by time | Date, hour, or point-in-time data | Exactly 1 | LapQueTheoNgay (the site's own convention) |
Why does the same hexagram interpreted through different casting methods give different readings?
Because the probabilities of moving lines differ, the distribution of changed hexagrams differs too. With yarrow, since moving yang is three times as frequent as moving yin, hexagrams with moving yang lines appear more often, and the changed hexagrams lean in one direction accordingly. With coins, moving yin and moving yang are equal, so the changed hexagrams are more balanced. With casting by numbers and by time, since there is only one moving line, the changed hexagram always differs from the original by exactly one line.
This leads to a practical reality: two people asking about the same matter, one casting by yarrow and one by coins, may get two different hexagrams, or the same primary hexagram but a different changed hexagram. The schools usually disagree on which method is more trustworthy. Some hold that yarrow is the standard because of its traditional character and because the 3:1 ratio more faithfully reflects the movement of yin and yang. Others hold that coins are enough, provided the querent is sincere and keeps the convention consistent throughout the tossing.
According to the Văn Vương kim tiền khóa, the convention for the back and character sides is written explicitly in the text, and the diviner should follow that convention rather than invent one. The text also instructs the querent to be sincere: the opening of the book says "chí thành chi đạo, khả dĩ tiền tri" (the way of utmost sincerity can know beforehand), and holds that a querent who is not sincere cannot reach the spirits, and a diviner who speaks at random is not efficacious. The book also criticises those who come to ask about a hexagram while drunk, having eaten meat, or without keeping themselves pure, calling it delusion. These are the words of the text, not something this article asserts to be true.
After casting, how is the hexagram read?
Once the primary hexagram is in hand, the interpreter reads the hexagram statement and the line statements. If the hexagram has no moving lines, reading the hexagram statement alone is enough. If there is one or more moving lines, read the statement of each moving line as well, then change the old lines into lines of the opposite polarity to obtain the changed hexagram and read its statement. The rules for reading according to the number of moving lines (one line, two lines, three lines, and so on) are a separate topic, outside the scope of this article. Readers who want to go deeper can look at the articles on the changed hexagram, the nuclear hexagram, the reversed hexagram and the opposite hexagram on Nhật Nguyệt.
The Văn Vương kim tiền khóa does not stop at casting. The text also includes a method for assigning stem and branch to the six lines (the section "hỗn thiên giáp tử", which records the earthly branches from the bottom up by palace), a method for placing the six relations according to the element of the palace (for example, the Càn and Đoái palaces belong to metal, so the elder brother is metal, the parent is earth, the wife and wealth is wood, the officer and ghost is fire, and the descendant is water), the nobleman verse ("Giáp Mậu kiêm ngưu dương, Ất Kỷ thử hầu lang..."), and a method for choosing the focus spirit according to the matter asked: for questions about parents, teachers, house or documents, take the parent as the focus spirit; for questions about children, medicine or livestock, take the descendant; for questions about wife, money or storehouses, take the wife and wealth; for questions about office, lawsuits or thieves, take the officer and ghost; for questions about siblings or friends of one's own generation, take the elder brother. That is, the coin toss in this text goes together with the Six Lines style of interpretation, not merely reading the hexagram statement as in purely I Ching reading.
Note that every casting method gives only a frame of reference, not an absolute verdict of fortune or misfortune. Classical books may say different things about the same hexagram, and different schools may interpret the same moving line differently. Readers should treat this as a tool for reflection, not as a verdict on finances, health or destiny.
Are yarrow stalks and coins really equivalent?
No. The total probability of a moving line is the same for both methods (4/16), but the distribution of moving yin and moving yang is quite different. Yarrow gives moving yang three times as often as moving yin; coins give the two types equally. So if you interpret by the changed hexagram, the two methods produce two different distributions of changed hexagrams. This is the point on which the schools usually disagree, and also why some people choose yarrow despite the extra time.
Philosophically, according to the Stanford Encyclopedia of Philosophy on Chinese philosophy of change, the I Ching is regarded as a system of signs that helps people orient themselves in a changing world, and divination is part of that system. Choosing which casting method to use also sits within that system, not outside it.
