Among the many forms of divination is a method using the I Ching (易經) 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. Confucius said that one would not be ready to attempt to use the I Ching for divination until quite old. This work discourages compulsion (i.e., asking the same question over and over in hopes of either a different/better answer or some kind of enlightenment as to the meaning of the answers one gets). The Hexagram 4 description talks about the problems with "the youthful and inexperienced" asking the same question three or more times. ^[1]

The text is extremely dense reading. A list of English translation can be found in the main article --- I Ching#Translations. It is not unknown for experienced soothsayers to ignore the text, building the oracle from the pictures created by the lines, bigrams, trigrams, and final hexagram.

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). Old yin is seen as more powerful than young yin, and old yang is more powerful than young yang. Any line in a hexagram that is old ("changing") adds additional meaning to that hexagram.

Taoist philosophy holds that powerful yin will eventually turn to yang (and vice versa), so a new hexagram is 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.

Contents 1 Methods 1.1 Plastromancy - turtle shell cracks 1.2 Yarrow stalks 1.3 Coins 1.3.1 Three-coin method 1.3.1.1 How the coins are tossed 1.3.1.2 How the line is determined from the coin toss 1.3.2 Two-coin method 1.3.3 Four coins 1.3.4 Six coins 1.3.5 Ba Qian 1.4 Dice 1.5 Marbles or beads (method of sixteen) 1.6 Rice grains 1.7 Calligraphy brush strokes 1.8 Calendric systems 2 Probability analysis of I Ching divination 3 References

Methods

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.

Plastromancy - turtle shell cracks

Plastromancy or 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, a practice called scapulimancy. When thick material was to be cracked, the underside was thinned by carving with a knife.

Yarrow stalks

Hexagrams may be generated by the manipulation of yarrow stalks. The following directions are from the ten wings of the I Ching. Other instructions can be found here, and a calculation of probabilities here.

One takes fifty yarrow stalks, of which only forty-nine are used. These forty-nine are first divided into two heaps (at random), then a stalk from the right-hand heap is inserted between the ring finger and the little finger of the left hand. The left heap is counted through by fours, and the remainder (four or less) is inserted between the ring finger and the middle finger. The same thing is done with the right heap, and the remainder inserted between the forefinger and the middle finger. This constitutes one change.

Now one is holding in one's hand either five or nine stalks in all. The two remaining heaps are put together, and the same process is repeated twice. These second and third times, one obtains either four or eight stalks. The five stalks of the first counting and the four of each of the succeeding countings are regarded as a unit having the numerical value three; the nine stalks of the first counting and the eight of the succeeding countings have the numerical value two.

When three successive changes produce the sum 3+3+3=9, this makes the old yang, i.e., a firm line that moves. The sum 2+2+2=6 makes old yin, a yielding line that moves. Seven is the young yang, and eight the young yin; they are not taken into account as individual lines.

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.

Note that only the remainders after counting through fours are kept and laid upon the single stalk removed at the start. The piles of four are re-used for each change, the number of piles of four is not used in calculation; it's the remainders that are used. The removing of all the fours is a way of calculating the remainder, those fours are then re-used for the next change so that the total number of stalks in use remains high to keep all remainders equally probable.

Coins

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. A three-coin method with adjusted probabilities can be found here.

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.

How the coins are tossed

• use three coins with distinct "head" and "tail" sides
• for each of the six lines of the hexagram, beginning with the first (bottom) line and ending with the sixth (top) line:
• toss all three coins
• write down the resulting line
• once six lines have been determined, the hexagram is formed

How the line is determined from the coin toss

The numerical method:

• assign the value 3 to each "head" result, and 2 to each "tail" result
• total all the coin values
• the total 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.

An alternative is to count the "tails":

• 3 tails = old yin
• 2 tails = young yang
• 1 tail = young yin
• 0 tails = old yang

Another alternative is this simple mnemonic based on the dynamics of a group of three people. If they are all boys, for example, the masculine prevails. But, if there is one girl with two boys, the feminine prevails. So:

• all tails = old yin
• one tail = young yin
• one head = young yang
• all heads = old yang

Two-coin method

Some purists contend that there is a problem with the three-coin method because its probabilities differ from the more ancient yarrow-stalk method. In fact, over the centuries there have even been other methods used for consulting the oracle.

