How the three-coin method works: three coins, six tosses, one hexagram
Casting a hexagram here uses the three-coin method, in use for well over a thousand years: three coins, one line per toss, six tosses, and you hold one of the sixty-four hexagrams of the Book of Changes. It is simple, and every step has its reason.
From yarrow stalks to coins
The oldest way to cast a hexagram was with yarrow stalks, divided into heaps and counted again and again; one hexagram took dozens of steps. People later found an easier way: coins instead of stalks, and one toss settles a line. The coin method is generally thought to have grown common after the Han dynasty, and from the Song dynasty on it was the one most used among ordinary people, which is why it is also called the coin hexagram or simply "shaking a hexagram".
The tool changed but the point did not. Whether stalks or coins, you end up with six yin or yang lines stacked into a hexagram, and then you read the words that belong to it.
Three coins at a time: inscribed is 2, blank is 3
You shake three coins in your hand and drop them together. The side with writing counts as 2, the plain side counts as 3. Added together, the three coins can only give 6, 7, 8 or 9.
Three inscribed sides make 2+2+2=6, old yin. Two inscribed and one plain make 2+2+3=7, young yang. One inscribed and two plain make 2+3+3=8, young yin. Three plain sides make 3+3+3=9, old yang. Odd numbers are yang and are drawn as one solid line; even numbers are yin and are drawn as a line broken in the middle.
Why "old" and "young"
The 7 and the 8 are "young": a steady yang or yin that stays as it is. The 6 and the 9 are "old", and what is old to the extreme turns round: old yin becomes yang and old yang becomes yin. This is "when a thing reaches its limit it reverses" as it appears in a hexagram.
The odds make it clear. Three coins have eight arrangements; 6 and 9 each come up in only one, 7 and 8 in three each. So each line has a one-in-four chance of being old, and the chance that none of the six lines is old is about 18%. Meeting a changing line is very common and nothing to worry about.
From the bottom up, six times
The first toss gives the bottom line, which sits at the foot of the figure; the second goes on top of it, and so on to the sixth toss, the top line. The order is not arbitrary: a hexagram is like something growing up from the ground, what happens first at the bottom and what comes last at the top.
The six lines divide into the lower three and the upper three, each a small figure called a trigram: the lower (inner) trigram and the upper (outer) trigram. Each has eight possibilities, and eight times eight is exactly sixty-four.
What to do after the sixth toss
Once you have six lines, first identify the lower and upper trigrams and find the name of the hexagram. Then see whether any line is old, that is, a changing line. With none, you read the hexagram itself. With some, you also look at the hexagram they turn into (the resulting hexagram); which words to read has its own rules, explained in the article on changing lines.
In our game you see the coins fall on every toss, and it is no different from shaking coins in your hand. The old reader then goes through the picture and the original text with you. She does not pronounce lucky or unlucky and she does not foretell. She treats the hexagram as a mirror in which to see where you yourself stand.
Questions people ask
Can I use ordinary coins if I have no old Chinese ones?
Yes. Take three coins of the same size, agree which face counts as the inscribed side (2) and which as the plain side (3), and keep to that agreement. In our game you need nothing: one tap and the coins are tossed.
Should I bathe or burn incense before casting?
No. Ritual itself does not change the result, but a few quiet minutes and a clear question help a great deal, because what is finally read is your question.
Can I cast again for the same question?
The judgement on the hexagram Meng says: "At the first divination I tell; ask a second and a third time and it is a bother, and when it is a bother I do not tell." Ask sincerely once and you are answered; asking over and over shows disrespect for the question. If the same question gives a different hexagram, the hexagram is not wrong. It is worth asking yourself why you cannot let the matter go.