The Total Number of Ba Zi Chart Permutations, & Why it’s a Useful Thing to Know

[CyberDaoist]

Before we begin, I’d like to clarify how the term Ba Zi is being used in this article:

When I speak of Ba Zi, I am speaking explicitly about the 8 characters that make up the 4 pillars of a calendrical date.

I am not speaking about Da Yun, or about any particular school of Ba Zi.

 I am referring very specifically to the four pillars containing the 8 characters & their qualities.

Ok, let’s go!

I know, I know. This topic AGAIN. As if it hasn’t been written about & discussed enough through the ages and online!

...but here’s the thing about this calculation.

It’s important because the answer to this question is a lot like a password or a secret handshake that lets practitioners find their peers.

By peers, I mean two things: on the one hand, it’s a way of determining the level of knowledge that practitioners have, and on the other, it’s a way of determining whether or not someone is from the same school of thought.

As far as level of knowledge is concerned, the determination is basic.

We all know that there are demonstrably inaccurate answers to the question!

For example, when we meet someone who’s claiming to be practicing Chinese Astrology & they tell us that there are 12 animals so therefore 12 possibilities, we know that they are probably not aware of the Ba Zi or even the sexagenary cycle.

Likewise, someone who claims that there are 60 possibilities is aware of the sexagenary cycle, but not of Ba Zi.

When someone claims that there are 12,960,000 possibilities, it’s a clear indication that they know about Ba Zi.

But it’s ALSO an indicator that they might not know much!

They may have calculated this number themselves, in which case they may be doing self-study, which is both difficult & prone to mistakes.

There’s nothing wrong with self-study, but it requires an inquisitive & insightful mind.

An answer of 12,960,000 indicates that they either have not yet had the insight needed to bring them to the next answer.

In a similar vein, they may have read the answer in a book, or been taught this number by a teacher. It’s very common for students to accept what their teacher has to say unquestioningly, but it raises the possibility that any other material they are learning is also missing a level of detail & understanding.

Here’s where things get interesting, though.

Any answer besides those first three begin to point not to knowledge level, but to school of thought!

For example, 518,600 is the standard answer given by many trained practitioners.

This answer sends a clear signal that the practitioner has, at the very least, studied from a source that understands the fundamental way that the Chinese calendar works.

On the other hand some practitioners might give an answer of 561,600. This answer is no better or worse than 518,600.

It does point to a different approach in date calculation, but one that still understands the fundamentals.

So whichever answer is given signals the school of thought that the practitioner is studying & practicing.

Other answers DO, however, exist!

Both of the answers above are, I would say, the two main answers given by practitioners studying from sources that have a decent understanding of Ba Zi.

Most popular schools use one of the above calculations.

When someone gives a different answer than 518,600 or 561,600, then it is very likely that they are studying something besides mainline Ba Zi Analysis.

Their answers might seem weird or inaccurate to practitioners who do not practice the same style, but it’s important to give them the benefit of the doubt: their answer might be logical within the context of their style’s calculations!

The bottom line, however, is that the answer to “how many charts are there” is a quick & easy way to determine whether or not the person you’re talking to has awareness of Ba Zi, & if so, whether or not they have correct fundamental knowledge of Ba Zi, & if so, what school of thought they belong to.

Armed with this information makes it easier to decide how much Ba Zi knowledge you have in common, as well as on what level you wish to discuss Ba Zi with them.


Oof, that was a lot!

But I needed to get all that out of the way in order to set up this next section.

You see, I’ve recently changed my answer to this question DRASTICALLY.

Like most practitioners, I went through all of the various stages of answers: twelve, sixty, 12,960,000, & then 518,600, until I finally settled on 561,600.... until recently.

Something I’d always wondered about was the effects of the 24 solar terms on a chart.

I understood the importance of the Jie (节) in determining the start of a season or month, but I knew that each month had both a Jie & a Qi (气), which determined the mid-point of the month.

