Methods Of Consulting the Yi Jing (I Ching) Oracle

compiled by Mo Lei-Li ²ö¹p²z

Prefnote First become familiar with the very basic concepts of consulting the Yi Jing before reading this simple survey. You should aready know at least one method of casting a hexagram and the meaning of terms such as "trigram," "changing line," and "static line." Nothing here is original -- all credits go to the original authors; and apologies for any misrepresentations.

1. Turtle shell / ox bone Crack a turtle shell with heated rocks or sticks. Read the pattern of the cracks.I

2. Yarrow (milfoil plant) sticks Along with shell and bone cracking, the manipulation of a group of yarrow stalks is the oldest method of consulting the oracle. The procedures in use today are complex and time-consumingII; but they do serve to focus and clear the questioner's mind. This is an example of how the yarrow method can work:

Preparation: Concentrate on your question (the whole time you are doing this). Take a bundle of 50 yarrow stalks (or straws, or rocks, or ...). Remove one; it is set aside. (The symbolism of this and all elements in the procedure is a matter of interpretation.) Now you have 49 to work with. Step 1: Divide the bundle randomly into two parts. Take 1 stalk from the right hand batch and place it in a "remainder pile." Step 2: Count out the left bundle 4 stalks at a time; when you are down to 1-4 stalks, place them in the remainder pile. Now do the same thing with the right bundle. Step 3: Gather up all the stalks except those in the remainder pile and repeat steps 1 and 2. Step 4: One more (a third) time! This time, as you count out by 4 as usual, place each group of 4 in separate piles. You will end up with 6, 7, 8, or 9 piles:

6 = changing yin (broken) line. This is also called an "old yin" line. 7 = static yang (solid) line. This is also called a "young yang" line.

8 = static yin ("young yin") 9 = changing yang ("old yang")

Of course, you may also count the number of stalks in the remainder pile -- but that goes by a different chart.III You have now determined the first (bottom) line of your six-line hexagram. Now gather all 49 stalks together and:

Repeat steps 1-4 all over again for each of the five remaining lines.

3. Three coins A quicker -- and therefore more popular -- procedure involves tossing three coins (preferably copper or Chinese coins). Assign the value 3 to "heads" and 2 to "tails." (On a Chinese coin, the side with four markings is "tails.") The total of the coins determines the first (bottom) line of the hexagram. (Use the same 6-9 chart as above.)IV

Repeat five times to determine the remaining five lines of the hexagram. Multiple changing lines are possible (more so than with the yarrow stick method). Some schools provide systems for limiting the number of changing lines recognized when using the yarrow and three-coin methods.V

4. Four coins The tossing of 3 coins and the dividing of yarrow stalks do not have the same statistical probabilities in producing lines. In the belief that the yarrow method is more reliable and/or more ancient, some 4-coin methods have been developed that duplicate the probabilities of yarrow divination.[VI] For example:

Step 1: Toss 1 coin. "Heads" = a yang (strong) line; "tails" = a yin (weak) line. Leave the coin where you tossed it. Step 2: Toss 3 more coins next to the first one. If you see exactly 3 heads among all 4 coins, then the line is changing; otherwise unchanging.

5. Method of 16 [Shoenholtz, 1975] This system was also developed to be statistically equivalent to the yarrow stick method. It uses sixteen objects of the same size and shape, but of only four different colors or markings ("looks"). These are placed into a bag. One object is withdrawn and noted, then placed back into the bag. This is repeated five more times until the hexagram is built. The distribution of the objects is:

7 objects of look #1 representing static yin lines (43.75%) 5 objects of look #2 representing static yang lines (31.25%)

3 objects of look #3 representing changing yang lines (18.75%) 1 object of look #4 representing a changing yin line (6.25%)

The objects can be anything: marbles of different colors or designs; marked sticks, coins, stones, cards, etc.

6. Six coins [Sorrell/Sorrell] Toss 5 pennies and 1 dime with eyes closed. (Six pennies, one of which is visually different, would also be acceptable.) Use hands to form coins into a column representing the hexagram. Open eyes and read:

"heads" coins = yang lines "tails" coins = yin lines

The odd coin -- yin or yang -- denotes the changing line. Only one changing line is possible.VII

7. Six sticks Six four-sided sticks are used. Yin and yang lines -- static and changing -- are marked on the four faces of each stick. The distribution of the line markings varies. Sometimes each stick is marked with all four types of lines. Cast the sticks and form them into the shape of a hexagram. Even more that the 3-coin method, this increases the probability of receiving changing lines.VII

8. Sixty-four sticks Place 64 numbered bamboo slips into a wooden or bamboo cup. Shake the cup until one or two slips slip out. Read the corresponding hexagram(s).IX

