Among the many forms of divination is a method using the I Ching or Book of Changes. The book is structured as an 8x8 matrix of sixty-four hexagrams representing the states and the dynamic relationships of the eight elements, each represented by a trigram. Throughout China's region of cultural influence (including Korea, Japan and Vietnam), scholars have added comments and interpretation to this work, one of the most important in ancient Chinese culture; it has also attracted the interest of many thinkers in the West. See the I Ching main article for historical and philosophical information.

The process of consulting the book as an oracle involves determining the hexagram by a method of random generation and then reading the text associated with that hexagram, and is a form of bibliomancy.

Each line of a hexagram determined with these methods is either stable ("young") or changing ("old"); thus, there are four possibilities for each line, corresponding to the cycle of change from yin to yang and back again:
old yin (yin changing into yang), which has the number 6 and symbol ---x---
young yang (unchanging yang), which has the number 7 and symbol --------
young yin (unchanging yin), which has the number 8 and symbol ---  ---
old yang (yang changing into yin), which has the number 9 and symbol ---o---

Once a hexagram is determined, each line has been determined as either changing (old) or unchanging (young). Since each changing line is seen as being in the process of becoming its opposite, a new hexagram can be formed by transposing each changing yin line with a yang line, and vice versa. Thus, further insight into the process of change is gained by reading the text of this new hexagram and studying it as the result of the current change.

Several of the methods use a randomising agent to determine each line of the hexagram. These methods produce a number which corresponds to the numbers of changing or unchanging lines discussed above, and thus determines each line of the hexagram.

The turtle shell oracle is probably the earliest record of fortune telling. The diviner would apply heat to a piece of a turtle shell (sometimes with a hot poker), and interpret the resulting cracks. The cracks were sometimes annotated with inscriptions, the oldest Chinese writings that have been discovered. This oracle predated the earliest versions of the Zhou Yi (dated from about 1100 BC) by hundreds of years.

A variant on this method was to use ox shoulder bones. When thick material was to be cracked, the underside was thinned by carving with a knife

The yarrow stalk method of divination was the next major oracular method after the turtle shell. It was comparatively quick and easy to perform. A yarrow stalk is a piece of dried stem from the yarrow plant, approximately 15-18 inches in length.

However, the yarrow divination is not a truly randomized method, since it is statistically biased toward certain answers. While it is unlikely that the ancient Chinese knew the mathematical justification for why this was so, some ancient practitioners were probably aware of the bias through the empirical evidence of many repeated divinations.

The yarrow stalk method is performed as follows:
use fifty dried stalks of the yarrow plant and a large clear table space
set aside one stalk to represent unity, using forty-nine stalks for the remainder of the ritual
for each of the six lines of the hexagram (starting from the bottom and moving up)
divide and count the stalks three times as follows
gather the stalks into the left hand
split them randomly into two bundles with the left thumb
place the two bundles separately, as left and right piles, onto the table
take one stalk from the right side pile, hold it between the little finger and ring finger of the left hand
pick up the left side pile in the left hand
count the stalks from the pile into separate piles of four, until four or fewer remain
hold this remainder between the ring and middle finger of the left hand
pick up the right side pile in the left hand
count the stalks from the pile into separate piles of four, until four or fewer remain
hold this remainder between the index and middle finger of the left hand
set aside all the stalks held between fingers of the left hand
count the number of piles of four stalks
if this is not the third iteration, gather all the piles of four together to repeat the dividing and counting process
after the third iteration, the number of piles of four stalks will be six, seven, eight or nine
determine the current line of the hexagram from this number: 6 = old yin, 7 = young yang, 8 = young yin, 9 = old yang.
once six lines have been determined the hexagram is formed

Using this method, the probabilities of each type of line are as follows:
old yin: 1 in 16 (0.0625)
young yang: 5 in 16 (0.3125)
young yin: 7 in 16 (0.4375)
old yang: 3 in 16 (0.1875)

By way of explanation:

You start with 50, then subtract 1 to become 49. Then divide into two piles, P and 49-P, on the table and then keep 1 on the left hand

If P mod 4 is 1, 49 - 1 - P would be 3  )  all results into 4
If P mod 4 is 2, 49 - 1 - P would be 2  )
If P mod 4 is 3, 49 - 1 - P would be 1  )

and hence the number will become 49 -1 - 4 = 44 with a probability of 3/4.

If P mod 4 is 4, 49 - 1 - P would be 4  ) results into 8

and hence the number becomes 49 - 1 - 8 = 40, with a probability of 1/4.

As hereafter the pile is divisible by 4, from the second iteration (which repeat in the third iteration) the probability is quite different, as follows (using example of 44):

From 44 it divides into two piles X and 44-X on the table with 1 on the left hand

If X mod 4 is 2, 44 - 1 - X would be 1  )  all reseults into a pile of 3
If X mod 4 is 1, 44 - 1 - X would be 2  )


and hence the number will become 44 - 1 - 3 = 40 with a probability of 2/4.

If X mod 4 is 4, 44 - 1 - X would be 3  )  all reseults into a pile of 7
If X mod 4 is 3, 44 - 1 - X would be 4  )

and hence the number becomes 44 - 1 - 7 = 36, with a probability of 2/4.

Altogether that would generate the following probability tree:

 50 - 1 -> 49

 -> 44 (3/4) -> 40 (2/4) -> 36 (2/4) i.e. as 9 at probability 3*2*2/64 = 12/64
                         -> 32 (2/4) i.e. as 8 at probability 3*2*2/64 = 12/64
             -> 36 (2/4) -> 32 (2/4) i.e. as 8 at probability 3*2*2/64 = 12/64
                         -> 28 (2/4) i.e. as 7 at probability 3*2*2/64 = 12/64
 -> 40 (1/4) -> 36 (2/4) -> 32 (2/4) i.e. as 8 at probability 1*2*2/64 =  4/64
                         -> 28 (2/4) i.e. as 7 at probability 1*2*2/64 =  4/64
             -> 32 (2/4) -> 28 (2/4) i.e. as 7 at probability 1*2*2/64 =  4/64
                         -> 24 (2/4) i.e. as 6 at probability 1*2*2/64 =  4/64

Collecting all these branches one arrives at:

  Probability(6) should be (       4)/64 =  4/64 =  1/16 for old yin
  Probability(9) should be (12      )/64 = 12/64 =  3/16 for old yang
  Probability(7) should be (12+ 4+ 4)/64 = 20/64 =  5/16 for young yang
  Probability(8) should be (12+12+ 4)/64 = 28/64 =  7/16 for young yin

This is the same from the probability above. The correct probability has been used also in the marble, bean, dice and two or four coin methods below. This probability is significantly different from that of the three-coin method, because the required amount of accuracy occupies four binary bits of information, so three coins is one bit short. In terms of chances-out-of-sixteen, the three-coin method yields 2,2,6,6 instead of 1,3,5,7 for old-yin, old-yang, young-yang, young-yin respectively.

Three-coin method

The three coin method came into currency over a thousand years later. The quickest, easiest, and most popular method by far, it has largely supplanted the yarrow stalks. However, it is significant that the probabilities of this method differ from the yarrow stalks.

Using this method, the probabilities of each type of line are as follows:
old yang: 1 in 8 (0.125)
old yin: 1 in 8 (0.125)
young yang: 3 in 8 (0.375)
young yin: 3 in 8 (0.375)

While there is one method for tossing three coins (once for each line in the hexagram), there are several ways of checking the results.