Sources
Every faan value on this site is checked against written Hong Kong references, and the game is scored by the same table. This page lists what we checked, how to read a faan chart without being misled, and where the references genuinely differ.
One chart says Small Dragons is 3. Another says 5. Both are right, and both describe the same hand.
Some tables quote the increment: 3 faan, with the two dragon pungs still counting on top. Others quote the inclusive total: 5 faan, 不再計三元牌, do not count the dragons again. 3 + 2 = 5.
Every number on this site is the inclusive total: what the whole hand is worth. When two published charts look like they disagree, line the conventions up first. Most of the time the disagreement evaporates.
Four patterns divide the written sources for real. We picked a reading for each and say why, so you can disagree with an argument instead of a mystery.
One Chinese table says the wind pungs are already inside the 6 and stop counting. Most others allow stacking them.
What we score: We stack them, following the majority reading. The 13 cap absorbs most of the difference anyway. Pattern page
Hong Kong sources say 8 as an ordinary pattern. The tournament books say 10, but 10 is their entire ceiling, so that is the cap speaking. One commercial chart says 13.
What we score: We score 8. "8, ordinary" and "10, a limit" are the same hand seen from two different ceilings, and under our 13 cap the graded reading is the coherent one. Pattern page
The tournament books file it in their ten-faan tier, and most references agree. Two implementations pay the cap.
What we score: We score a flat 10. A 13-faan Nine Gates reads as a bug to a Hong Kong player. Pattern page
The tournament reading is 7. A coherent older lineage scores 6.
What we score: We score 7, with the tournament books. Pattern page