On the Dayan Yarrow Stalk Method

III. God Does Not Play Dice Fairly: The Probability Aesthetics of Da Yan

This is the most fundamental difference between the Da Yan method and the Coin Oracle. The Coin Oracle is based on a simple binomial distribution with relatively uniform probabilities. The Da Yan method, through its complex "suspending one and counting by fours," constructs a highly asymmetrical probability model.

1. The Logic of Variations

In the three changes, the stalks removed (Suspended + Left Remainder + Right Remainder) follow specific patterns:

• 1st Change removal: 5 or 9
• 2nd Change removal: 4 or 8
• 3rd Change removal: 4 or 8

To get the final result, we look at the combinations of remaining stalks:

• To get Old Yang (9): One must have 36 stalks left. This means $49 - (5 + 4 + 4) = 36$.
  • Condition: Each of the three changes must result in the minimum number of stalks being removed.
• To get Old Yin (6): One must have 24 stalks left. This means $49 - (9 + 8 + 8) = 24$.
  • Condition: Each of the three changes must result in the maximum number of stalks being removed.

2. Probability Calculation

Based on the derivations in Zhu Xi's Introduction to the Study of the I Ching and modern mathematics, the probabilities of the four line types are as follows:

3. The Philosophical Meaning Behind the Data

This yields a startling discovery: The probability of Old Yang (9) is three times that of Old Yin (6)! Simultaneously, the probability of Young Yin (8) is much higher than that of Young Yang (7).

This imbalance contains the profound worldview of the pre-Qin era:

1. Yang is Abundant, Yin is Scarce: Yang energy (creativity, movement) is generally dominant and active. However, when it reaches its peak and begins to decline (Old Yang), it occurs more easily than when Yin reaches its peak to turn into Yang (Old Yin). This symbolizes that "achieving success (Yang) is difficult, yet Yang energy itself is plentiful."
2. The World's Keynote is "Young Yin": The most probable result, Young Yin (8) at 43.75%, represents a state of stillness, latency, and material existence. This implies that for most of the time, the real world is in a state of quietude, preservation, and non-radical change.
3. Six is Rare, Nine is Frequent: In I Ching studies, "Six" represents the ultimate Yin—symbolizing total collapse or transformation, a condition extremely difficult to achieve in nature. "Nine" represents the ultimate Yang—reaching the limit of energy release is relatively easier.

This makes the Da Yan method closer to the complex rhythms of the real world than the coin toss—the world is not black and white, nor is it a perfectly fair randomizer; it is an evolutionary system with specific tendencies.