I Ching divination

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Among the many forms of divination is a cleromancy method using the I Ching (易經) or Book of Changes. I Ching comprises 64 hexagrams and commentary upon these symbols. Each hexagram comprises 6 lines, either broken or solid, representing either yin or yang. By randomly generating these six lines and then reading the text associated with it the book is used as an oracle. Lines can also be called either young (stable) or old (changing). Any hexagram that contains "old yin" or "old yang" can change into a new hexagram when the any "old" lines change into their opposites, thus the person consulting the oracle will read both commentary specific to the changing lines as well as looking up the newly formed hexagram.

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. Historical and philosophical information, as well as a list of English translations, can be found here. The text is extremely dense reading. 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.


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 and thus determines each line of the hexagram. Certain schools of Chinese philosophy (such as the School of Yin-Yang whose tenets were largely adopted by Daoism, though both are centuries younger than I Ching) maintain that powerful old yin will eventually turn to young yang and vice versa so a new hexagram is formed by transposing each changing line with its opposite. 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 described below force exactly one or no moving lines when the traditional yarrow stick method allows from zero to six moving lines. The yarrow stick method favours static lines to moving lines in the ratio 3:1 and favours moving yang to moving yin in the same ratio.

Plastromancy - turtle shell cracks[edit]

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[edit]

A bunch of 50 yarrow Achillea millefolium subsp. m. var. millefolium stalks, used for I Ching divination.

Hexagrams may be generated by the manipulation of yarrow stalks. Yarrow stalks occur as sets of fifty of which one is set aside and takes no part in the process. The remaining forty-nine are roughly divided in half and then each pile is cast off in lots of four. The remainders from each half are combined and the process is repeated twice. The remainder piles assigned a value of either two or three depending on their size. These values give a total from 6 - 9 and so indicate the first line. The forty-nine stalks are then gathered and the process repeated to generate the remaining five lines. This leads to unequal probabilities[1][2] of obtaining each total as shown in the table.

Number Yarrow stick probability Three coin probability YinYang Signification Symbol
6 1/16 8/16 2/16 8/16 old yin yin changing into yang ---x---
8 7/16 6/16 young yin yin unchanging ---  ---
9 3/16 8/16 2/16 8/16 old yang yang changing into yin ---o---
7 5/16 6/16 young yang yang unchanging --------

"The Yarrow Algorithm" is the name of a particular algorithm for generating random numbers. It is named after the I Ching yarrow method, although the details of the algorithm are unrelated to it.

Yarrow Stalks prepared for regular usage

Comparison of yarrow and three coin method[edit]

Whereas yarrow sticks produce four different probabilities for each of the four values coin tossing produces pairs of probabilities. The probability of getting a yin or a yang line is the same (p = 8/16 = 1/2) by both methods so the probability of getting any particular hexagram is the same in each method. However, the probabilities of getting old, changing lines are different. While in both methods there is a p = 4/16 = 1/4 chance of getting a changing line in the coin method this is equally likely to be old yin or old yang (p = 2/16) whereas in the yarrow stick method it is 200% more likely to be old yang than old yin (p = 3/16 compared to p = 1/16).


Three-coin method[edit]

Two heads and one tail of the original I-Ching Divination Coins.

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, but produces outcomes with different likelihoods. Three coins are tossed at once. Each coin is given a value of 2 or 3 depending upon whether it is tails or heads respectively. Six such tosses make the hexagram.

Two-coin method[edit]

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.

The two coin method involves tossing one pair of coins twice. On the first toss two heads give a value of 2 and anything else is 3. On the second toss the each coin is valued separately to give a sum from 6 - 9 as above. This results in the same distribution of probabilities as for the yarrow stalk method

Four coins[edit]

Four coins tossed at once can be used to generate a four bit binary number. The left most coin becoming the first bit, the next coin being the next bit etc. Tails assume a value of 0, heads a value of 1. The number 0000 is called old yin; the next three numbers 0001, 0010, and 0011 (being decimal numbers whose decimal equivalents are 1, 2 and 3) are called old yang with a similar principal applied to the remaining twelve outcomes. This gives identical results to the yarrow stick method.

Coins Binary Decimal Line
T T T T 0000 0 ---x---
T T T H 0001 1 ---o---
T T H T 0010 2 ---o---
T T H H 0011 3 ---o---
Decimal Coins Line
4 T H T T -------
5 T H T H -------
6 T H H T -------
7 T H H H -------
Decimal Coins Line
8 H T T T -------
9 H T T H --- ---
10 H T H T --- ---
11 H T H H --- ---
Decimal Coins Line
12 H H T T --- ---
13 H H T H --- ---
14 H H H T --- ---
15 H H H H --- ---

Four coins can also be used at once by having two large coins and two small coins. The two large coins stand for the first toss and the two small coins stand for the second toss of the two coin method described above.

