Hong Kong Mahjong · 8 fan
Great Three Dragons (大三元) in Hong Kong Mahjong: Fan, Examples and Odds
In Hong Kong mahjong, Great Three Dragons (大三元) is worth 8 fan: when you win, Red, Green and White Dragons are all pungs (or kongs), plus any fourth set and a pair.
At 8 fan it is two fan short of the 10-fan limit: No Flowers plus a self-draw, or Mixed One Suit or All Pungs on top, takes it straight to the limit.
On this page
The rules for Great Three Dragons
- Three or four of each dragon — Red, Green and White: punged, kongs or drawn yourself all count
- The fourth set can be any chow or pung, and the pair can be anything
- Claiming is fine — it doesn't need to be concealed
- Only the highest in the family counts: no extra fan for the three dragon pungs, and no Small Three Dragons on top
Great vs Small Three Dragons
| Hand | Red, Green, White | Fan |
|---|---|---|
| Dragon pung | one or two pungs | 1 fan each |
| Small Three Dragons | two pungs + the third as the pair | 5 fan |
| Great Three Dragons | three pungs | 8 fan |
One tile makes a big difference: if one dragon is only a pair, it's Small Three Dragons.
How Great Three Dragons is scored
The fan below are computed live by the same scoring code the game uses.
Won on a discard
| Great three dragons (大三元) | 8 |
| No flowers (無花) | 1 |
| Total | 9 fan |
|---|
Anything over 10 fan scores 10 (the limit).
Self-drawn
| Self-drawn (自摸) | 1 |
| Great three dragons (大三元) | 8 |
| No flowers (無花) | 1 |
| Total | 10 fan · Limit |
|---|
Anything over 10 fan scores 10 (the limit).
| Combination | Fan |
|---|---|
| Great Three Dragons | 8 fan |
| Great Three Dragons + No Flowers | 9 fan |
| Great Three Dragons + self-draw + No Flowers | 10 fan · Limit |
| Great Three Dragons + Mixed One Suit | 10 fan · Limit |
| Great Three Dragons + All Pungs | 10 fan · Limit |
How it relates to other hands
- Small Three Dragons: two pungs plus the third dragon as the pair, 5 fan — one tile away.
- Dragon pung: 1 fan for each Red, Green or White pung, already included here.
- Mixed One Suit: three dragon pungs plus one suit is naturally Mixed One Suit, and together they hit the limit.
- All Pungs: if the fourth set is a pung too, add 3 fan — also the limit.
- All Honours: if the fourth set and the pair are winds, the whole hand is honours: the limit hand All Honours.
Great Three Dragons odds
How many dragons in the opening hand
Great Three Dragons needs nine dragon tiles out of only 12. A 13-tile opening hand has three or more dragons about 9.1% of the time and five or more only 0.19%; it starts with two dragon pairs about 0.46% of the time.
| Dragon tiles in the opening hand | Chance |
|---|---|
| 1+ tiles | 72% |
| 2+ tiles | 32% |
| 3+ tiles | 9.1% |
| 4+ tiles | 1.6% |
| 5+ tiles | 0.19% |
| 6+ tiles | 0.018% |
Source: 1,000,000 random 13-tile deals (flowers already replaced).
How hard it is in play
Over 100,000 hands of computers playing normally on this site, Great Three Dragons came up 7 times and Small Three Dragons 26 times. As soon as one dragon is punged by someone else or two of it are discarded, Great Three Dragons is impossible — which is why it's so rare.
Which hands suit Great Three Dragons
- Two dragon pairs and one of the third dragon: pung the pairs first and hope to draw the third.
- The third dragon hasn't been discarded: once two are out, forget it and aim for Small Three Dragons or Mixed One Suit.
- Others will defend: with two dragon pungs on show, nobody will discard the third — you'll mostly have to draw it.
If it doesn't come off, Small Three Dragons is still 5 fan. To try it, open a table of online Hong Kong mahjong — the computers play with you and count the fan for you.
Great Three Dragons in other mahjong styles
Great Three Dragons is a big hand in many styles, but scores differently:
- Taiwanese mahjong: see the Taiwanese mahjong tai table
- Japanese mahjong: Daisangen is a yakuman, see the Japanese mahjong yaku list
- Chinese Official (Guobiao): see the Guobiao fan table
- American mahjong: dragons have their own hand category (American mahjong Winds and Dragons)
FAQ
How many fan is Great Three Dragons?
In Hong Kong mahjong Great Three Dragons is worth 8 fan, not a limit hand; two more fan (say No Flowers plus a self-draw) take it to the 10-fan limit.
What's the difference between Great and Small Three Dragons?
Great Three Dragons is pungs of all three dragons, 8 fan; Small Three Dragons is two pungs plus the third dragon as the pair, 5 fan.
Do the dragon pungs score extra on top?
No. Only the highest in the family counts, and Great Three Dragons already covers the three dragon pungs.
Can you claim tiles for Great Three Dragons?
Yes. The dragon pungs can be claimed, konged or drawn yourself; the hand doesn't need to be concealed.
Related hands
Small Three Dragons 5 fan
Two dragon pungs and a pair of the third dragon — 5 fan. Examples, the difference from Great Three Dragons, combos and how many dragons you need to go for it.
Dragon Pung 1 fan
1 fan for every pung of Red, Green or White — the easiest fan in the game: how it scores, when to pung, and how it leads to the three-dragon hands.
All Honours Limit
Every tile a wind or dragon — a limit hand scored at the maximum at once, always All Pungs, and how it overlaps the three-dragon and four-wind hands.
Try it at the table
Hong Kong Mahjong — Play classic Hong Kong (Cantonese) mahjong free in your browser against three computer opponents. 13-tile hands, flowers, 3-fan minimum, 10-fan limit and automatic fan scoring. No sign-up, works on phone and desktop.