Yin year plus female: forward Luck Pillars

The fourth and final matrix cell: a Yin year stem with a female input, running forward. Same birth moment as the previous case, same four pillars, opposite direction. Together the four cases cover every combination of the two inputs.

With the matrix complete, the useful reader takeaway is that Luck Pillar direction is one of the few parts of a chart that is fully determined by stated inputs rather than by interpretive judgement. Polarity comes from the year stem, which is computed. Gender is recorded. There is no room for a school to disagree about the direction itself, only about what the direction means.

That makes direction a good diagnostic. If your chart disagrees with another tool's on direction, the disagreement is mechanical and traceable, and finding it usually reveals a difference in year pillar or gender input that affects more than just the Luck Pillars.

One caveat belongs with that. Because direction is fully determined, it is also fully dependent on the year pillar being right. If your birth sits near Lichun, a boundary error propagates straight through this category, and the direction you calculated correctly from a wrong input will be wrong. The mechanical reliability of the rule is not a guarantee about the input it consumes.