If you want an easier and faster way of consulting the oracle with a method that has nearly the same probabilities as the yarrow stalk method, here's a method using two coins (with two tosses per line):

• first toss of the two coins: if both are "heads," use a value of 2; otherwise, value is 3
• second toss: a "head" has a value of 2, a "tail" a value of 3. Add the two values from this toss and the value from the first toss.
• the sum of the three values will be 6 (old yin), 7 (young yang), 8 (young yin), or 9 (old yang). This provides the first (bottom) line of the hexagram.

Repeat the process for each remaining line.

The probabilities for this method are: old yin 0.0625, young yang 0.3125, young yin 0.4375, and old yang 0.1875.

Four coins

If you're comfortable with binary, four coins can be very quick and easy, and like 2 coins matches the probabilities of the yarrow-stalk method. Here's a table showing the different combinations of four coin throws and their binary sum and corresponding line (six lines making a full changing hexagram starting at the bottom). To calculate the binary sum of a four coin throw, place the coins in a line, then add up all the heads using 8 for the left-most coin, then 4, 2 and 1 for a head in the right-most position. The full explanation relating it to the yarrow stalk method is at OrganicDesign:I Ching / Divination.

Sum Coins Line 0 T T T T ---x--- 1 T T T H ---o--- 2 T T H T ---o--- 3 T T H H ---o---

Sum Coins Line 4 T H T T ------- 5 T H T H ------- 6 T H H T ------- 7 T H H H -------

Sum Coins Line 8 H T T T ------- 9 H T T H --- --- 10 H T H T --- --- 11 H T H H --- ---

Sum Coins Line 12 H H T T --- --- 13 H H T H --- --- 14 H H H T --- --- 15 H H H H --- ---

Another 4 coin method uses two different pairs of coins. Each coin in the higher pair counts as one coin, but the lower pair acts as a single coin. If the coins are valued as follows, the mathematics are identical to the use of yarrow sticks. In the following example, heads will count as 3, and tails as two. The lower pair are tails if and only if both are tails.

HH (hh)= 9 HH (ht)= 9 HH (tt)= 8 HT (hh)= 8 HT (ht)= 8 HT (tt)= 7 TT (hh)= 7 TT (ht)= 7 TT (tt)= 6

Therefore the odds of 6 = 1/16 Therefore the odds of 7 = 5/16 Therefore the odds of 8 = 7/16 Therefore the odds of 9 = 3/16

Six coins

Take five identical coins, and a sixth that is similar to the five.

• Shake them in your hand for a couple of seconds.
• Toss them up into the air.
• The coin that lines the furtherest from one is the sixth line.
• The coin that lands the closest to one is the first line.
• The coin that is different from the others is the moving line.
• Generally, "heads" is considered to be yang, and "tails" to be yin.

This method has been criticized on the grounds that it:

• Forces every hexagram to be a "Moving Hexagram";
• Ignores the statistical probabilities of both the standard three coin method, and the traditional yarrow stalk method.

Ba Qian

Step 1:

• Take eight identical coins.
• Mark one in a small way.
• Shake them up in your hand while focusing on your wish or problem.
• Place the coins counter-clockwise on a diagram of the Fu Xi Order of the triagrams.
• The marked coin indicates the lower triagram of the hexagram.

Step 2:

• Shake the coins again.
• Place the coins counter-clockwise on a diagram of the Fu Xi Order of the triagrams.
• The marked coin indicates the upper triagram of the hexagram.
• Remove two unmarked coins from the set.

Step 3:

• Shake the coins.
• Starting at the bottom, place on the lines of the hexagram.
• The line with the marked coin is the moving line.