Each of the 24 solar terms has its own name and its own energetic quality.

If that was the case, then shouldn’t the solar term that a person is born in play a role in the layout & structure of their Ba Zi?

If two people were born in 巳 month, but one was born in the 节 of the month & the other was born in the 气 of the month, wouldn’t that impact the energetic quality of 巳 in their chart?

The answer was, yes!

Of course it would.

But how?

As I started my research, I came across Yuan Hai ZiPing’s Lùn tiān gàn dìzhī àncáng zǒng jué (论 天 干 地 支 暗 藏 总 诀, “On the hidden general secret of the Heavenly stems & earthly branches”).

This text clearly laid out the idea that the energetic qualities of a particular branch were directly influenced by both its 节 & 气, and that the energetic variations were encoded using the hidden stems!

Each earth branch has one, two or three hidden stems.

In my school, the hidden stems were initially divided into two categories: each branch has a major hidden stem, and one or two lesser hidden stems.

When determining the primary energetic quality of an earthly branch, we looked to the major hidden stem.

It was what we used to determine whether or not a branch was supporting or depleting the Day Master & whether or not a branch was providing a root to an element in the heavenly stems, & whether or not it was vetoing heavenly specific heavenly stem combinations, among other things.

I had always assumed that the major hidden stem was so named because it was the strongest of the hidden stems... until I learned about the concept of variable hidden stem “dominance” as determined by the 节气!

ZiPing’s text explained that each hidden stem dominated, or became strongest, during a particular time of the month.

For example, in the 气 of any given month branch, the hidden stem traditionally called the “major hidden stem” always dominated, whereas the hidden stems traditionally called the “lesser hidden stems” always dominated during the 节 of the month.

Let’s look at branch 寅 as an example.

寅 has three hidden stems - “lesser hidden stems” 戊 & 丙,  & “Major hidden stem” 甲.

The two solar terms contained within 寅 are the 节 of Li Chun (立春 beginning of spring) & the 气 of Yu Shui (雨水 rain water).

Li Chun & Yu Shui are each ~15 days long.

During Yu Shui, the last 15 days of 寅, the hidden stem of 甲 is the dominant energy.

However, during Li Chun, the first 15 days of 寅, the hidden stems of 戊 or 丙 are the dominant energy!

Hidden stem 戊 is the dominant energy for the first five days of Li Chun, & then hidden stem 丙 is the dominant energy for the next ten days.

Together, the days of 寅 month where hidden stems 戊 & 丙 are dominant make up the full 15 days of Li Chun.

This revelation gave me a whole new perspective on the meaning of “major hidden stem” & “lesser hidden stem”.

The term “major hidden stem” referred not to the strength of the stem, but to the AMOUNT OF TIME that it was dominant during the month!

Likewise, the “lesser hidden stems” were so named not because they were weaker, but because they were dominant for a LESSER AMOUNT OF TIME.

My mind was blown.

This meant that, for any given month branch, I shouldn’t be looking to the major hidden stem to determine the main energetic quality... instead, I should be looking to the hidden stem that was DOMINANT at the time of birth!

This changed everything.

It meant that each earthly branch could have up to three different dominant energetic qualities... or three different “flavors”.

Since the twelve branches have a total of twenty eight hidden stems, it meant that every year, there were not just twelve, but actually TWENTY EIGHT different energetic qualities that could manifest in the month pillar!

Now, there’s a chapter in the Huang Di Nei Jing Ling Shu (yellow emperor’s inner classic of the spiritual pivot) that explains how the divisions of a day correspond to the divisions of a year... namely, each day has 24 hours which are divided by the 12 earthly branches into 4 periods - midnight corresponds to winter solstice, 6am corresponds to spring equinox, noon to summer solstice & 6pm to autumn equinox.

The important point is that each Chinese double hour can therefore be divided into a first hour which corresponds to the 节, or first 15 days of a month, & a second hour which corresponds to the 气, or last 15 days of a month.

