I Cast 262,980 Charts to Find Out How Rare Zi Wei Dou Shu Configurations Really Are

The least useful phrase in a Zi Wei Dou Shu reading is one in a hundred. Whoever says it will not tell you what share of the population actually carries the configuration, and in most cases has never counted. Rarity in this field travels as an adjective. It does not have to. It can be computed.

I wrote my own Zi Wei Dou Shu engine, star placement, the four transformations, the decade and annual cycles, all of it in code. To give the engine a physical, I enumerated every day from 1 January 1965 to 31 December 2024, cast one chart for each of the twelve double-hours of every day, and ran the lot. That is 262,980 charts. The transformation table is locked to the San He school. I ran the same batch twice, once against loose criteria and once against strict criteria, and the gap between the two runs is what this article is about.

Start with the half that turns out to be uniform. The Life Palace lands on each of the twelve branches 8.33% of the time, dead even. The Five Element Class splits almost perfectly into fifths, Water 2 at 19.99%, Wood 3 at 20.01%, Metal 4 at 19.99%, Earth 5 at 19.97%, Fire 6 at 20.04%.

Now the half that is not uniform. Here is where the star Zi Wei itself lands, by branch.

Branch	Share	Branch	Share
Chen	11.19%	Wei	8.48%
Wu	10.52%	Shen	7.45%
Yin	10.16%	You	6.77%
Mao	10.16%	Hai	6.14%
Si	10.16%	Xu	6.10%
Chou	8.13%	Zi	4.74%

Chen at 11.19% is 2.36 times Zi at 4.74%. One chart carries a uniform layer and a lopsided layer at the same time, and every claim about rarity you will ever hear grows out of the lopsided one.

Empty palaces come next. The count per chart takes only three values. Charts with no empty palace at all make up 17.61%, charts with exactly two make up 66.10%, charts with four make up 16.30%. An odd count never appeared once. A Life Palace holding no major star occurs in 16.46% of charts, roughly one chart in six.

The classical line for that case, in the Zi Wei Dou Shu Quan Shu, runs 「命无正曜，夭折孤贫」, a Life Palace without a proper star meaning early death and lonely poverty. That is a verdict in the rhetorical sense, not a sentence handed down. One chart in six lands on it. A judgement that covers a sixth of everybody is, by that fact alone, not something you can apply to an individual on its own.

Then the core of it. The configuration called Ji Xiang Li Ming, read loosely as Zi Wei seated in the Wu palace, hits 10.52%. But the classical line in the Zi Wei Dou Shu Quan Shu runs 「紫微居午无杀凑位至三公」, Zi Wei in Wu, with no malefics gathered, reaching the rank of the three highest ministers. The weight sits on the clause about malefics. That clause is a filter, not decoration. Require the Wu palace and its opposite Zi palace to be clear of the six malefic stars, and the hit rate falls to 2.645%. One short qualifier removes nearly three quarters of the field.

The same inflation shows up in aggregate. Under loose criteria, 91.70% of charts carry at least one auspicious configuration. Under the strict criteria with the qualifiers restored, it is still 86.95%. Being told that you have an auspicious configuration therefore carries almost no information.

The census also caught a broken rule of my own, which is the part I would keep if I had to throw the rest away. My engine carries an inauspicious configuration called Lu Feng Liang Sha, defined as the Lu Cun star being flanked by Qing Yang and Tuo Luo. Every one of the 262,980 charts matched it, without exception. The reason is in the placement rules. Qing Yang is fixed one palace ahead of Lu Cun and Tuo Luo one palace behind, by definition of how those stars are placed. The rule can never fail to fire, its information content is zero, and it has been quietly stamping an inauspicious label on every chart. It is now on my fix list.

A few boundaries. This is an enumeration, not a sample, and what is enumerated is moments rather than people. Casting one chart per double-hour assumes births are spread evenly across the day, and real births are not, with fewer in the small hours than in daylight. So these figures answer how much of the space of possible birth moments falls into a configuration. They do not tell you how many people in a room of a hundred carry it.

Second, frequency is not accuracy. This article computes geometry and calendar arithmetic. Whether a configuration describes a life well is a separate question and I have not touched it.

Third, schools differ. Mine is locked to the San He transformation table. Change the table and the qualifiers change with it, and so do the numbers. Every percentage above carries that premise.

What you can take away is a pair of questions. Next time a configuration is described as rare, ask what its complete condition is and whether a qualifier has been dropped, then ask what share of people still qualify once the qualifier is back. Anyone who cannot answer the second question was giving you an adjective. The same goes for an empty Life Palace. Ask for the share first. The figure 16.46% argues its own case.

Common questions

Is an empty Life Palace bad

This article cannot tell you good from bad, only the denominator. One chart in six has no major star in the Life Palace, which is far too common a trait to carry a verdict. An actual reading would borrow the major stars from the opposite palace and weigh the three harmonies, and that is interpretation work rather than counting work.

Why is the number of empty palaces always even

One thing I can state with certainty. Two palaces facing each other across the same axis are never both empty. Across 262,980 charts, that is 1,577,880 axes, not a single one came up doubly empty. Empty palaces are therefore always spread across different axes, which means borrowing the major stars from the opposite palace always has something to borrow.

Why the count of empty palaces is always even, I have not worked out. That one stays open.

(Correction, 26 August 2026: this passage previously said I had guessed that an empty palace forces its opposite to be empty, tested it on 43,836 charts, and found 7,714 fitting. The figure 7,714 was wrong. The true count is zero, and the verification script had been indexing palaces incorrectly. A reader on Zhihu pointed out that a doubly empty axis is impossible. He was right. The original wording is preserved here rather than quietly amended.)

Can I reproduce these numbers myself

In principle yes. You need a charting program, one chart for each of the twelve double-hours of every day from 1965 to 2024, and a tally by palace. If your numbers disagree with mine, compare conventions before assuming an error. Which school's transformation table, how the six malefics are counted, and how an empty palace is defined will each move the result on their own.

What happens to the broken rule

It moves from always true to conditional, most likely by requiring other malefic or affliction stars alongside, or it comes out of the engine entirely. Errors of that shape do not surface by rereading the code. Running a census makes them announce themselves.

Whether the system means anything is a separate matter from whether it is interesting. Treated as a table that older astronomers and diviners built to organise the variables of a life, the structure repays a look. Every number above came out of calendar arithmetic and geometry, and none of it has any bearing on anyone's luck.