Six coins[edit]

Six coins - five identical coins and one different - can be thrown at once. The coin that lands closes to a line drawn on the table will make the first line of the hexagram and so on, heads for yang, tails for yin. The distinct coin is a moving line. This has the dual failings that it forces every hexagram to be a changing hexagram and it only ever allows exactly one line to be changing.

Eight coins on Ba Qian[edit]

Eight coins, one marked, are tossed at once. They are picked up in order and placed onto a Bagua diagram; the marked coin rests on the lower trigram. The eight process is repeated for the upper trigram. After a third toss the first six coins are placed on the hexagram to mark a moving line. This has the deficiency or allowing at most one moving line whereas all six lines could be moving in traditional methods.

Zhang Shaizi

Zhang Shaizi, or "Long Dice"[edit]

A set of 3 dice: the rectangular sides are marked with 2 or 3 dots, or "pips". One of the 3 dice has three sides marked with 3 pips and the fourth side with 2 pips. The other shaizi alternate 2 pips on two sides and 3 pips on the other sides. The dice are cast six times on a flat surface to obtain whole lines or broken lines. The possible sums of the pips are 6, 7, 8, or 9. In this way, the probabilities mimic the probabilities of the Yarrow Stalk oracle. It is uncertain how far in the past these have been available, but they are in keeping with the tradition of the Oracle.


Any dice with an even number of faces can also be used in the same fashion of the coin tosses with even die rolls for heads and odd for tails. An eight sided die (d8) can be used to simulate the chances of a line being an old moving line equivalent to the yarrow stick method. For example, because the chances of any yin line or any yang line are equal in the yarrow stick method there is a one in eight chance of getting any basic trigram, the same chance held under the ba qian method so the ba qian method can thus be used to determine the basic hexagram. The d8 can then be used by rolling it once for each line to determine moving lines. A result of 1 on a yin line or 3 on a yang line will make that line a moving line, preserving the yarrow stick method's outcomes.

Marbles or beads (method of 16)[edit]

Sixteen marbles can be used in four different colours. For example:

  • 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)

The marbles are drawn with replacement six times to determine the six lines. The distribution of results is the same as for the yarrow stick method.

Methods = It may be simpler to understand the Yarrow and Way of 16 methods by probability.

A yarrow cast of 9 has a probability of 1/4, and a 5 of 3/4. Both 4 and 8 have probability of 1/2.

If P(cast) <= sqr(1) / 16 then a moving yin value 6 1/16 49 - 6 * 4 = 25 (9, 8, 8)

Else if P(cast) <= sqr(2) / 16 then a moving yang value 9 3/16 49 - 9 * 4 = 13 (5, 4, 4)

Else if P(cast) <= sqr(3) / 16 then a static yang value 7 5/16 49 - 7 * 4 = 21 (5, 8, 8), (9, 4, 8), (9, 8, 4)

Else if P(cast) <= sqr(4) / 16 then a static yin value 8 7/16 49 - 8 * 4 = 17 (5, 4, 8), (5, 8, 4), (9, 4, 4)

Even is yin, Odd is yang. Extrema are changing.

Yang and Yin are equally likely. Static is more likely than changing.

The yarrow method produces 'near' probabilities dependent upon the initial splits differing within two standard deviations of the mean. The diviner must attempt to divide equally, or the algorithm is lost.

The Way of 16 simply produces the correct amounts using 16 instances of some element of equal probability, such as marbles, subdivided into 4 subsets of the correct amounts, i.e. 1, 3, 5, 7. The diviner just selects one marble at random.


Rice grains[edit]

For this method, either rice grains, or small seeds are used. Six small piles of rice grains are made by picking up rice between finger and thumb. The number of grains in a pile determines if it is yin or yang. This has the deficiency of forcing zero and exactly zero lines in the hexagram to be a moving line when using the traditional yarrow method there can from zero to six moving lines.

Calendric cycles and astrology[edit]

There is a tradition of Taoist thought which explores numerology, esoteric cosmology, astrology and feng shui in connection with the I Ching.

