I Ching Reading Online (Coins)

Continue in the tool

More pages for this tool

yarrow stalks vs coins i ching probability

Yarrow stalks or coins in the I Ching: probabilities

In the tool, the Casting method selector switches between Three coins and Yarrow stalks. The hint right below shows the probability of each line value for the chosen method.

The two methods differ in a single detail

The yarrow-stalk method uses 50 stalks, of which 49 enter the cast, and takes 18 manipulations (three changes for each of the six lines). It is the older, slower method. The coin method is an established shortcut that uses three coins per line. In both, the yin (6 and 8) and yang (7 and 9) lines have exactly a 50% chance each, so the starting hexagram is one of 64 equally likely ones, with a 1 in 64 chance. The difference lies in how frequent each kind of changing line is.
With coins, the probabilities of 6, 7, 8 and 9 are 1/8, 3/8, 3/8 and 1/8: changing yin and changing yang appear at the same frequency. With stalks, they are 1/16, 5/16, 7/16 and 3/16: changing yang (9) comes up three times as often as changing yin (6), and stable yin (8) is the most common value. Even so, the chance of a line being changing is the same, 1/4, and the average number of changing lines per cast is 1.5 in both methods. What changes is which resulting hexagram appears: with stalks, the change from yang to yin is more frequent than the reverse.
This tool does not simulate the 18 stalk manipulations, which depend on how the querent splits the bundle. It draws each line directly in the classic 1:5:7:3 proportion, with 16 equally likely outcomes, which reproduces exactly the probabilities in the manuals. The automated test checks both distributions by enumeration and by a simulation of 200 thousand lines, using the chi-square criterion. For a consultation with practical meaning, either method will do; pick the one that suits the ritual you want to follow.

The two distributions side by side

Changing yin (6)

Input: 6
Expected output: moedas 12,5% | varetas 6,25%

1/8 versus 1/16.

Stable yang (7)

Input: 7
Expected output: moedas 37,5% | varetas 31,25%

3/8 versus 5/16.

Stable yin (8)

Input: 8
Expected output: moedas 37,5% | varetas 43,75%

3/8 versus 7/16.

Changing yang (9)

Input: 9
Expected output: moedas 12,5% | varetas 18,75%

1/8 versus 3/16.

Chance of a line changing

Input: 6 ou 9
Expected output: 25% nos dois métodos

1/8 + 1/8 and 1/16 + 3/16.

Full tool FAQ

What is the I Ching?

It is a Chinese classic of divination and philosophy with 64 hexagrams, figures of six solid or broken lines. Its core, the Zhouyi, comes from the Western Zhou dynasty (around the 9th century BCE). Each hexagram has a judgment, an image and six line texts.

How does the three-coin cast work?

What is the difference between coins and yarrow stalks?

What are changing lines?

What is the resulting hexagram?

What is the nuclear hexagram?

Are the texts the Wilhelm translation?

What does King Wen order mean?

Can I share my cast?

Does the I Ching predict the future?

Frequently asked questions

Which method is more faithful to tradition?

The yarrow stalks are the older method and the one described in the classic commentaries. Coins became popular centuries later because they are quick. Both are used to this day.

Do the stalks make some hexagrams more likely?

Not the starting ones: all 64 have a 1/64 chance in both methods. The difference shows in the resulting hexagrams, because old yang and old yin do not have the same frequency with stalks.

Is simulating the stalks as valid as using stalks?

For the probabilities, yes, because the draw follows the classic proportion. For those who value the ritual of the 18 manipulations, the simulation does not replace the hands-on practice.

Next steps

The two methods differ in a single detail

The yarrow-stalk method uses 50 stalks, of which 49 enter the cast, and takes 18 manipulations (three changes for each of the six lines). It is the older, slower method. The coin method is an established shortcut that uses three coins per line. In both, the yin (6 and 8) and yang (7 and 9) lines have exactly a 50% chance each, so the starting hexagram is one of 64 equally likely ones, with a 1 in 64 chance. The difference lies in how frequent each kind of changing line is.

With coins, the probabilities of 6, 7, 8 and 9 are 1/8, 3/8, 3/8 and 1/8: changing yin and changing yang appear at the same frequency. With stalks, they are 1/16, 5/16, 7/16 and 3/16: changing yang (9) comes up three times as often as changing yin (6), and stable yin (8) is the most common value. Even so, the chance of a line being changing is the same, 1/4, and the average number of changing lines per cast is 1.5 in both methods. What changes is which resulting hexagram appears: with stalks, the change from yang to yin is more frequent than the reverse.

This tool does not simulate the 18 stalk manipulations, which depend on how the querent splits the bundle. It draws each line directly in the classic 1:5:7:3 proportion, with 16 equally likely outcomes, which reproduces exactly the probabilities in the manuals. The automated test checks both distributions by enumeration and by a simulation of 200 thousand lines, using the chi-square criterion. For a consultation with practical meaning, either method will do; pick the one that suits the ritual you want to follow.

The two distributions side by side

Changing yin (6)

Input: 6
Expected output: moedas 12,5% | varetas 6,25%

1/8 versus 1/16.

Stable yang (7)

Input: 7
Expected output: moedas 37,5% | varetas 31,25%

3/8 versus 5/16.

Stable yin (8)

Input: 8
Expected output: moedas 37,5% | varetas 43,75%

3/8 versus 7/16.

Changing yang (9)

Input: 9
Expected output: moedas 12,5% | varetas 18,75%

1/8 versus 3/16.

Chance of a line changing

Input: 6 ou 9
Expected output: 25% nos dois métodos

1/8 + 1/8 and 1/16 + 3/16.

Full tool FAQ

What is the I Ching?

How does the three-coin cast work?

What is the difference between coins and yarrow stalks?

What are changing lines?

What is the resulting hexagram?

What is the nuclear hexagram?

Are the texts the Wilhelm translation?

What does King Wen order mean?

Can I share my cast?

Does the I Ching predict the future?

Frequently asked questions

Which method is more faithful to tradition?

The yarrow stalks are the older method and the one described in the classic commentaries. Coins became popular centuries later because they are quick. Both are used to this day.

Do the stalks make some hexagrams more likely?

Not the starting ones: all 64 have a 1/64 chance in both methods. The difference shows in the resulting hexagrams, because old yang and old yin do not have the same frequency with stalks.

Is simulating the stalks as valid as using stalks?

For the probabilities, yes, because the draw follows the classic proportion. For those who value the ritual of the 18 manipulations, the simulation does not replace the hands-on practice.