I Ching divination

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Among the many forms of divination is a cleromancy method using the I Ching (易經, yì jīng) or Book of Changes. I Ching consists of sixty-four hexagrams and commentary upon those symbols. Each hexagram is six lines, each one of which is either yin (represented by a broken line) or yang (a solid line). By randomly generating the six lines by one or other of various methods and then reading the commentary associated with the resulting hexagram, the sense(s) of that commentary is (are) then used as an oracle.

Certain schools of Chinese philosophy (such as the School of Yin-Yang, whose tenets were largely adopted by Taoism, though both are centuries younger than I Ching) maintain that powerful old yin will eventually turn to young yang and vice versa, so in addition to lines' being considered either yin or yang, they are also either young (i.e., stable) or old (i.e., changing); any hexagram that contains old yin or old yang lines (both being referred to as moving lines) thus also produces a second, different hexagram in which the moving lines of the first hexagram become their opposites (i.e., old yin becomes yang, and old yang becomes yin). The person consulting the oracle then also studies both the commentary specific to any moving line(s) and the commentary associated with the second hexagram formed when the indicated changes of lines have been made to the first.

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, interpreting the oracle from the pictures created by the lines, bigrams, trigrams, and final hexagram.


Several of the methods of consultation produce one number (6, 7, 8, or 9, corresponding to old yin, young yang, young yin, and old yang, respectively) per application of a more or less complex procedure, so that six passes through the procedure are required to generate one hexagram (or two hexagrams, if the first has any changing lines). Simpler (and sometimes less traditional) procedures can also be used.

Several of the methods described below force exactly one, or no, moving lines, whereas the traditional yarrow-stalk method allows from zero to six moving lines. The yarrow-stalk method favours static lines over moving lines in the ratio 3:1, and favours old yang to old yin in the same ratio.

The `Consult I Ching` app guides through the divination process and automatically map the results to curated interpretations.

Precursor to I Ching: Cracks in turtle shell[edit]

Plastromancy or the turtle shell oracle is probably the earliest recorded form 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. millefolium var. millefolium) stalks, used for I Ching divination.

Hexagrams may be generated by the manipulation of yarrow stalks. These are usually genuine Achillea millefolium stalks that have been cut and prepared for such purposes or any form of wooden rod or sticks (the quality ranging from cheap hardwood to very expensive red sandalwood etc.) which are plain, lacquered or varnished. When genuine Achillea is used, varieties local to the diviner are considered the best as they would contain qi closer to and more in-tune with the diviner, or they may come from a particularly spiritual or relevant place such as on the grounds of a Confucian temple. When not in use, they are kept in a cloth or silk bag/pouch or a wooden case/box.

Fifty yarrow stalks are used, though one stalk is set aside at the beginning and takes no further part in the process of consultation. The remaining forty-nine stalks are roughly sorted into two piles, and then for each pile one stalk is initially 'remaindered' then the pile is "cast off" in lots of four (i.e., groups of four stalks are removed). The remainders from each half are combined (traditionally placed between the fingers of one hand during the counting process) and set aside, with the process then repeated twice (i.e., for a total of three times). The total stalks in the remainder pile will necessarily (if the procedure has been followed correctly) be 9 or 5 in the first count and 8 or 4 in the second. 9 or 8 is assigned a value of 2, 5 or 4 a value of 3. The total of the three passes will be one of just four values: 6 (2+2+2), 7 (2+2+3), 8 (2+3+3), or 9 (3+3+3); that count provides the number of the first line.[1] The forty-nine stalks are then gathered and the entire procedure repeated to generate each of the remaining five lines of the hexagram. (Each succeeding line is written above its predecessor, i.e., the first line is at the bottom of the "stack" of lines, and the final, sixth line is at the top.)

The yarrow-stalk method produces unequal probabilities[2][3] for obtaining each of the four totals, 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 --------

Note that the Yarrow algorithm is the name of a particular algorithm for generating random numbers. While it is named for the I Ching yarrow-stalks method, 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 stalks produce four different probabilities for each of the four lines occurring, 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-stalk 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.

Modified Three-coin method[edit]

The 3 coin method can be modified to have the same probabilities as the yarrow-stalk method by having one of the coins be of a second coin type, or in some way be marked as special. All three coins are tossed at once. The results are counted just as the original three-coin method with two special exceptions. One to make yang less likely to move, and one to make yin more likely to move.

In the case where you have all three heads, re-flip the marked coin. If it remains heads, then you have a 9 (moving yang). Otherwise, it is treated as a 7 (static yang).

