How rare is each main star?

• · Sample: 24,000 birth moments, drawn with a fixed PRNG seed (20260610) so the whole table can be regenerated exactly.
• · Birth years uniform across 1950–2010; month and day uniform within each month's real length; hour and minute uniform, which keeps all twelve 时辰 uniform after true-solar-time correction.
• · Each sample is cast by the production engine — the same code path as a chart you cast yourself — and its Self-palace main stars and BaZi day master are recorded.
• · Main-star percentages count a multi-star Self palace toward each star it holds, so a two-star palace is counted twice and the fourteen sum to 116.97%. The combination table counts each palace once, toward its exact set, and leaves out the starless palaces — add those 16.15% to the 83.88% below and you are back at 100.

Rarest to most common, the fourteen span just 0.63 of a percentage point — the folk claim that one main star is dramatically rarer than the rest does not survive measurement. What is genuinely uncommon is a starless Self palace and the specific two-star pairings below.

The ten day masters sit close to one tenth each, as the sexagenary day cycle implies. The small spread is a real artefact of the sampled year range, not noise we smoothed away.

Machine-readable JSON: /api/public/rarity. Licensed CC BY 4.0 — use it anywhere, commercially included, as long as you credit 14 Main Stars with a link to this page. If you want a configuration re-measured with a different year range or sample size, ask and we will run it.

What this dataset is not: it counts how often a configuration occurs in the calendar. It says nothing about the people who hold one. Zi Wei Dou Shu and BaZi are traditional symbolic systems offered for reflection, not verified prediction.