One Chart in 2.8 Has to Change Its Sentence
Shift the boundary and a planet can change house — the line about career has to be rewritten as wealth. Last time we wrote 41.7%, crossed it out and admitted the simulation was still unrun. Now it is run: eighty thousand birth moments, an answer near 36%, and two errors behind the old figure — the second one undiscoverable by reasoning alone.
Move the boundary east by one degree, and a planet has roughly a one-in-thirty chance of landing in a different house. That figure appeared in the previous piece, and it came from geometry: compare the equal 30° grid against the twelve palace boundaries fixed by the Yuan calendar, add up the absolute deviations of the twelve boundaries, and you get 17.2167°. Divide by 360°, and you get 4.78%.
But that is one planet. Nobody reads a chart one planet at a time. They read the whole chart — Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, plus Rahu, Ketu and Yuebo. Ten bodies. So the real question is not 4.78%. It is: what are the chances that at least one of the ten has to change its sentence?
In the previous piece we gave no such figure. We quoted someone else's: that roughly 41.7% of charts would flip at least one planet — and we pointed out what was wrong with the method behind it. That method assumes the ten bodies are independent. They are nowhere near. Rahu and Ketu sit exactly 180° apart. Mercury never strays more than 28° from the Sun, Venus no more than 48°. They move together. A wrong model can still produce a tidy number, and tidy is not the same as right.
What that piece left owing was its closing line: the true figure needs a real ephemeris and a simulation. At the time, we had not run it. This piece is that run.
1. Eighty thousand birth moments
There is no cleverness in the method, only a refusal to cut it short. Take eight consecutive thirty-year windows covering 1850 to 2090. Draw ten thousand birth moments from each, eighty thousand in total. For every moment, cast the chart twice — once on the equal grid, once on the Yuan palace boundaries — and compare house numbers planet by planet.
The conventions need stating. Ten bodies take part; Ziqi does not, because it has no astronomical position and therefore no house to be in. The Yuan boundaries use ζ And as the determinative star of the Kui mansion. The eight windows carry equal weight.
The answer is 36.02%.
Before memorising that, three things matter more.
It agrees with the 4.78%. Per-planet marginal rates land between 4.713% and 4.909%; the geometric measure gives 4.7824%. All ten in the same order of magnitude. One method is geometry, the other is an ephemeris, and they just nodded at each other. That was the most reassuring line of this round.
The independence assumption errs in the wrong direction. Correcting the count from eleven bodies to ten, the independence formula gives 38.7%. Measured: 36.02%, which is 2.72 points lower. (Both percentages are shown rounded; the 2.72 comes from the unrounded intermediate values, so do not subtract the displayed figures.) Correlation pushes the "at least one" figure down, because the ten prefer to change together or hold together. You cannot reason your way to that direction; you have to measure it. Our first version of the script got the direction backwards, for a reason that is not remotely flattering: the labels were compared wrongly. Same data, different labels, conclusion flipped from "raises" to "lowers". The data did not move. The reader did.
It is not a constant. The eight windows range from 34.27% to 37.98%, a spread of 3.71 points — far wider than the sampling wobble of the pooled eighty thousand (±0.17%). But one sentence we will not overstate: each individual window holds only ten thousand samples and carries its own sampling wobble, so "the entire 3.71-point spread comes from real differences between eras" is more than we can support. What we can say: slow bodies like Jupiter and Saturn do not cover the cycle uniformly once you reduce longitudes modulo 30°. Jupiter's own rate swung from 3.3% to 6.8% depending on the window.
2. How to use the number
First, what it is not.
It does not mean "a third of all charts are wrong". Nor does it mean "any two sets of boundaries differ by this much". It says something quite specific: between these two conventions, roughly one chart in 2.8 has at least one planet whose sentence about its house has to be reworded. Among the charts that trip, most flip a single planet, but about three in ten flip more than one. The chart does not collapse. That sentence — or those two or three sentences — does.
One figure is easy to misread, so let us pin it down. "Only 0.48 of ten bodies affected on average" is an average taken across all charts, including the sixty-four per cent that trip on nothing. It answers "pick a chart at random, how many sentences move", not "how many move in the charts that trip".
So what do we do about the 36%? Printing a single confident number would be easiest and least honest. Instead, on every chart we mark the planets sitting near a boundary as a separate group, and say alongside them that these two conventions put them in different houses. That warning travels with the chart itself rather than living only inside this article.
Nor should 36% be treated as a precise constant. Beyond the era difference, there is a convention risk: with ζ And as the determinative star we get 36%; switch to η And and the start of the Kui mansion shifts by about 2.6°, which moves the figure with it. Two independent lines of evidence support ζ And, but the sources themselves disagree about that star, so we can say "compatible", not "established".
One small aside that may be closer to our readers: the eighty thousand samples spread their birth years evenly, while actual users cluster in the modern era. Narrowing to 1940–2030 and running again gives 36.40% — 0.37 points above the full range. The direction matches "slow bodies bunch up in a modern window"; the size is small. We publish both: "about 36%, and about 36–38% if you look only at people born recently."
3. What the crossed-out line left behind
Back to 41.7%. It was wrong in two places, and neither was a matter of digits. Both were model errors.
The first was a miscount: only ten bodies have positions, and the formula used eleven. That one is easy — change a number and move on.
The second is the substance: the independence assumption does not hold. And the only way to discover that is to actually run the ephemeris, because which way correlation pushes the answer is not something you can think your way to. Our own first script thought its way to the wrong direction.
So the point of this piece is not 36%. It is this: the old number was set aside not because someone later was cleverer, but because the experiment we had skipped finally got run. What held it up was never difficulty. It was "this is good enough".
Things we have not done. The Yuan boundaries enter here as an equal-division approximation, while the real boundaries are unequal — individual widths run from 27.89° to 32.23° — and that information is not yet in the simulation. And a more important boundary: 36% answers only whether a planet changes house, never which side is more correct. We do not know whether the Yuan boundaries or the equal grid suits your chart better. We know they differ. That is not evasion; that is as far as this sentence reaches.
If you have a counterexample, or know of prior work we have missed, tell us. We will correct the article and say so.