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: 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 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. 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. Pick up the remaining yarrow stalks from the pile on the LEFT with your LEFT hand. 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. 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. 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.) 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. 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. 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: Number Yarrow stick probability YinYang Signification Symbol 6 1/16 8/16 old yin yin changing into yang ---x---87/16young yinyin unchanging ---  ---9 3/16 8/16 old yang yang changing into yin ---o---7 5/16 young yang yang unchanging -------- 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 remaining second and third steps is that we have 4 possibilities - one possibility generates 8 stalks and three possibilities generates 4 stalks - a biased result. That is the key difference between this step, and the following steps. This is because the number 49 - 1 = 48 is divisible by 4, while all the following second step is has 40 or 44. The odds of getting an 8 over a 4 is 1:3 or in other words getting 8 sticks has a 1/4 chance and getting 4 sticks has a 3/4 chance. On the second and third steps, the number of remaining yarrow stalks will start off as a multiple of four. However, since the rules require that we remove 1 stalk before counting any remainders, we have an odd number that is not divisible by 4 (whose remainder is 3). Hence, in the second castling, the left pile produces 1, 2, 3 or 4 stalks, while the corresponding right produces 2, 1, 4, or 3 stalks respectively. If we add back the 1 stick we removed earlier, we have two possibilities of 4 stalks and two possibilities of 8 stalks. Hence, the odds of getting 8 sticks or 4 sticks is 1:1. Note that if we did not have the process of removing 1 stick at first and simply split the piles in two, we would have mainly even chances with (1/2) probabilities at all steps. Instead, if we map out all possibilities, we can see that the possibilities are step 1 with (1/4) chance to get 8 sticks or with (3/4) chance to get 4 sticks and remove these from the pile, i.e., 49 -> (1/4) 40 or (3/4) 44 step 2 with (1/2) chance to get 8 sticks or (1/2) chance to get 4 sticks and remove these 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) chance to get 8 sticks or (1/2) chance to get 4 sticks and remove these 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 we chain all these possibilities together, we can see the probability distribution of the yarrow stick method: 49 -> (1/4) 40 -> (1/2) 32 -> (1/2) 24 (2+2+2=6) with probability chain as 1/4 * 1/2 * 1/2 = 1/16 chance for 24 sticks 49 -> (1/4) 40 -> (1/2) 32 -> (1/2) 28 (2+2+3=7) with probability chain as 1/4 * 1/2 * 1/2 = 1/16 chance for 28 sticks 49 -> (1/4) 40 -> (1/2) 36 -> (1/2) 28 (2+3+2=7) with probability chain as 1/4 * 1/2 * 1/2 = 1/16 chance for 28 sticks 49 -> (1/4) 40 -> (1/2) 36 -> (1/2) 32 (2+3+3=8) with probability chain as 1/4 * 1/2 * 1/2 = 1/16 chance for 32 sticks 49 -> (3/4) 44 -> (1/2) 36 -> (1/2) 28 (3+2+2=7) with probability chain as 3/4 * 1/2 * 1/2 = 3/16 chance for 28 sticks 49 -> (3/4) 44 -> (1/2) 36 -> (1/2) 32 (3+2+3=8) with probability chain as 3/4 * 1/2 * 1/2 = 3/16 chance for 32 sticks 49 -> (3/4) 44 -> (1/2) 40 -> (1/2) 36 (3+3+3=9) with probability chain as 3/4 * 1/2 * 1/2 = 3/16 chance for 36 sticks 49 -> (3/4) 44 -> (1/2) 40 -> (1/2) 32 (3+3+2=8) with probability chain as 3/4 * 1/2 * 1/2 = 3/16 chance for 32 sticks Collecting all these probabilities 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) Which is a highly uneven probability distribution for all four possibilities, all because of our initial starting point, 49 - 1 = 48.