The Han period (206 BCE-220 CE)… saw the combination and correlation of the I Ching, particularly in its structural aspects of line, trigrams, and hexagrams, with the yin-yang and wu hsing (Five Element) theories of the cosmologists, with numerical patterns and speculations, with military theory, and, rather more nebulously, with the interests of the fang-shih or "Masters of Techniques," who ranged over many areas, from practical medicine, through alchemy and astrology, to the occult and beyond.
— Hacker, Moore and Patsco, I Ching: an annotated bibliography, "The I Ching in Time and Space", p. xiii

The eleventh century Neo-Confucian philosopher Shao Yung contributed advanced methods of divination including the Plum Blossom Yi Numerology, an horary astrology[4] that takes into account the number of calligraphic brush strokes of one's query.[citation needed] Following the associations Carl Jung drew between astrology and I Ching with the introduction of his theory of synchronicity, the authors of modern Yi studies are much informed by the astrological paradigm.[5] Chu and Sherrill provide five astrological systems in An Anthology of I Ching[6] and in The Astrology of I Ching[7] develop a form of symbolic astrology that uses the eight trigrams in connection with the time of one's birth to generate an oracle from which further hexagrams and a daily line judgement are derived.[4] Another modern development incorporates the planetary positions of one's natal horoscope against the backdrop of Shao Yung's circular Fu Xi arrangement and the Western zodiac to provide multiple hexagrams corresponding to each of the planets.[4]

Wen Wang Gua method[edit]

This method goes back to Jing Fang (78–37 BC). While a hexagram is 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 Branches and then the picture can be analyzed with the use of 5 Elements (Wu Xing).[8]

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 Ching and the Four Pillars of Destiny.

Probability analysis of I Ching divination[edit]

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

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,[9] 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%

In popular culture[edit]

  • Profiler Season 1 Episode 3 'Holy Alliance' 1996. A serial killer uses I Ching and the Hexagram determines what and how someone is chosen and killed.
  • In the Mad Men season 6 episode, "Crash", Frank Gleason's flower child daughter, Wendy, uses the three-coin method to tell fortunes at the offices of the newly merged firm.[10][11][12]
  • in "The Man In the High Castle" by Philip K. Dick, several characters consult the I Ching at various points, and consider the answers given. Dick apparently used the I Ching while writing his novel, to help him decide on the direction of the plot.
  • In the song "God" by John Lennon, he states that he "doesn't believe in I Ching", among many other religious and cultural phenomena that he claims to not believe in or follow.
  • In Philip Pullman's The Amber Spyglass, Mary Malone uses the I Ching as a way to communicate with Dust.


  1. ^ "I Ching / Divination - Organic Design". www.organicdesign.co.nz. Retrieved 2015-09-03. 
  2. ^ "The Invisible Basilica: Probability and the Yi Jing". hermetic.com. Retrieved 2015-09-03. 
  3. ^ Just math
  4. ^ a b c Hacker, E.A.; Moore, S.; Patsco, L. (2002). I Ching: an annotated bibliography. Routledge. p. 6,21,68,87–88,125,250. ISBN 978-0-415-93969-0. 
  5. ^ Grasse, R.; Houck, R.; Watson, B.; Erlewin, M.; Defouw, H.; Braha, J. (1997). Eastern Systems for Western Astrologers: An Anthology. S. Weiser. ISBN 978-1-57863-006-6. LCCN 97001457. 
  6. ^ Sherrill, W.A.; Chu, W. (1978). An Anthology of I Ching. Routledge & Kegan Paul. ISBN 978-0-7100-8590-0. LCCN 78303708. 
  7. ^ Chu, W.; Sherrill, W.A. (1993). The Astrology of I Ching. Penguin Group USA. ISBN 978-0-14-019439-5. LCCN 93234616. 
  8. ^ Wen Wang Gua, Joseph Yu
  9. ^ Andrew Kennedy, [1] Briefing Leaders, Gravity Publishing, UK, 2006, ISBN 0-9544831-3-8
  10. ^ "Last Night’s Mad Men: The Vietnam Theory author= Forrest Wickman". Slate. May 20, 2013. 
  11. ^ Ed Coin (May 20, 2013). "The Chinese "I Ching" Coins as Seen on "Mad Men"". Educational Coin Company. 
  12. ^ SEAN T. COLLINS (05.20.133:55 PM). "The Ultimate Don Draper Pitch Is Don Draper: Seeing Mad Men Through Its Ads". Wired.  Check date values in: |date= (help)

External links[edit]

  • The Yin Yang Horoscope An online version of the astrological system described by Chu and Sherrill in their book The Astrology of the I-Ching.
  • Eight Houses Basic information on the interpretive system of Jing Fang known as Wen Wang Gua.