TL;DR: Tam Hoi cuc is three consecutive Earthly Branches belonging to one season, such as Dần Mão Thìn meeting as Wood, reflecting the qi of an entire direction. Tam Hop cuc is three branches one step apart, matching the Trường Sinh, Đế Vượng and Mo states of the same element, such as Thân Tý Thìn combining as Water. Most sources rank Tam Hoi stronger than Tam Hop, but some place them equal, and Tử Bình Chân Thuyên uses the word hoi for Tam Hop, so naming is not consistent across books.
How are Tam Hoi cuc and Tam Hop cuc defined?
Tam Hoi cuc is a group of three Earthly Branches sitting next to each other on the twelve branch cycle, belonging to the same season and the same direction: Dần Mão Thìn meeting as Wood cuc in the East, Tỵ Ngọ Mùi as Fire cuc in the South, Thân Dậu Tuất as Metal cuc in the West, Hợi Tý Sửu as Water cuc in the North. Tam Hop cuc also has three branches, but one step apart: Thân Tý Thìn combining as Water, Dần Ngọ Tuất as Fire, Hợi Mão Mùi as Wood, Tỵ Dậu Sửu as Metal.
The core difference is that Tam Hoi takes the season as its base, while Tam Hop takes the Trường Sinh (Growth) cycle of one element as its base. This distinction is stated clearly in discussions on the Lý Số Vietnam forum and in Bát Tự articles circulating in Vietnam.
Why is Tam Hoi considered the qi of an entire direction?
The three branches in one Tam Hoi are exactly the three months of one season in the Can Chi calendar. Dan, Mao and Thin are the first, middle and last months of spring, so when these three branches appear together, Wood qi is no longer a single branch but the whole of spring gathered. This explanation is recorded in current Bát Tự materials and matches how the question was framed on the Lý Số forum: hoi means meeting by direction, gathering qi along an orientation.
Why is Tam Hop tied to Trường Sinh, Đế Vượng and Mo?
Tam Hop takes the three operating states of one element as its axis. For Water, Trường Sinh is at Than, Đế Vượng at Ty, Mo at Thin, so Thân Tý Thìn combines as Water cuc. This reasoning is also presented in discussions on Lý Số Vietnam and in Bát Tự articles circulating in Vietnam. In other words, Tam Hop describes an element going from arising, through its peak, to storage; Tam Hoi describes an element ruling an entire season.
Table placing Tam Hoi beside Tam Hop for the same element
| Element | Tam Hoi cuc (three months of one season) | Tam Hop cuc (Trường Sinh, Đế Vượng, Mo) |
|---|---|---|
| Wood | Dần Mão Thìn, East | Hợi Mão Mùi |
| Fire | Tỵ Ngọ Mùi, South | Dần Ngọ Tuất |
| Metal | Thân Dậu Tuất, West | Tỵ Dậu Sửu |
| Water | Hợi Tý Sửu, North | Thân Tý Thìn |
This table shows something easily overlooked: the Tam Hoi of one element may contain a branch that is the Mo storage of another element. For instance Hợi Tý Sửu meets as Water, but Suu is the Mo storage of Metal; Thân Dậu Tuất meets as Metal, but Tuat is the Mo storage of Fire and is also Earth. So when interpreting, one should not look only at the cuc element and ignore the original qi of each branch.
Does Tam Hoi need all three characters?
Yes. Tam Hoi only forms a cuc when all three branches are present. If one branch is missing it is no longer Tam Hoi but shifts to the ban hoi form. This point is stated clearly in discussions on the Lý Số Vietnam forum and in Bát Tự articles circulating in Vietnam.
What is ban hoi and which pairs count?
Ban hoi is the case where only two of the three branches of a Tam Hoi appear together. For the Eastern Wood direction, ban hoi includes Dần Mão and Mão Thìn; for the Southern Fire direction, Tỵ Ngọ and Ngọ Mùi; and similarly for the other directions. Notably, Dần Thìn is not counted as ban hoi, because these two branches are not adjacent within the Tam Hoi. This rule is given in discussions on the Lý Số Vietnam forum.
When does ban hoi take effect?
According to Bát Tự articles circulating in Vietnam, ban hoi only takes effect when the missing branch appears in the Da Van or Luu Nien, at which point ban hoi becomes a full Tam Hoi. When the four pillars simultaneously contain clashing force, ban hoi cannot fully control the clash, unless the element of the combination transformation is strong enough in qi to block the clash.
Do they need to be adjacent?
