I Ching/The Ancient Yarrow Stalk Method

The Ancient Yarrow Stalk Method of Casting a Hexagram

In the ancient yarrow stalk method, fifty yarrow stalks are used. If it is hard to find yarrow stalks, substitutes such as bamboo skewers, wooden sticks, etc may be used.

The procedure of the modified yarrow stalk method to obtain a hexagram is as follows:

Casting The Hexagram
For one line of the hexagram:
 * 1) Remove one yarrow stalk from the fifty stalks, and put it in front of you, in a direction parallel to your body. This is the observer stalk, you will not be using it again while casting the hexagram
 * 2) Randomly divide the remaining 49 sticks into 2 piles. Put the 2 piles on both sides of you, pointing away from you, in a direction perpendicular to your body.
 * 3) Pick up a yarrow stalk from the pile on the RIGHT, and put it between the little finger and the ring finger of the LEFT hand. This is the 2nd stalk.
 * 4) Pick up the remaining yarrow stalks from the pile on the LEFT with your LEFT hand.
 * 5) Remove 4 stalks at a time from the LEFT hand, and put them on the table, in individual piles of 4 stalks each. This process is stopped when there are 4 or less stalks left. Put these remaining stalks held on the LEFT hand between the ring finger and the middle finger of the LEFT hand.
 * 6) Now, pick up the RIGHT hand heap, and sort it by fours in the same way, placing the remainder into the next gap between your fingers.
 * 7) Count the stalks you are holding in your LEFT hand.  This first total is either 5 or 9. (The various possibilities are 1+4+4, or 1+3+1, or 1+2+2, or 1+1+3.)
 * 8) Set these counted stalks separately, and gather the uncounted stalks into a new pile. Repeat the steps above, to obtain a second total of 4 or 8. This time the possible combinations are 1+4+3, or 1+3+4, or 1+1+2, or 1+2+1. Likewise, these stalks are separated.
 * 9) Repeat the procedure one last time, to get a third set of 4 or 8 stalks.  You should now have three counted piles of 4/5 or 8/9.
 * 10) The counted stalks are in groups of 4/5 or 8/9.  For each group of 8 or 9, count 2. For each group of 4 or 5, count 3. This count should match the final number of removed piles of four, and determines the hexagram line.  The result shown in the table below:

Gather the 49 yarrow sticks and repeat the process above for the five other lines, going from the bottom to the top.

Notes on Probability
Initially, there are 49 yarrow stalks.

There are 6 rounds (for six lines). For each line, we have 3 steps.

In step 1 when we have 49 -1 stalks and based on the rules above, the left pile will produce 1, 2, 3, or 4 stalks, and the corresponding right pile will produce 3, 2, 1 or 4 stalks respectively. This means the first casting will produce 8 stalks or 4 stalks.

The key difference between this and reminding 2 step is that you can see we have 4 possibility - one generate 8 and three generate 4, a bias result. That is the key difference between this and the following steps. This is due to the number 49 - 1 = 48 is divided by 4 whilst all the following is 40/44 (step 2). Probability of getting an 8 and 4 is 1:3 or 8 is 1/4 and 4 is 3/4.

On the second and third castings, the number of yarrow stalks is a multiple of four. However, as the rule require 1 is removed first before we do reminder, we have odd number and NOT DIVISIBLE by 4. Hence, in this two steps/castlings, the left pile produces 1, 2, 3 or 4 stalks, while the corresponding right produces 2, 1, 4, or 3 stalks respectively. Together with the stick removed, we have two 8 and two 4. Hence, the probability to get an 8 or an 4 is equal.

Hence, as long as you do it in the middle of the pile (and or just select 1-4 sticks say on the left or right), the process mainly is random. But the all sticks are 1/8 * 1/8 * 1/8 but instead it its

step 1 with (1/8) get 8 or (3/8) get 4 and remove from the pile i.e.

49 -> (1/4) 40

or (3/4) 44

step 2 with (1/2) get 8 or (1/2) get 4 and remove from the pile i.e.

40 -> (1/2) 32

or (1/2) 36

44 -> (1/2) 36

or (1/2) 40

step 3 with (1/2) get 8 or (1/2) get 4 and remove from the pile i.e.

32 -> (1/2) 24

or (1/2) 28

36 -> (1/2) 28

or (1/2) 32

36 -> (1/2) 28

or (1/2) 32

40 -> (1/2) 32

or (1/2) 36

If you chain them together you can see the odd probability of the yellow stick method:

49 -> (1/4) 40 -> (1/2) 32 -> (1/2) 24 with probability chain as 1/4 * 1/2 * 1/2 = 1/16 for 24

49 -> (1/4) 40 -> (1/2) 32 -> (1/2) 28 with probability chain as 1/4 * 1/2 * 1/2 = 1/16 for 28

49 -> (1/4) 40 -> (1/2) 36 -> (1/2) 28 with probability chain as 1/4 * 1/2 * 1/2 = 1/16 for 28

49 -> (1/4) 40 -> (1/2) 36 -> (1/2) 32 with probability chain as 1/4 * 1/2 * 1/2 = 1/16 for 32

49 -> (3/4) 44 -> (1/2) 36 -> (1/2) 28 with probability chain as 3/4 * 1/2 * 1/2 = 3/16 for 28

49 -> (3/4) 44 -> (1/2) 36 -> (1/2) 32 with probability chain as 3/4 * 1/2 * 1/2 = 3/16 for 32

49 -> (3/4) 44 -> (1/2) 40 -> (1/2) 36 with probability chain as 3/4 * 1/2 * 1/2 = 3/16 for 36

49 -> (3/4) 44 -> (1/2) 40 -> (1/2) 28 with probability chain as 3/4 * 1/2 * 1/2 = 3/16 for 28

Collecting all these we have

1/16                      for 24 i.e 1/16 for 6 (old ying)

1/16 + 1/16 + 3/16 for 28 i.e. 5/16 for 7 (young yang)

1/16 + 3/16 + 3/16 for 28 i.e. 7/16 for 8 (young yin)

3/16                      for 36 i.e. 3/16 for 9 (old yang)

1,5,7 and 3 over 16 very odd, all because the first number is 49 - 1 = 48.