9. Yarn sticks Pick a group of yarn sticks at random from a container of less than 50 sticks. This determines your lower trigram. Repeat the process for the upper trigram. There are no changing lines.X

Heaven: 1 09 17 25 33 41 sticks

Lake: 2 10 18 26 34 42 sticks

Fire: 3 11 19 27 35 43 sticks

Thunder: 4 12 20 28 36 44 sticks

Wind: 5 13 21 29 37 45 sticks

Water: 6 14 22 30 38 46 sticks

Mountain: 7 15 23 31 39 47 sticks

Earth: 8 16 24 32 40 48 sticks

10. Carnival Method A cloth with the eight trigrams arranged in a circle is laid out. The inquirer is given eight objects (coins, stones, etc.) -- all identical except for one that has a slight visual difference. The inquirer shakes the objects and lays them out in a circle over the pictures of the trigrams (starting at any point). The trigram on which the marked object lands forms the lower portion of the hexagram. The procedure is repeated to determine the upper trigram.

11. Six questions [Lofting] The inquirer is asked two sets of three questions about his inquiry. Based on the answers, a hexagram is built. The first three questions deal with the inquirer’s ("my") assessment of the situation:

Bottom line: Is the situation facts driven or values driven? Line 2: Is the situation one of what is or what could be? Line 3: Is the situation being driven by you or being reacted-to by you?

The second three questions deal with the "outside" -- with "their" point of view. (If "they" are present, they may be consulted.)

Line 4: Is the situation fact-based or value-based? Line 5: Is this considered something that is or something that could be? Top line: Is the situation being directed, or being reacted-to?

In each question, choosing the first of the two options presented yields a yang line; choosing the second option yields a yin. There is no provision for changing lines.XI

12. Gender method [Perrottet] In The Visual I Ching,XIIthe inquirer takes eight cards, each displaying a visual image of a trigram, and holds them or places them face-down. He then mixes them up, chooses one, and notes it. This is repeated five more times. Trigrams associated with male members of the family yield yang lines, and vice versa:

Heaven father yang line

Lake youngest daughter yin line

Fire middle daughter yin line

Thunder eldest son yang line

Wind eldest daughter yin line

Water middle son yang line

Mountain youngest son yang line

Earth mother yin line

No provision is made for changing lines.

13. Eight gems and a die [A. Huang] Place eight different stones into a bag (predetermining which stones represent each of the 8 trigrams). Pick a stone; this is your lower trigam. Place it back in the bag. Pick a stone; this is your upper trigram. Roll the die. The number on the die is the number of the hexagram's changing line.XIII

14. Sixteen cards and a die [A. Huang] On 8 red cards and 8 blue cards mark the symbols of the 8 trigrams. Shuffle the cards upside down and choose one blue card for the lower trigram and one red card for the upper trigram. Roll a die to determine the number of the changing line.

15. Cassia Tora seeds. [Ni] Six "pinches" of small seeds or grains of rice are placed on a plain sheet of paper, representing the 6 lines of a hexagram. If a cluster of seeds contains an even number of seeds, the line is yin; if odd, yang. One additional pinch of seeds is dropped and counted. This determines which line is the one on which to focus. If the number is greater than 6, 6 is subtracted and the remainder is the focus line. ("Focus line" is my term to indicate no additional hexagram is to be consulted.)XIV

16. Situation-related trigrams [Shao Yong, c. 1066] In this method, aspects of a particular situation are used to determine the trigrams which relate to it. The relationships of the trigrams' imagery are then examined to determine a reading.XV "Aspects" include such things as:

The time and date of the situation The gender and ages of people involved The material (eg, wood, water) involved The number of objects involved Relevant compass directions Areas of the body

17. Personalized systems In addition, some people who take the Yi Jing seriously develop their own personalized systems. Some use different systems depending on the situation. For example, when I wish to consult the oracle, I normally pick three pennies out of my change bin that "look right" to me at the time. If, however, I am dealing with an issue that I have already overthought, I use the yarrow method with a special reserved set of 50 polished semi-precious stones.

18. And finally, just open the book at random and read it.

_____________ Footnotes:

I A small hole is drilled on one side of the shell. The heat source is applied there and the cracks form on the other side. One "cracking" requires approximately 1.5 square inches of shell. This method was used with turtle shells and with bones -- usually the shoulder blades -- of oxen.

II The methods in use today are from 1,000 to 3,000 years old. The exact date is a subject of much scholarly debate. Most methods today are based on a description in a collection of Confucian-style commentaries on the Yi Jing known as the Ten Wings (in particular, see Chapter 9 of the Great Treatise/Appended Judements of the Ten Wings). The language in all the Ten Wings is full of imagery. Here is just one passage about the yarrows:

The number of the Great Expansion is fifty, Of which forty-nine are used. Divide them into two, symbolizing the two primary forces. Suspend one, symbolizing the three supreme powers. Manipulate by four, symbolizing the four seasons. Return the remainder, symbolizing the intercalary month. In five years there is another intercalation. Afterward the process is repeated.