This in turn means that the hour, even the MINUTE of birth has great importance on determining the energetic quality of the hour branch.

For example, two people are born on the same day, one at 3:50pm and another at 4:15pm. They are both born in 申 hour, which is from 3pm to 5pm.

However, since the second hour is equivalent to the 气 of the month, it means that the person born at 4:15pm is actually born at a time when hidden stem 庚 is the dominant energy, whereas the person born at 3:50pm is actually born at a time that is equivalent to the later part of 节... so the dominant energy is actually hidden stem 壬!

Now, depending on your school of thought, each day has either 28 or 29 hidden stems in the hour pillar. So that means that, in a single given day, there are up to 29 different energetic qualities that could manifest in the hour pillar!

The correspondences extend to both the year & the day pillars as well.

The first half of a day & first half of a year correspond to the 节 of a month, while the last half of a day & last half of a year correspond to the 气 of a month.

However since the days & years are not restricted to cyclic relationships in the same way as the months & hours, it means that the 5x12 rule of sexagenary combination applies... meaning 28 hidden stems multiplied by the 5 elements of the heavenly stems gives a total of 140 different energetic combinations that can appear in either the day pillar or the hour pillar!

When I realized this, I could barely contain my excitement.

After testing this new (to me) method of calculation out on a variety of charts, I realized that it provided much more accurate information & actually helped me understand the “tricky” charts I had which never seemed to quite match up to their owner’s reality.

Very soon, I began to wonder how many total charts were now possible with this new level of complexity.

My initial calculation was as follows:

29 hour pillar flavors
x 140 day pillar flavors
x 28 month pillar flavors
x 140 year pillar flavors
= 15,915,200 possible chart permutations!

I was flabbergasted.

I knew that this added complexity was going to increase the total number of permutations, but I didn’t expect the number to be THAT high.

...and then I saw my mistake.

As it turns out, not every flavor would match up with every other flavor in the other pillars.

For example, in a 巳 year, the dominant energy of 庚, which appeared in the last half of the year, would only match up with the last 6 month branches of the year.

It wouldn’t be dominant during the first six branches.

This meant that only 13 of the 28 month pillar flavors would match up with a 巳 year branch with 庚 as the dominant hidden stem.

Likewise, a 巳 branch day with the dominant energy of 戊 would only appear in the first four hours of the day.

This meant that only 6 of the 29 hour pillar flavors would match up with a 巳 day branch that had 戊 as the dominant energy.


The total number of restrictive permutations was a chore to derive & calculate.

But, it could be done, and so I set about figuring out the exact number of chart permutations that were possible.

The final answer ends up being (drumroll)....

2,264,125 total chart permutations.

So that’s my answer.

It’s my “secret code” to help determine whether or not someone is practicing along the same lines as I am.

Is it better than 518,600 or 561,600?

No, it’s just a different school of thought.

One that I am happy to share here in the hopes that someone might find it useful...

...or that someone might recognize my code... because as of right now, I’m the only person I know who uses it.

Get in touch if you use the same approach!

[Rapanui]

You did big manipulation. 
First you wrote:

Before we begin, I’d like to clarify how the term Ba Zi is being used in this article:
When I speak of Ba Zi, I am speaking explicitly about the 8 characters that make up the 4 pillars of a calendrical date.

I agree that BaZi chart is erected from 8 characters and these 8 characters are sufficient to erect BaZi chart. For example:
Xin......Wu.....Yi......Geng
You.....Chen...You...Zi
In the chart there can be in first line one of 10 HS and in second line one of 12 EB.
So....depending of the BaZi school it can be 60 x 12 x 60 x 12 = 518 400 BaZi charts or 60 x 12 x 60 x 13 = 561 600 BaZi charts.
But............
 
...next you wrote:

I am referring very specifically to the four pillars containing the 8 characters & their qualities.

Where in the BaZi chart you can wrote these "qualities"?
 