Dice

Using coins will quickly reveal some problems: while shaking the coins in cupped hands, it's hard to know whether they are truly being tumbled; when flipping the coins, they tend to bounce and scatter. It's much easier to use a die as a coin-equivalent: if an odd number of pips shows, it counts as "heads"; if an even number of pips shows, as "tails." Obviously, the 50/50 probability is preserved — and rolling dice turns out to be easier and quicker than flipping coins. Thus the three-coin method will use three dice.

Dice can also be used for the two-coin method. It is best to use two pairs of dice, each pair having its own color — e.g., a pair of blue dice and a pair of white dice, such as are commonly found in backgammon sets. One pair can then be designated the "first toss" in the two-coin method, and the other the "second toss." One roll of four dice will then determine a line, with probabilities matching the yarrow-stalk method.

The number values on a single die can also be used to determine the hexagram's lines. Designate odd numbers as yang, even numbers as yin, and roll a six-sided die once for each of the six lines. Roll the die a seventh time to determine the moving line. This method mimics Zhou court divinations in which yarrow stalks were used in a two-stage divinatory process, first casting the hexagram, then designating one line as moving (see Shaughnessey, 1996, pp. 7-8).

Since a single toss of three distinct coins allows for eight possible combinations of heads & tails, the three-coin method's probabilities can be duplicated with a single eight-sided die, rolling it once to generate each line. Use an odd and an even number on the die, 1 and 8 for instance, to designate a moving line when either number is obtained. This preserves the equal 1/4 chance that a given yin or yang line will be moving.

A similar distribution to yarrow stalks is possible using two dice, 1 eight-sided (1d8), and 1 twenty-sided (1d20). Roll both of them at once per line.

If the 1d20 is an even number
 then 
   if the 1d8  = 1      -X-  moving yin (1/16 probability) 
   if the 1d8  = 2 - 8  - -  yin (7/16 probability)
If the 1d20 is an odd number: 
 then 
     if the 1d8 = 1 - 5  --- yang (5/16 probability) 
     if the 1d8 = 6 - 8  -0- moving yang (3/16 probability)

Another duplication of the yarrow stalks' probabilities can be done by taking the total of two eight-sided die rolls (2d8; odd totals indicating yang lines and even totals indicating yin), to produce each hexagram line. The 1:1 distribution of yin and yang is preserved, and the chances of obtaining certain totals will be used to match the yarrow stalks' weighted distributions of moving yin and yang lines.

The 2d8 roll provide four possible instances where the total is either two or four, which equates to the yarrow stalks' chances of a yin line being moving. This can be demonstrated by mapping all totals on an 8x8 grid, each axis representing the numbers on one die. The chance of an even (yin) total being two or four (moving) is then 4/32, equaling 1/8. Weight the distribution of moving yang lines similarly, by using totals that equate to a 3/8 (or 12/32) chance of obtaining that result among the 32 odd possibilities, such as seven and eleven (which can likewise be diagrammed on the 8x8 grid). So a total of two, four, seven or eleven, when yielded by one 2d8 roll, can indicate that the resulting yin or yang line is moving.

Marbles or beads (method of sixteen)

This method is a recent innovation, designed to be quick like the coin method, while giving nearly the same probabilities as the yarrow stalk method.

• use sixteen marbles of four different colours but the same size, distributed as follows
  • 1 marble of a colour representing old yin (such as blue)
  • 5 marbles of a colour representing young yang (such as white)
  • 7 marbles of a colour representing young yin (such as black)
  • 3 marbles of a colour representing old yang (such as red)
• place all the marbles in a bag or other opaque container
• for each of the six lines of the hexagram
  • shake all sixteen marbles together in the container to "shuffle" them
  • draw out one marble
  • the marble drawn determines the current line of the hexagram
  • replace the marble in the container
• once six lines have been determined, the hexagram is formed

A good source of marbles is a (secondhand) Chinese checkers set: 6 colors, 10 marbles each.

Using this method, the probabilities of each type of line are the same as the distribution of the colours, 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)

An improvement on this method uses 16 beads of four different colors but with the same size and shape (i.e., indistinguishable by touch), strung beads being much more portable than marbles. You take the string and, without looking, grab a bead a random. The comments above apply to this method as well.

