A new method to draw hexagram lines for the ancient book I Ching

1. 易經
The binary divination
method for the I Ching
0110 6
Designed by Luciano Ramalho, programmer, game inventor and Yi Jing student

2. Classic divination methods
● Yarrow stalk ● Coins
● material: ● material:
50 yarrow stalks 3 identical coins
● probabilities: ● probabilities:
6 1/16 6.25% 6 1/8 12.50%
7 5/16 31.25% 7 3/8 37.50%
8 7/16 43.75% 8 3/8 37.50%
9 3/16 18.75% 9 1/8 12.50%

3. Binary divination method
● Material: 1 coin
● Probabilities: same as the yarrow stalk method
6 1/16 6.25%
7 5/16 31.25%
8 7/16 43.75%
9 3/16 18.75%
● Procedure: for each line, flip the coin 4 times;
record result according to table on next slide...

4. two zeroes,
0110 interrupted by 6
two ones
1001
two ones,
1011 interrupted by 9
one or two zeroes
1101
0000
any other
0010
...
sequence ending 8
in zero
1110
0001
any other
0011
…
sequence ending 7
in one
1111

5. How to remember
● Tails is Yin:
8
● Heads is Yang:
7
● A changing Yin is Yin interrupted by Yang:
6
● Also, 0110 is 6 in binary

6. How to remember
● A changing Yang is Yang interrupted by Yin:
9
● Also, 1001 is 9 in binary, while 1011 is 11 and
1101 is 13 (the next odd numbers)

7. How to remember
● Any other sequence ending in Yin is
unchanging Yin:
8
● Any other sequence ending in Yang is
unchanging Yang:
7

8. Designer's notes
● The smallest probability in the yarrow method is 1/16
● For 16 combinations we need 4 bits = 4 coin tosses
● It's better to use 1 coin than 4, and write down each bit from
left to right, because the ordering is important
● Even combinations, ending in 0, are Yin
● Odd combinations, ending in 1, are Yang
● 6 in binary is 0110, which reminds me of
● for the 9, we need three combinations to get
the same probabilities of the yarrow method, in which
Yin lines are less likely to change than Yang lines:
● 9 in binary is 1001, which reminds me of
● the next odd values 11 (1011) and 13 (1101) we read as 9