Dayuan Method in the I Ching: Why Is It Considered the Most Canonical Divination Method?

slug: dayuan-method-i-ching-why-is-it-considered-the-most-canonical-divination-method

title: "Dayuan Method in the I Ching: Why Is It Considered the Most Canonical Divination Method?" lang: en excerpt: "The Dayuan Method (大衍筮法) is the oldest divination method recorded in the I Ching – Xici Zhuan. Using 50 yarrow stalks, an 18-step process, and a 1:5:7:3 probability distribution, many scholars consider it the orthodox method closest to the spirit of the Book of Changes." publishedat: "2026-07-29T22:11:28.708Z" updatedat: "2026-07-31T13:23:39.859Z"

Dayuan Method in the I Ching: Why Is It Considered the Most Canonical Divination Method?

The Dayuan Method (大衍筮法) is the oldest divination method recorded in the I Ching – Xici Zhuan (Great Commentary). Unlike the three-coin method popular today, the Dayuan method fully simulates the principles of Yin and Yang, the Three Powers (Tian-Di-Ren), and the operation of the Heavenly Dao. For this reason, many scholars view it as the orthodox method closest to the original spirit of the Book of Changes.

What Is the Dayuan Method?

The Dayuan Method (大衍筮法) utilizes 50 yarrow stalks (蓍草) to determine each individual line of a hexagram.

In the Xici Zhuan I, there is a famous passage:

大衍之數五十，其用四十有九。

Which translates to:

The number of Great Expansion $Dayuan$ is 50, of which 49 are used.

One stalk is set aside to represent Taiji (The Supreme Ultimate), while the remaining 49 stalks are manipulated through three changes (三變) to generate a single line.

Repeating this process six times produces a complete six-line hexagram.

Why Are Only 49 Stalks Used?

This is a detail many casual readers overlook.

50 symbolizes the Number of Great Expansion, representing the cosmic totality.

The single stalk set aside represents:

Taiji
The Dao
The "Unchanging Constant"

The remaining 49 stalks represent the world in dynamic motion.

This concept reflects the core philosophy:

The Dao remains still, yet gives birth to all changing things.

The 18-Step Dayuan Process

Each line undergoes 3 changes $transformations$ .

Each transformation involves:

Randomly dividing the stalks into two bundles.
Taking one stalk from the right bundle and placing it between fingers (symbolizing the Three Powers: Heaven, Earth, Humanity).
Counting through each bundle in groups of four (symbolizing the Four Seasons).
Collecting the remainders.
Combining the remainders.
Proceeding to the next change.

Three changes form a single line.

Six lines complete a hexagram.

In total:

3 × 6 = 18 changes $transformations$

This is why many modern sources refer to it as the 18-Step Dayuan Method.

The Probability of Dayuan Differs Fundamentally from the Three-Coin Method

This is the single most critical distinction when comparing divination techniques.

The Three-Coin Method

Old Yin (6): 12.5%
Young Yang (7): 37.5%
Young Yin (8): 37.5%
Old Yang (9): 12.5%

Ratio:

1 : 3 : 3 : 1

The Dayuan Method

Old Yin (6): 6.25% (1/16)
Young Yang (7): 31.25% (5/16)
Young Yin (8): 43.75% (7/16)
Old Yang (9): 18.75% (3/16)

Ratio:

1 : 5 : 7 : 3

This distribution emerges naturally from the procedural mechanics of the Dayuan algorithm itself, rather than human post-hoc convention.

Why Is Dayuan Held in Higher Regard?

1. Direct Scriptural Origin in the I Ching

The Three-Coin method appeared relatively late in historical records.

The Dayuan method is explicitly detailed within:

The Xici Zhuan (Great Commentary)
The Ten Wings (十翼)

These texts form the foundational philosophical backbone of the I Ching.

2. Full Simulation of the Dynamic Process of Transformation

The Three-Coin method delivers only an instantaneous end state.

