THE ARCANE ARCHIVE
	a cache of usenet and other text files pertaining to occult, mystical, and spiritual subjects.

Subject: I Ching Methods Probabilities

compiled from usenet, 1995 - present

spelling and format editing has occurred within these
posts; some email addresses may be out of date.

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At the request of Amacker Bullwinkle
(abullwin@mv.us.adobe.com), i have compiled information
about I Ching probabilities taken from posts in the usenet
newsgroup alt.divination and the e-mail list hexagram-8 that
ran in 1995. Placing the data here -- in alt.lucky.w -- was
Amacker's idea, and it is not a bad one, since the "16 Item
Method" carries definite overtones of object-oriented,
talismanic work.

But first, here is credit where it is due:

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HEXAGRAM-8

The hexagram-8 list is for discussion and serious study of
the ancient Chinese Book of Changes, or I Ching. The name
comes from an I Ching reading the list owner has been
getting persistently throughout the months preceding the
founding of the list (April 1995). Hexagram 8, which various
translators have rendered as "Alliance" or "Teamwork,"
represents something which the list owner sincerely hopes
will emerge from discussions on the list.

To subscribe to hexagram-8, send the word "subscribe"
(without the quotes) alone in the body of an email message
to the following address:

hexagram-8-request@webcom.com

If you are having trouble subscribing or unsubscribing, send
your question to the human list owner, Ron Hale-Evans, at
rwhe@webcom.com

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I CHING TERMINOLOGY

Second: I assume y'all know that the I Ching is an ancient
system of divination based on the random generation of
binary choices of

solid (---) and broken (- -)

lines, arranged in groups of six, called hexagrams.

There are images and judgements attached to each hexagram
and because the solid and broken lines can "move" or change
their state from one to the other

(-o- means --- changes to - -) 
(-x- means - - changes to ---),

there are further images and judgements assigned to the
"changing lines" as well.

The oldest traditional method of determining the lines for
divinatory purposes is through a complex process involving
the manipulation of 50 dried yarrow stalks (yarrow is an
herb used for healing wounds, incidentally). Another, far
quicker method of determining the lines involves throwing
three coins (usually those pretty bronze Chinese coins with
square holes in the middle, but any coins will do). The
trouble is, the two methods give entirely different
distribution-patterns for the generation of solid,
solid-to-broken, broken, and broken-to-solid lines.

Okay, here is the compiled information on probabilities, the
"16 Item Method," and the "2 Dice Method."

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QUESTION ABOUT PROBABILITIES

Unknown Person (possibly seilerjp@telerama.lm.com) wrote:

Question: I prefer to almost always use the stalk method to
determine my hexagram. I know that the probabilities are
towards generating moving lines. I always get the feeling
that by using this method I am "loading" the answers or
hexagram. If I use the coin methods, the probability of
obtaining a 6, 7, 8, or 9 are all equal.  Anyone else get
this gnawing feeling?

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YARROW STALK, COIN, and "DUTCH STICK"  PROBABILITIES

hmesker@pi.net (Harmen Mesker) wrote:

You say that using the coin method, the probabilities of
obtaining a 6, 7, 8, or 9 are equal, but I'm afraid I have
to correct you on this point. According to Edward Hacker,
the probabilities for each method are:

      Yarrow    Coin 
      
6      1/16     2/16 
7      5/16     6/16 
8      7/16     6/16 
9      3/16     2/16

Most methods don't have equal probabilities.

Here in Holland are oblong sticks for sale (but you can
easily make them yourself), which have one line on each
side. With this method the probabilities of each line are
the same, namely 25%. I think this also means that for each
line of a hexagram you have 50% chance of obtaining a moving
line. If you use this method you'll have to deal with a lot
of moving lines, and I don't find that preferable.

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THE WAY OF 16 (THE 16 ITEM METHOD)

The following was re-posted by Carlos Griffin
(CGRIFFIN@ABQ-ROS.COM) but attributed to Dr. Lightning,
a.k.a. Francis Szot (szot@bcfreenet.seflin.lib.fl.us):

Another method is the "Way of 16", which someone posted as
an excerpt from  a book. I have used I Ching 20+ years using
coins, and found this method to be much more reliable and
even handed. -- Carlos Griffin

I found this method in "The I Ching: An Illustrated Guide to
the Chinese Art of Divination," illustrated by Tan Xiaochun
and translated by Koh Kok Kiang. According to that book,
Larry Schoenholtz first proposed this method in his book,
"New Directions in the I Ching". I switched from using the
Coins Method which I had used for over 20 years. --Dr.
Lightning, a.k.a. Francis Szot

The Method of 16 is, in my opinion, a much better way to do
the I Ching than the Three Coin Method. First, I'll explain
the Method of 16, then I'll tell you why it's better.