In the case where the special coin is tails and the other two are both heads, which would normally produce an 8, re-flip the marked coin. If it remains tails, then treat it as a 6 (moving yin). Otherwise, it remains an 8 (static yin).

This method retains the 50% chance of yin:yang, but changes the ratio of moving yang to static yang from 1:4 to 1:7. Likewise it changes the ratio of moving yin to static yin from 1:4 to 3:5. Which is the same probabilities as the yallow-stalk method.

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, each coin is valued separately, to give a sum from 6 to 9, as above. This results in the same distribution of probabilities as for the yarrow-stalk method

Four coins[edit]

With tails assigned the value 0 and heads the value 1, four coins tossed at once can be used to generate a four-bit binary number, the right-most coin indicating the first bit, the next coin indicating the next bit, etc. The number 0000 is called old yin; the next three numbers—0001, 0010, and 0011 (the binary numbers whose decimal equivalents are 1, 2, and 3, respectively)—are called old yang, with a similar principle applied to the remaining twelve outcomes. This gives identical results to the yarrow-stalk 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 --- ---

The two-coin method described above can be performed with four coins, simply by having one pair of coins be alike—of the same size or denomination—while the other two are of a different size or denomination; the larger coins can then be counted as the first toss, while the two smaller coins constitute the second toss (or vice versa).

Six coins[edit]

Six coins—five identical coins and one different—can be thrown at once. The coin that lands closest 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.


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-stalk method. For example, because the chances of any yin line or any yang line are equal in the yarrow-stalk 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-stalk method's outcomes.

Another dice method that produces the 1:7:3:5 ratio of the yarrow-stalk method is to add 1d4 + 1d8. All odd results are considered yang, with the result of eleven denoting an old yang. Any even results would be considered yin and both fours and tens are treated as old yin.

Long Dice, a.k.a. Zhǎng Shǎizi[edit]

(See article: Long Dice)

A recent innovation in I Ching divination—長色子 zhǎng shǎizi, "long dice"—is a variation on older dice-rolling methods using a set of three specially made dice. The long-dice method was created by an artisan in the United States to mimic the probabilities of the traditional yarrow-stalk method. The long dice each have four faces marked with either two or three dots, called "pips". Two of the zhǎng shǎizi are identical, and possess equal probabilities of rolling a 2 or a 3; the final die has three sides with three pips and one side with two pips. The dice are cast six times to obtain the six lines of an I Ching hexagram.

Marbles or beads (Method of Sixteen)[edit]

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

  • 1 marble of a colour (such as blue) representing old yin
  • 5 marbles of a colour (such as white) representing young yang
  • 7 marbles of a colour (such as black) representing young yin
  • 3 marbles of a colour (such as red) representing old yang

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

Methods = It may be simpler to compare the yarrow-stalk and the Method of Sixteen procedures with probabilities.

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 divisions into piles differing within two standard deviations of the mean. The diviner must attempt to divide equally, or the algorithm is lost.

The Method of Sixteen simply produces the correct numbers using sixteen instances of some element of equal probability, such as marbles, subdivided into four subsets of the correct numbers, i.e., 1, 3, 5, 7. The diviner just selects (with replacement) 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[5] 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.[6] Chu and Sherrill provide five astrological systems in An Anthology of I Ching[7] and in The Astrology of I Ching[8] 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.[5] 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.[5]

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 Twelve Earthly Branches, and then the picture can be analyzed with the use of 5 Elements (Wu Xing).[9]

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.

Software methods[edit]

The preceding ("concrete"/physical) methods can be simulated in ("abstract"/conceptual) software. This has the theoretical advantage of improving randomness aspects of I Ching ("not-doing" in the personal sense, enhancing the "universal" principal), but the practical disadvantage of not pre-focusing/preparing the mind.

Here is a typical example (for the "modified 3-coin" method but you can change to 3-coin if you want to):

# iChing_Modified_3_coins.py
#   see https://github.com/kwccoin/I-Ching-Modified-3-Coin-Method
#   Create (two) I Ching hexagrams: present > future (might be same).
# With both "3-coin method" and "modified 3-coin method" (see https://en.wikipedia.org/wiki/I_Ching_divination).
# 3-coins Probabilities:
#   old/changing/moving yin    "6 : == x ==" = 1/8
#   (young/stable/static) yang "7 : =======" = 3/8
#   (young/stable/static) yin  "8 : ==   ==" = 3/8
#   old/changing/moving yang   "9 : == o ==" = 1/8
# Modified 3-coins Probabilities: 
# (only 1/8 chance with the special coin tail and 2 head; and 8/9 throw one more time)
#   old/changing/moving yin    "6 : == x ==" = 1/8 + 1/8*1/2   = 3/16
#   (young/stable/static) yang "7 : =======" = 3/8 + 1/8*1/2   = 7/16
#   (young/stable/static) yin  "8 : ==   ==" = 3/8 - 1/8*1/2   = 5/16
#   old/changing/moving yang   "9 : == o ==" = 1/8 - 1/8*1/2   = 1/16

import random

rng = random.SystemRandom()  # (auto-)seeded, with os.urandom()