Therefore four operations produce a change, And eighteen changes yield a gua. (--Translation A. Huang)

On the web, a very clear yarrow description is detailed at http://www.power-press.com/yarrow.html (Power Press's wu wei site). It even has pictures!

III Here is the basic chart when counting "leftovers:"

27 = An "old" (changing) yin (broken) line 21 = A "young" (static) yang (solid) line 17 = A young yin line 13 = An old yang lineThere are also symbolism-based formulas that convert these numbers into the tradtional codes 6, 7, 8, and 9 (respectively). Wilhelm/Baynes is a good resource for that.

IV Diana ffarington Hook's The I Ching and You (0-7100-7381) includes one description of the symbolism involved in the 3-coin method. (Thanks to Isabeau Vollhardt for the quotation):

...where there is a mixture of heads and tails, that is 7 or 8 in a single throw, there is a more or less balanced condition, part yang and part yin, and the answer is a yang or yin line. However, when all three coins fall the same way up, that is three heads (9) or three tails (6), the situation is unbalanced, being either too yang, or too yin. These lines are then in an important state of change or movement, changing because of the excessive imbalance.

V For details, see Hacker or Whincup (ISBN's below).

VI There are multiple methods that use four coins and exactly duplicate the probabilities of using yarrow stalks. Edward Hacker presents his in his book The I Ching Handbook (ISBN 0-912111-36-4). Stuart Anderson, whose description of "Alternate Coin Method #2" appears above, has laid out the mathematics (along with another 4-coin method) in his article at Charlie Higgins YJ Mensionization site http://www.mension.com/probab1.htm . A third 4-coin method was mentioned by Al Franken. In this method, four coins are tossed at once; however two of these are pre-designated to work together and count as only one coin. Again, "heads" = 3, and "tails" = 2. However, if either of the predesignated pair is a "heads," they both count as one "heads." The resulting hexagram lines are then the same as in the 3-coin method where 6 = changing yin, etc. Al Franken pointed out he prefers a 'statistically correct' 4-coin method because hexagrams obtained by yarrow or 4-coin methods are less pessimistic than those of the traditional 3-coin method. Ralph Abraham ( http://www.ralph-abraham.org/ ) demonstrates mathematically why yarrow probabilities are more "optimistic" than those of the coin oracle:

[In regard to the probabilities of obtaining a particular type of line using the yarrow method:] All this is explained in detail in Wilhelm, pp. 721-722. In summary:6 -x- old yin 1/16 7 --- young yang 5/16 8 - - young yin 7/16 9 -o- old yang 3/16This is radically different from the coin oracle, and this is just one reason for preferring the yarrow method.

In practice, an experienced hand will not achieve these probabilities, for the reason described above. In avoiding the very unequal divisions, a small advantage is gained to the remainder 8 and its score 2, and so the expectation of a 6 line, old yin, will be a bit larger than 1/16. This effect is included in our simulation by the use of a chaotic attractor to arrange the heap. By a series of experiments, you may choose a heap algorithm to match your own hand.

Line probabilities in the first hexagram Casting a hyperhexagram with 18 divisions of yarrow determines two hexagrams. A yang line in the first hexagram results from either a young yang or an old yang hyperline in the hyperhexagram. Thus the probability of an initial yang line is the sum of the probabilities of old yang (3/16) and young yang (5/16) or 8/16: 50%.

The chances of an initial yin line are similarly the sum of old yin (1/16) plus young yin (7/16), or 8/16: 50%. Initially, yang and yin are equiprobable. This is the same as the coin oracle, in which initial yin and yang are also balanced 50-50.

Probabilities for changing lines The chances of a changing yarrow hyperline are (1/16) for old yin, plus (3/16) for old yang, or 4/16: 25%. Again, this is the same as in the coin oracle.

Line probabilities in the second hexagram In the second hexagram, a yin line results from either an original young yin (7/16) or an old yang (3/16) or 10/16 = 5/8. Similarly, a yang line results from either an initial young yang (5/16) or an old yin (1/16) pr 6/16 = 3/8. Here we have a significant difference between the yarrow-stalk oracle and the coin oracle.

With the YSO, final yin is 5/3 times more likely than yang. This is the reason for thinking that the coin oracle has contributed to world problems.

