The decade pillars, and which way they run
The 大運 are not a second chart. They are the month pillar walked along the sixty-pair cycle, one pair per decade, and the only questions are which way it walks and when it starts.
Decades that run forward
Where the decades run forward, the reason is a rule with only two inputs.
The 大運, the luck pillars, are not a separate chart. They are the month pillar continued along the sixty-pair cycle, one pair per decade. The only question is which way along it you travel, and 《淵海子平》 settles that with a pairing of the year stem's polarity against sex: yang stem with a man, yin stem with a woman, and the count runs forward.
The starting age is counted, not chosen. From the moment of your birth the method counts forward to the next solar term, then converts at three days to one year — so a birth nine days before the coming term begins its decades at three, and one born a day before it begins at four months. The page states the age at which the first decade opens.
Running forward means the months ahead of your birth month are the ones you walk into: the season keeps advancing. If you were born in early spring your decades move through late spring, then summer. The classical reading of that is not better or worse than the reverse — it is a different order of arrival. What a forward chart tends to meet early is the maturing of the season it was born into, and what it meets late is the season's opposite.
Decades that run backward
Where the decades run backward, the rule that decides it has only two inputs.
The 大運 are not a second chart. They are the month pillar stepped along the sixty-pair cycle, one pair per decade. Direction is fixed by the year stem's polarity set against sex — 《淵海子平》 gives yin stem with a man and yang stem with a woman as the reverse cases.
The opening age is counted rather than assigned. From your birth the method counts back to the solar term just passed, then converts at three days to one year. Born six days after a term began, the decades open at two; born a day after it, they open at four months. The page states the age at which the decades open.
Running backward means your decades retrace the months before your birth: the season unwinds rather than advances. Born in early autumn, you move back through late summer, then high summer. Nothing in the classics ranks this against the forward direction, and the difference is one of sequence, not of quality — a reverse chart meets the season it grew out of before it meets the one it was heading into. One practical consequence is worth naming: reverse charts often reach the opposite of their birth season late in life rather than early, which changes when the chart's own imbalance gets its correction.
Cast the chart this page describes
The four pillars, the Day Master, the five-phase count, the day’s almanac read against the chart and the true solar time working — about 2,700 words — are free and need no account. The chart is computed in the browser; nothing about the birth is sent anywhere.