The Method of 16 uses 16 small, aesthetically attractive
objects, such as beads, shells, coins, buttons, pebbles etc.
They must all be of the same size and shape, but you must be
able to choose from four different  patterns or colors.
Select 7 items of one pattern or color (7 pink beads, for
example), 5 of a different pattern or color (5 blue beads,
for example), 3 of another pattern or color (3 white beads),
and 1 of a unique pattern or color (1 black bead). Each of
the four groups now represents a different type of line:
7/16 (the pink beads) = 8 (a broken unchanging line - -
[young yin]), 5/16 (the blue beads) = 7 (a solid unchanging
line --- [young yang]), 3/16 (the white beads) = 9 (a solid
changing line -0- [old yang]), and finally, 1/16 (the black
bead) = 6  (a broken changing line -x- [old yin]). To
complete the ritual's paraphernalia, thoughtfully select a
small bowl and a small container to store the 16 items when
not in use.

Mix the 16 items together in the small bowl and randomly
choose one. Note which of the four possible lines it
represents, record it as the first line of the hexagram
(building from the bottom up), then place it back in the
bowl. (of course, don't look as you select)  It is extremely
important to place each item back into the bowl so there is
always 16 objects to choose from!  Randomly choose again,
and record the second line.  Replace it, and continue in a
similar manner until the six lines of the hexagram have been
obtained. As one performs the ritual, keep in mind the
question you are inquiring about, and maintain an
appropriate attitude.

The main advantage of the Method of 16 over the Three Coin
Method, though certainly not its only advantage, is a
statistical one.  With the Yarrow Stalk Method, which will
remain the purist's choice, the probabilities of obtaining
each of the four different kinds of lines are not the same.
For example, the chances of getting a broken unchanging line
(8 - -), are 7 out of 16; the odds of getting a solid
unchanging line (7 ---), are 5 out of 16; for a solid line
that changes (9 -o-), 3 out of 16; for a broken line that
changes (6 -x-), the odds are only 1 out of 16.

Using the Three Coins Method, the chances of obtaining
either type of unchanging line is 6 out of 16, and the
chances of obtaining either type of changing line is 2 out
of 16.  The Method of 16 precisely duplicates the
probabilities of the Yarrow Stalk Method, something that the
Coin Method obviously does not do!

Good luck.  Perhaps this method will suit you.

Signed,  Dr. Lightning Francis Szot,
szot@bcfreenet.seflin.lib.fl.us

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THE TWO DICE METHOD

Jason A. Wolcott (jason-wolcott@uiowa.edu) wrote:

The probabilities of the different yarrow stalk results are:

1/16  -X-  moving yin 
3/16  -0-  moving yang 
5/16  ---  yang
7/16  - -  yin

I often use a dice method for casting hexagrams.  I wanted
something that  gave me the same distribution as the yarrow
stalks, but that was a little  more "portable."  My method
is to use 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 pobability) 
    if the 1d8  = 2 - 8  - -  yin (7/16 pobability)

If the 1d20 is an odd number: 
  then 
      if the 1d8 = 1 - 5  --- yang (5/16 pobability) 
      if the 1d8 = 6 - 8  -0- moving yang (3/16 pobability)

I still use the yarrow stalks at home, when I have time to
meditatively consider the question.  But sometimes I just
need quick advice. ;-)

Jason A. Wolcott 
Computer Consultant                        
University of Iowa           
(319)335-5523
jason-wolcott@uiowa.edu

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In summary, then, here are the probabilities for the five
methods.

No.   Line    Yarrow  Three   Dutch   16      2 
              Stalk   Coins   Stick   Items   Dice

6     -x-     1/16    2/16    4/16    1/16    1/16 
7     ---     5/16    6/16    4/16    5/16    5/16 
8     - -     7/16    6/16    4/16    7/16    7/16 
9     -o-     3/16    2/16    4/16    3/16    3/16

There you go, folks. Now it's up to you to find two
role-players' dice or "16 small, aesthetically attractive
objects" and "a small bowl and a small container to store
the 16 items when not in use." I think that the latter two
pieces of paraphernalia could be combined in one by using an
antique, decorative Chinese enamel covered rice bowl for
storage *and* random selection...or maybe an art deco
Noritake covered bowl...or a carved gourd bowl with lid. As
for the 16 items, i predict that someone will come up with a
better concept than mere "beads." I keep on getting this
image of 16 little Mexican milagros, or 16 of those tiny
multi-racial dolls you can buy from the Archie McPhee
catalogue...

Like the man said,

Good Luck.

catherine yronwode cat@luckymojo.com