He goes on to give the coin probabilities: In each coin toss there is one chance in two or probability of 1/2 of obtaining a head or a tail. As three coin tosses determine a line, it is easy to compute the probabilities of the four lines:6 -x- old yin 1/8 7 --- young yang 3/8 8 - - young yin 3/8 9 -o- old yang 1/8After casting a hyperhexagram with six tosses of three coins, a yang line in the first hexagram results from either a young yang or an old yang hyperline. Thus the probability of a yang line is the sum of the probabilities of old yang (1/8) and young yang (3/8) or 4/8, 50%. The chances of a yin line are likewise 50%. This is an equal opportunity system.

The chances that a hyperline will be changing, old yang or old yin, is (1/4 + 1/4) or 25%.

VII Roderic Sorrell and Amy Max Sorrell's I Ching Made Easy (ISBN 0-06-251073-8) is an accessible, good introduction to the Yi Jing. They also have a website at: http://www.teleport.com/~bioching/iching.html

VIII Hacker describes two similar methods using 6 or 12 flat "wands." Same idea; flatter sticks. (See Chapter 10 in Hacker.)

IX For example, see Zhao Xiamin & Martin Palmer's Chinese Fortune Stalks (ISBN 1-55670-985-4).

X Based on Evelyn Lip's Chinese Numbers (ISBN 0-89346-376-0).

XI See Chris Lofting's Book of Changes (IC+) at: www.ozemail.com.au/~ddiamond/index1.html

XII ISBN 0-8048-3102-5. Visual I Ching also includes a set of 64 cards, each representing one of the hexagrams. A "pick one" method suggests itself.

XIII For more details, see Alfred Huang's The Complete I Ching (ISBN 0-89281-656-2)

XIV See pp. 208-211 of Ni's I Ching (ISBN: 0937064815). http://taostar.com/

XV See http://www.netowne.com/eastern/iching/ for a good brief overview. This provides just a sample of the master mathematician's methods in the Meihua Xinyi (Plum Flower Mind Yi Jing) There is no full English translation of that work available as yet.

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EncyclopediaAmong the many forms of divinationis a bibliomancymethod using the I Ching(易經) or Book of Changes. The book is structured as 32 pairs of hexagrams, divided in half after the first 30. The text was a subject for civil service exams in Imperial China. To aid in learning these 64 hexagrams, an 8x8 matrix of the 64 hexagrams in terms of all the hexagrams having the same top three lines, called a trigram. Throughout China's region of cultural influence (including Korea, Japanand 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 Chingmain article for historical and philosophical information).

The process of consulting the book as an oracleinvolves 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 should not consult the Oracle for divination until over the age of 40.. 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.

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 yinto yangand 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.

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

Plastromancyor the turtleshell 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 oxshoulder 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-16, 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.

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, and produces outcomes with different likelihoods. 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 three, and tails as two. The lower pair are tails if and only if both are tails.

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

Therefore the odds of 6 = 1/16Therefore the odds of 7 = 5/16Therefore the odds of 8 = 7/16Therefore 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 farthest 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 dieas 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 backgammonsets. 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 numberthenif 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:thenif 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 11 (which can likewise be diagrammed on the 8x8 grid). So a total of two, four, seven or 11, when yielded by one 2d8 roll, can indicate that the resulting yin or yang line is moving.

Marbles or beads (method of 16)

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 (see Probability Analysis below).

use 16 marbles

of four different colours but the same size, distributed as follows

o 1 marble of a colour representing old yin (such as blue)

o 5 marbles of a colour representing young yang (such as white)

o 7 marbles of a colour representing young yin (such as black)

o 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

o shake all 16 marbles together in the container to "shuffle" them

o draw out one marble

o the marble drawn determines the current line of the hexagram

o 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) old yang: 3 in 16 (0.1875) young yang: 5 in 16 (0.3125) young yin: 7 in 16 (0.4375)

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 at 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

also see "Plum Blossom Oracle" in Calendric systems (below).

Calendric systems

There is a component of Taoist thought which is concerned with numerological/cosmologicalsystems. 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 here 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.

Wen Wang Gua Method

This method goes back to Jing Fang(78–37 BC). While a hexagramis derived with one of the common methods like coin or yarrow stalks, here the divination is not interpreted on the basis of the classic I Ching text. Instead, this system connects each of the six hexagram lines to one of the 12 Earthly Branchesand then the picture can be analyzed with the use of 5 Elements (Wu Xing).

By bringing in the Chinese calendar, this method not only tries to determine what will happen, but also when it will happen. As such Wen Wang Gua makes a bridge between I Chingand the Four Pillars of Destiny.

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. Examples are

http://www.dentato.it/iching/, an alternative calculation of the yarrow stalk probabilities; OrganicDesign:I Ching / Divination, explains the traditional probabilities 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, , which is that of including the selection of zero as a quantity for either hand. The traditional method was designed expressly to produce four 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%