The Original Method: Yarrow Stalk Algorithm (Da Yan Method)
The most ancient and orthodox I Ching divination algorithm, detailed in the "Commentaries on the Appended Phrases" (系辞传) from the Ten Wings. Called the "Great Expansion Divination Method", it uses fifty yarrow (shī) stalks through a series of complex, rigorous, and ritualistic mathematical steps (dividing by two, hanging one, counting by fours, returning remainders, etc.), requiring eighteen calculations to determine one line.
This process is very time-consuming—a complete hexagram (six lines) may take 15 to 20 minutes. It emphasizes achieving inner calm, clearing distractions, and aligning with the Tao through slow, focused calculation.
Later Simplified Version: Three-Coins Method
Because the "Great Expansion Method" was too complex for daily use, during the Han Dynasty, I Ching masters like Jing Fang developed simplified methods to make divination more accessible, eventually evolving into today's "three-coins method."
Three-Coins Method Rules:
- Toss three coins simultaneously: heads = 3 points (yang), tails = 2 points (yin)
- Record total: 6 = old yin (changing), 7 = young yang, 8 = young yin, 9 = old yang (changing)
- Repeat six times, recording from bottom to top to get six lines
Why Was the Simplified Version Widely Accepted?
Later scholars proved through mathematical calculation that the three-coins method's probability of producing old yin, old yang, young yin, and young yang closely approximates the ancient Great Expansion Method. Though slight differences exist, the overall distribution aligns with I Ching's principles of yin-yang transformation.
Statistical Analysis: Probability Comparison
Three-Coins Method Probabilities (8 total combinations):
- Old Yang (9): 1/8 = 12.5%
- Young Yang (7): 3/8 = 37.5%
- Young Yin (8): 3/8 = 37.5%
- Old Yin (6): 1/8 = 12.5%
Yarrow Stalk Method Probabilities (analyzed by scholars like Zhu Xi):
- Old Yang (9): 3/16 = 18.75%
- Young Yang (7): 7/16 = 43.75%
- Young Yin (8): 5/16 = 31.25%
- Old Yin (6): 1/16 = 6.25%
Key Differences:
- Old Yang probability: Yarrow method is 6.25% higher
- Young Yang probability: Yarrow method is 6.25% higher
- Young Yin probability: Yarrow method is 6.25% lower
- Old Yin probability: Yarrow method is 6.25% lower
In simple terms: The yarrow method tends toward yang-biased results (higher old yang and young yang probabilities), while the coins method has a more symmetrical, balanced distribution. But the differences are minor, and both effectively embody I Ching's principle of transformation.
In the computer age, this tool uses the coins method algorithm, completing calculations in seconds and greatly enhancing the efficiency of I Ching study and research.