Taiwanese Mahjong · 8 tai
Big Three Dragons (Da San Yuan) in Taiwanese Mahjong: Tai, Examples and Odds
In Taiwanese mahjong, Big Three Dragons (大三元, da san yuan) is worth 8 tai: when you win, Red, Green and White Dragon are all pungs (or kongs). It already includes Little Three Dragons and the three dragon pungs; those are not added again.
On this page
The rules for Big Three Dragons
- Red, Green and White are all pungs or kongs: claimed, self-drawn, exposed or concealed kongs all count
- The other two sets and the pair are free: chows and pungs, any suit or winds
- No need to stay concealed
How Big Three Dragons waits
The most common shape is two pairs: two dragon pungs done, a pair of the third dragon and another pair, so either tile wins.
Once all three dragon pungs are in place, the rest can wait any way you like — two-sided, edge or single wait, it's still Big Three Dragons.
How Big Three Dragons is scored
The tai below are computed live by the same scoring code the game uses (dealer and dealer-streak tai are added on top).
Won on a discard
| Big three dragons (大三元) | 8 |
| Total | 8 tai |
|---|
Dealer and dealer-streak tai are added on top.
Won on a discard
| Big three dragons (大三元) | 8 |
| All pungs (碰碰胡) | 4 |
| Total | 12 tai |
|---|
Dealer and dealer-streak tai are added on top.
Won on a discard
| Big three dragons (大三元) | 8 |
| All honors (字一色) | 16 |
| Total | 24 tai |
|---|
Dealer and dealer-streak tai are added on top.
Common combinations:
| Combination | Tai |
|---|---|
| Big Three Dragons | 8 |
| Big Three Dragons + Half One Suit | 12 |
| Big Three Dragons + All Pungs | 12 |
| Big Three Dragons + Half One Suit + All Pungs | 16 |
| Big Three Dragons + All Honors | 24 |
How it relates to other hands
- Dragon Pung, Little Three Dragons: one family, only the highest counts — Big Three Dragons adds neither.
- All Pungs: the three dragons are already pungs; if the other two sets are pungs too, it's All Pungs as well, 12 tai.
- Half One Suit: if the other two sets and the pair are one suit, it's Half One Suit too, 12 tai.
- All Honors: if the other two sets and the pair are winds, it's All Honors, 24 tai. All Honors already includes All Pungs, which is not added again.
- Concealed pungs: if the three dragon pungs were self-drawn, add Three Concealed Pungs (2 tai) or more.
Big Three Dragons odds
What your opening hand needs
Big Three Dragons needs three of each dragon. There are only four of each, and every player scores them, so they're hard to come by. In a random 16-tile opening hand:
| Opening hand | Chance |
|---|---|
| Two or more dragons as a pair (or better) | 1.1% |
| All three dragons as a pair (or better) | 0.02% |
Pairs of all three dragons at the start happen only about 0.02% of the time — and even then you still need one more of each.
Big Three Dragons in computer play
In 12,000 hands of normal-level computer play there were 11,677 wins, and only 2 were Big Three Dragons. The computers never hold tiles for it and the sample is far too small, so this isn't its real frequency — it just shows that it almost never happens by accident.
When to go for Big Three Dragons
- Pairs of all three dragons, or two pairs plus one of the third: worth a try — pung dragons as they come, each pung already scores.
- After two pungs: nobody will discard the third dragon, since everyone can see what you're doing. You'll mostly need to draw it yourself or catch a careless discard.
- Two of the third dragon already out: Big Three Dragons is dead. Switch to Little Three Dragons or two dragon pungs and take the win.
- Defending: when someone has two dragon pungs out, never discard the third dragon — hold it to the end if you must.
To try it, open a table of online Taiwanese mahjong — the computers play with you and count the tai for you.
Big Three Dragons in other mahjong styles
- Japanese mahjong: Daisangen is a yakuman (Japanese mahjong yaku list)
- Hong Kong mahjong: Big Three Dragons, 8 fan (Hong Kong mahjong fan list)
- Chinese Official (Guobiao): Big Three Dragons, 88 fan (Guobiao mahjong fan list)
FAQ
How many tai is Big Three Dragons?
In Taiwanese mahjong Big Three Dragons is worth 8 tai, including Little Three Dragons and the three dragon pungs. It stacks with All Pungs, Half One Suit, All Honors, concealed pungs, concealed self-draw and more.
Can you chow in Big Three Dragons?
Yes. Dragons can only be punged, but the other two sets can be chows; the hand doesn't need to be concealed.
Do you add dragon pungs to Big Three Dragons?
No. Dragon Pung, Little Three Dragons and Big Three Dragons are one family; only Big Three Dragons counts.
How many tai is Big Three Dragons with All Honors?
Big Three Dragons 8 tai plus All Honors 16 tai, 24 tai in total; if the wind pungs include the round or seat wind, add those too.
Related hands
Little Three Dragons 4 tai
Two dragon pungs with the third dragon as the pair — 4 tai. Examples, the two-pair wait, and how it differs from Big Three Dragons.
Dragon Pung 1 tai
Each pung of Red, Green or White is 1 tai: how it's counted, what two pungs score, and when it turns into Little or Big Three Dragons.
All Honors 16 tai
A hand made only of honor tiles, 16 tai: it always brings dragons or four winds along, so it starts at 20 tai.
Try it at the table
Taiwanese Mahjong — Play authentic Taiwanese 16-tile mahjong free in your browser against three computer opponents. Flowers, chow, pung, kong, dealer streaks and automatic tai scoring. No sign-up, works on phone and desktop.