For ban hoi, yes. Two branches must stand next to each other on the twelve branch cycle to be called ban hoi; two branches one step apart do not count. For a full Tam Hoi the three branches are adjacent by definition, so the question of adjacency only arises in the ban hoi form.
When Tam Hoi, Tam Hop and Luc Hop appear together, which is heavier?
Most documents rank strength from strongest to weakest as Tam Hoi, Tam Hop, half Tam Hop, then Luc Hop. This order is given in Bát Tự articles circulating in Vietnam and in discussions of Can Chi compatibility on Lý Số Vietnam. The consequence is that when a chart has both Tam Hoi and Luc Hop on the same group of branches, the main interpretation should follow Tam Hoi, while Luc Hop is overshadowed or reduced in effect.
For example Hợi Tý Sửu already forms a Water Tam Hoi, in which Ty and Suu are also a Luc Hop pair. Because Tam Hoi is stronger, the main direction of interpretation is the Water cuc, while the Tý Sửu Luc Hop only plays a secondary role.
Where the schools disagree
Not every book places Tam Hoi above Tam Hop. Some sources rank the two as equal, treating both as strong combinations and weighing them by birth season, leading stem transformation and root qi. Naming also diverges: in Tử Bình Chân Thuyên, the word hoi is used for Tam Hop, with the familiar phrasing tam hoi such as Thân Tý Thìn. Meanwhile Uyên Hải Tử Bình has no separate Tam Hoi section, and adds Thìn Tuất Sửu Mùi earth cuc to the Tam Hop group.
How should the Thìn Tuất Sửu Mùi earth cuc be understood?
This point needs to be stated clearly because it is easily confused. Thìn Tuất Sửu Mùi are the four Mo storages of the four elements, not a Tam Hoi in the sense of three months of one season. Grouping three of these four branches into an earth cuc is a phrasing found in some documents, but it is not mentioned by orthodox books. In discussions on the Lý Số Vietnam forum, the view put forward is that this phrasing does not belong to the orthodox system. So when Thìn Tuất Sửu Mùi appears in a chart, one should interpret by the original qi of each branch and by Mo storage, and should not assume it is a Tam Hoi of Earth.
Does Tam Hoi change the fortune of a chart?
Tam Hoi and Tam Hop can change the outlook of a chart, but they should not be viewed as a fixed auspicious or inauspicious sign. When an element is successfully transformed by Tam Hoi, that element becomes very strong and can dominate the situation. If the chart is already strong in that element, Tam Hoi can push it into imbalance; if the chart is lacking, Tam Hoi can partly compensate. Bát Tự articles circulating in Vietnam also stress that combination transformation is not always good: if the Day Master cannot turn the strength of the combination into something usable, or if the transformed element runs against the Useful God, the result can be unfavorable.
What role does leading transformation play?
According to Bát Tự articles circulating in Vietnam, Tam Hoi needs a Heavenly Stem of the same element to lead the transformation if it is to transform strongly. Dần Mão Thìn needs Giap or At for Wood qi to be firm; Tỵ Ngọ Mùi needs Dinh for Fire to flourish; Thân Dậu Tuất needs Canh or Tan; Hợi Tý Sửu needs Nham or Quy. Without a leading transformation stem, the branches still link but do not fully transform, and each branch will reveal its own qi.
Should one convert this into a strength number?
Some current documents assign Tam Hoi a strength of about 72 degrees and Tam Hop about 60 degrees. This conversion is not common in classical books, and it is itself inconsistent across modern documents, so it should only be treated as a relative quantification. What is more reliable is the principle: Tam Hoi gathers the qi of an entire season and is therefore usually judged stronger than Tam Hop, but the exact gap depends on each school's understanding.
Key points to remember when interpreting
Tam Hoi and Tam Hop differ in their construction axis: one is three months of one season, the other is the three states Trường Sinh, Đế Vượng and Mo of one element. Tam Hoi needs all three branches to form a cuc; missing one branch turns it into ban hoi, and ban hoi has only two adjacent pairs, with Dần Thìn excluded. When several combinations appear together, most documents prioritize Tam Hoi, then Tam Hop, then Luc Hop, but some sources rank Tam Hoi and Tam Hop as equal. Naming also differs between Tử Bình Chân Thuyên and Uyên Hải Tử Bình, and the Thìn Tuất Sửu Mùi earth cuc is a phrasing outside the orthodox system. Tam Hoi or Tam Hop should not be read as a fixed auspicious or inauspicious sign, but placed beside birth season, leading transformation stem, root qi and the Useful God of the whole chart.