Rice grains

For this method, either rice grains, or small seeds are used.

One picks up a few seeds between the middle finger and thumb. Carefully and respectfully place them on a clean sheet of paper. Repeat this process six times, keeping each cluster of seeds in a separate pile --- each pile represents one line. One then counts the number of seeds in each cluster, starting with the first pile, which is the base line. If there is an even number of seeds, then the line is yin, otherwise the line is yang --- except if there is one seed, in which case one redoes that line.

One then asks the question again, and picks up one more cluster of seeds. Count the number of seeds you have, then keep subtracting six, until you have six seeds or less. This gives you the number of the line that specifically represent your situation. It is not a moving Line. If you do not understand your answer, you may rephrase the question, and ask it a second time.

Calligraphy brush strokes

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion. (June 2008)

Calendric systems

There is a component of Taoist thought which is concerned with numerological/cosmological systems. This has also been applied to the I Ching as well. The noted Chinese Neo-Confucian philosopher Shao Yung (1011-1077 CE) is the one who has done the most work in popularizing this concept and in developing/publishing oracular systems based on them. This is the most sophisticated usage of I Ching oracular systems.

The most readily accessible of these methods (the easiest to learn to do, and also to use) is called the Plum Blossom Oracle. In fact, however, there are several variants of this method. One method uses the number of brushstrokes used in writing the question along with the date and time of the inquiry. Another method simply uses the date and time without an actual question. There are other variants as well, including not using date and time at all. The resulting numbers are used to select the trigrams (in either the Early Heaven or the Later Heaven sequence), which then identify the hexagram of the answer. It is also possible to find Plum Blossom Oracle computer programs to more easily and efficiently do the calculations.

The most accurate of these calendric methods is also the most complex. This is called the Ho Map Lo Map Rational Number method (and has been published in Sherrill and Chu's "Astrology of I Ching"). It uses a very complicated series of operations with a series of tables to generate series of predictions which are entirely calendar-based.

The method set out in "Astrology of I Ching" (description and external online calculator at http://www.hall-of-man.com) has been reported to contain an error, leading to improper hexagrams sometimes being generated. However, the system can never produce the "missing" trigrams Li and Tui as a representation of the earthly force at a particular moment in time, since they are both assigned odd numeric values when the Later Heaven cycle of trigrams is superimposed on the so-called Magic Square of Three:

4....9....2

3....5....7

8....1....6

The earthly numbers are all even and thus the system is not flawed even though—being a composite method involving several layers - it is far from being seamless.

Probability analysis of I Ching divination

Most analyses on the probabilities of either the coin method or yarrow stalk method agree on the probabilities for each method.

• http://www.dentato.it/iching/ - alternative calculation of the yarrow stalk probabilities
• OrganicDesign:I Ching / Divination - explanation of the traditional probabilites of 1,3,5,7 out of 16

The coin method varies significantly from the yarrow stalk method in that it gives the same probability to both the moving lines and to both the static lines, which is not the case in the yarrow stalk method. The calculation of frequencies (generally believed to be the same as described in the simplified method using 16 objects in this article) using the yarrow stalk method, however, embodies a further error, in the opinion of Andrew Kennedy, author of Briefing Leaders ([1]Gravity Publishing, UK, 2007), that of including the selection of zero as a quantity for either hand. The traditional method was designed expressly to produce 4 numbers without using zero. Kennedy shows, that by not allowing the user to select zero for either hand or a single stick for the right hand (this stick is moved to the left hand before counting by fours and so also leaves a zero in the right hand), the hexagram frequencies change significantly for a daily user of the oracle. He has produced an amendment to the simplified method of using 16 colored objects described in this article as follows,

take 38 objects of which

• 8 of one color = moving yang
• 2 of another color = moving yin
• 11 of another color = static yang
• 17 of another color = static yin

This arrangement produces Kennedy's calculated frequencies within 0.1%

References