#method = "3 coin"
method = "modified 3 coins"

special_coin = 0

def toss():

    val = 0

    for flip in range(3):        # 3 simulated coin flips
        val += rng.randint(2,3)  # tail=2, head=3
        if flip == 0:
            special_coin = val

    if method == "coin":
        return val
        # method similar to "yallow-stick"
            if val == 9:
                if rng.randint(2,3) == 3:
                    val = 9
                    value = 7
            if val == 8:
                if special_coin == 2:
                    if rng.randint(2,3) == 2: 
                        val = 6
                        val = 8
    return val

# We build in bottom to top

print("Method is ",method,"\n")
toss_array = [0, 0, 0, 0, 0, 0]

for line in range(0,6,1):
    toss_array[line] = toss()
    print("line is ",line+1,"; toss is ",toss_array[line],"\n")

# hence we print in reverse

def print_lines_in_reverse(toss_array):
    for line in range(5,-1,-1):
        val = toss_array[line]
        if   val == 6: print('6  :  == x == ||   ==   ==  >  -------')
        elif val == 7: print('7  :  ------- ||   -------  >  -------')
        elif val == 8: print('8  :  ==   == ||   ==   ==  >  ==   ==')
        elif val == 9: print('9  :  -- o -- ||   -------  >  ==   ==')



With a modified 3 coin method as default, this may avoid the Sung dynasty issue i.e. when you have an easy available and simple method you use it but lost the probability! (Also, the first number shall be in the bottom and hence the printing shall start from the bottom).

Probability analysis of I Ching divination[edit]

Most analyses of 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 the former 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.

However, the calculation of the frequencies for the yarrow-stalk method—generally believed to be the same as those described in this article in the simplified method using sixteen objects—contains a further error, in the opinion of Andrew Kennedy,[10] which is that of including the selection of zero as a quantity for either hand. The yarrow-stalk procedure expressly requires that the four numbers be produced without using zero; Kennedy shows that by not allowing the user to select zero for either hand, or a single stalk for the right hand (this stalk 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 modified the simplified method of using sixteen coloured objects described in this article as follows:

take 38 objects, of which

  • 8 are of one colour = moving yang
  • 2 are of a different colour = moving yin
  • 11 are of a different colour = static yang
  • 17 are of a different colour = 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.[11][12][13]
  • 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.
  • In episode 700 of the Dark Shadows original TV series, Barnabas Collins and Professor Elliott Stokes discover a set of I Ching wands in a drawer in an abandoned section of the Collinwood mansion. Barnabas casts himself into a trance using the wands, allowing his astral body travels back to the year 1897.


  1. ^ http://www.instructables.com/id/Consult-the-I-Ching-with-Yarrow-Stalks/
  2. ^ "I Ching / Divination - Organic Design". www.organicdesign.co.nz. Retrieved 2015-09-03.
  3. ^ "The Invisible Basilica: Probability and the Yi Jing". hermetic.com. Retrieved 2015-09-03.
  4. ^ Just math
  5. ^ 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.
  6. ^ 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.
  7. ^ Sherrill, W.A.; Chu, W. (1978). An Anthology of I Ching. Routledge & Kegan Paul. ISBN 978-0-7100-8590-0. LCCN 78303708.
  8. ^ Chu, W.; Sherrill, W.A. (1993). The Astrology of I Ching. Penguin Group USA. ISBN 978-0-14-019439-5. LCCN 93234616.
  9. ^ Wen Wang Gua, Joseph Yu
  10. ^ Andrew Kennedy, [1] Briefing Leaders, Gravity Publishing, UK, 2006, ISBN 0-9544831-3-8
  11. ^ Forrest Wickman (May 20, 2013). "Last Night's Mad Men: The Vietnam Theory". Slate.
  12. ^ Ed Coin (May 20, 2013). "The Chinese I Ching Coins as Seen on "Mad Men"". Educational Coin Company.
  13. ^ 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]