How you want to write BaZi chart (remember! you have only 8 characters!!!) with these "qualities"
 

[CyberDaoist]

LOL, Ok I guess I always saw the hidden stems as sitting “inside” the branches, not as “extra characters”. So I’ve always considered them to be part of the 8 characters.

My main point about that was that I wasn’t including luck pillars or any other pillars Other than the 4 pillars in my count. 🙂

[Rapanui]

LOL, Ok I guess I always saw the hidden stems as sitting “inside” the branches, not as “extra characters”. So I’ve always considered them to be part of the 8 characters.

You want to replace 12 EB by 28 HHS or by 24 ST.
 
Sorry... but in the second line MUST be EB.
 

[CyberDaoist]

LOL, Ok I guess I always saw the hidden stems as sitting “inside” the branches, not as “extra characters”. So I’ve always considered them to be part of the 8 characters.

You want to replace 12 EB by 28 HHS or by 24 ST.
 
Sorry... but in the second line MUST be EB.
 

I agree! I’m not suggesting that the EB be replaced with hidden stems. I’m saying that 9/12 EB have different flavors... green 寅，red 寅，yellow 寅，etc.

28 different flavors of the 12 branches. Almost like Baskin’ Robins 😁

[Rapanui]

I agree! I’m not suggesting that the EB be replaced with hidden stems. I’m saying that 9/12 EB have different flavors... green 寅，red 寅，yellow 寅，etc.
28 different flavors of the 12 branches.

Really!? 
so...who wrote this:

(...)
x 28 month pillar flavors
(...)
= 15,915,200 possible chart permutations!

Not you?
 

[CyberDaoist]

I agree! I’m not suggesting that the EB be replaced with hidden stems. I’m saying that 9/12 EB have different flavors... green 寅，red 寅，yellow 寅，etc.
28 different flavors of the 12 branches.

Really!? 
so...who wrote this:

(...)
x 28 month pillar flavors
(...)
= 15,915,200 possible chart permutations!

Not you?
 

Oh, the shame... 😭🤣

That was part of my process, yes.

That equation & answer was the equivalent of 60x60x60x60=12,960,000.

Not my final answer.

[Rapanui]

Not my final answer.

So...what is your final answer?
 
How many charts can be erected from HS & EB in 8 characters ("Ba Zi" means "8 characters").
 

[CyberDaoist]

Not my final answer.

So...what is your final answer?
 
How many charts can be erected from HS & EB in 8 characters ("Ba Zi" means "8 characters").
 

Ok, we seem to be stuck on a semantic, & it’s my fault for not being clear enough. I’ll keep that in mind for the future.

What I’m saying is that there are 561,600 flavorless Ba Zi charts (strictly 8 characters)

.... but 2,264,125 Ba Zi chart flavors (or 4,528,250 flavors if you factor gender into it). 😀

[JLim]

Hi all, I agree with Rapanui's calculation of number of Bazi charts.   About the hidden stems: you may analyze the hidden stems, depending on the school of Bazi.  But the hidden stems are details within the Bazi chart, and I don't think we need to include them in this calculation.

[Hellow]

How about taking in religion and countries in are born with into consideration? Can you imagine if trump is born in North Korea? What will his life story become

[CyberDaoist]

Hi all, I agree with Rapanui's calculation of number of Bazi charts.   About the hidden stems: you may analyze the hidden stems, depending on the school of Bazi.  But the hidden stems are details within the Bazi chart, and I don't think we need to include them in this calculation.

Oh, there’s definitely no NEED to.
It’s just that I do, personally, & that’s how many there are.

[JLim]

Hi CyberDaoist, would you be interested in calculating the number of Liu Yao charts in a new topic?  There are also the Month and Day of hexagram raising for the permutation calculation.

[CyberDaoist]

Hi CyberDaoist, would you be interested in calculating the number of Liu Yao charts in a new topic?  There are also the Month and Day of hexagram raising for the permutation calculation.

Done.