The Dayuan method simulates the entire cosmological evolution:

Taiji
Liangyi (Two Polarities)
Sixiang (Four Imagery)
Sancai (Three Powers)
The cycles of transformation

The procedural act of casting is itself an embodiment of I Ching philosophy.

3. Probability Distribution Reflecting Yin-Yang Philosophy

Within the Dayuan distribution:

Young Yin occurs with the highest frequency.
Old Yang occurs more frequently than Old Yin.

This mirrors natural cosmological laws:

Yang reaches its peak and wanes. Yin emerges gradually and flourishes.

Consequently, many scholars argue that the 1:5:7:3 distribution aligns far better with classical Yin-Yang theory than the symmetrical 1:3:3:1 of the coin method.

4. Ritual Solemnity and Mindfulness

A traditional Dayuan casting session typically takes 10 to 30 minutes.

This extended ritual encourages the practitioner to:

Attain mental stillness
Focus intent deeply
Avoid repetitive or casual casting

This stands in stark contrast to flipping coins in a matter of seconds.

Are There Drawbacks to the Dayuan Method?

Yes.

The process is lengthy.
It is difficult to learn and master.
Counting errors can easily occur.
It is impractical for quick, daily usage.

This is precisely why the Three-Coin method became the most popular technique today — fast, straightforward, and easy to teach and practice.

Can Computers Simulate the Dayuan Method?

Yes. There are two primary approaches.

1. Full 18-Step Algorithmic Simulation

The computer strictly executes:

Bundle partitioning
Group-of-four counting
Three changes per line
Six total lines

Advantage: Faithful to the ancient method, preserving the operational structure of the Xici Zhuan.

Disadvantage: More complex algorithmically compared to direct sampling.

In the Quizzman I-Ching tool, the Yarrow Stalk / Dayuan method is simulated directly as an 18-step pipeline on the server, utilizing server-side CSPRNG (Python secrets / os.urandom) for the bundle division step — avoiding browser-based Math.random or Web Crypto primitives. For details, see: About I-Ching.

2. Direct Probability Mapping

Some systems utilize a CSPRNG to generate cryptographically secure random integers, mapping them directly to the target distribution:

1/16 → Old Yin (6)
5/16 → Young Yang (7)
7/16 → Young Yin (8)
3/16 → Old Yang (9)

If the entropy source is cryptographically strong, the statistical output is identical to the traditional Dayuan method while operating instantaneously. This approach suits systems prioritizing speed and probability matching, though it does not recreate the individual partition-count-change steps of the ancient method.

Common Misconceptions About Dayuan

"Dayuan Is Simply Yarrow Stalks"

Incorrect.

Yarrow Stalks are merely the physical tools.

Dayuan is the underlying algorithm for generating hexagrams.

Today, that algorithm can be fully simulated via computation while perfectly preserving its probability laws.

"The Coin Method and Dayuan Are Identical"

Incorrect.

The two methods yield:

Different line probabilities
Different frequencies of moving $changing$ lines
Distinct foundational origins

The coin method is symmetrical (1:3:3:1); the Dayuan method is Yin-biased (1:5:7:3).

Conclusion

The Dayuan Method is not merely a divination technique, but a mathematical and philosophical model built directly into the classical I Ching corpus. Compared to the Three-Coin method, Dayuan offers a more rigorous procedure, a probability distribution faithful to the Xici Zhuan, and deeper symbolic resonance.

In the digital era, simulating the Dayuan method using a server-side CSPRNG (or through a full 18-step simulation like Quizzman) preserves the classical probability distribution while ensuring algorithmic objectivity, auditability, and reproducibility. This offers a balanced approach for modern I Ching platforms bridging academic authenticity with technology.

Try Yarrow Stalk / Dayuan divination: lab.quizzman.com/tool/iching-divination

Dayuan Method in the I Ching: Why Is It Considered the Most Canonical Divination Method?

slug: dayuan-method-i-ching-why-is-it-considered-the-most-canonical-divination-method