Hong Kong Mahjong · 5 fan
Small Three Dragons (Siu Sam Yuen) in Hong Kong Mahjong: Fan, Examples and Odds
In Hong Kong mahjong, Small Three Dragons (小三元) is worth 5 fan: when you win, two of the three dragons (Red, Green, White) are pungs or kongs, and the third dragon is your pair.
At 5 fan it is well over the 3-fan minimum. Each dragon pung normally scores one fan, but once you have Small Three Dragons those are not counted separately — you score the 5 fan of Small Three Dragons instead.
On this page
The rules for Small Three Dragons
- Two dragons as pungs (claimed, kongs or self-drawn all count)
- The third dragon as the pair
- The other two sets can be any chows or pungs
- Chows, pungs and kongs are allowed; the hand need not be concealed
If all three dragons are pungs it is Great Three Dragons (8 fan) and only that counts.
Dragon pung, Small and Great Three Dragons
| Hand | Requirement | Fan |
|---|---|---|
| Dragon pung | Each dragon pung | 1 fan (each) |
| Small Three Dragons | Two pungs + a pair | 5 fan |
| Great Three Dragons | Three pungs | 8 fan |
Only the highest in the family counts: Small Three Dragons doesn't add the two dragon pungs, and Great Three Dragons doesn't add Small Three Dragons.
How Small Three Dragons is scored
The fan below are computed live by the same scoring code the game uses.
Won on a discard
| Small three dragons (小三元) | 5 |
| No flowers (無花) | 1 |
| Total | 6 fan |
|---|
Anything over 10 fan scores 10 (the limit).
Won on a discard
| Mixed one suit (混一色) | 3 |
| Small three dragons (小三元) | 5 |
| No flowers (無花) | 1 |
| Total | 9 fan |
|---|
Anything over 10 fan scores 10 (the limit).
Common combinations:
| Combination | Fan |
|---|---|
| Small Three Dragons | 5 fan |
| Small Three Dragons + No Flowers | 6 fan |
| Small Three Dragons + Mixed One Suit | 8 fan |
| Small Three Dragons + All Pungs | 8 fan |
| Small Three Dragons + Mixed One Suit + All Pungs | 10 fan · Limit |
How it relates to other hands
- Dragon pung: each pung of Red, Green or White is 1 fan; if Small Three Dragons doesn't come off, two dragon pungs still give two fan.
- Great Three Dragons: one more tile of the paired dragon makes Great Three Dragons, 8 fan.
- Mixed One Suit: dragons are honours, so if the rest is one suit it stacks with Mixed One Suit.
- All Pungs: if the other two sets are pungs it stacks with All Pungs.
Small Three Dragons odds
How many dragons in the opening hand
There are 12 dragon tiles. A 13-tile opening hand holds 4 or more of them about 1.6% of the time, and 5 or more only 0.19%; two different dragon pairs show up 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).
Is it worth forcing Small Three Dragons?
In every hand, the player with the most dragon tiles had to go for Small Three Dragons — never discard a dragon, always pung one, otherwise play like the normal computer, and never win without Small (or Great) Three Dragons — while the other three played normally. Then we compared it with the same opening hands played normally.
| Dragon tiles in the opening hand | Opening hands | Made it | Made it anyway, playing normally | Someone else won | Exhaustive draw | Avg. result forcing it | Avg. result playing normally |
|---|---|---|---|---|---|---|---|
| 1 or fewer | 2,518 | 0.64% | 0% | 70% | 29% | −5.8 | −0.3 |
| 2 | 7,852 | 1.1% | 0% | 71% | 28% | −5.7 | −0.1 |
| 3 | 4,474 | 3.6% | 0.016% | 71% | 25% | −2.0 | +1.5 |
| 4+ tiles | 1,156 | 11% | 0.39% | 67% | 22% | +8.4 | +6.1 |
Source: computer play on this site. In each of 16,000 hands the seat with the best start forced Small three dragons (小三元); the other three played normally (Normal level). Results in base units (3-fan minimum, 10-fan limit, half-spicy scoring, discarder pays).
Unlike Mixed One Suit and Pure One Suit, Small Three Dragons is not always worth forcing:
- With 3 or more dragon tiles, forcing it only works 5.1% of the time and averages +0.2 base units — worse than the +2.3 of playing normally. There are only 12 dragon tiles, you need all three kinds, and others pung them away.
- Only with 4 or more does the success rate rise to 11%, averaging +8.4 and beating +6.1 for normal play (last row of the table).
- Finished hands averaged 7.3 fan.
- When the computers play normally, Small Three Dragons is only 0.032% of wins (26 times in 100,000 hands), while 23% of wins have at least one dragon pung.
Which hands suit Small Three Dragons
- Two dragon pairs to start: you are almost halfway; one pung and you have a set.
- Dragons not yet discarded: once two of a dragon are in the discards, that dragon can only be your pair.
- Don't cling to it: two dragon pungs alone are two fan, and No Flowers or a self-draw makes the minimum.
To try it, open a table of online Hong Kong mahjong — the computers play with you and count the fan for you.
Small Three Dragons in other mahjong styles
- Taiwanese and Japanese mahjong both have Small Three Dragons: see the Taiwanese mahjong tai table and the Japanese mahjong yaku list
- Chinese Official (Guobiao) mahjong has it too: see the Guobiao fan table
- Sichuan mahjong has no honour tiles, so no Small Three Dragons
FAQ
How many fan is Small Three Dragons?
In Hong Kong mahjong Small Three Dragons is worth 5 fan. The two dragon pungs aren't counted again, but Mixed One Suit, All Pungs, self-draw and other fan still add on.
Does the pair have to be a dragon?
Yes. Two dragon pungs plus a pair of the third dragon make Small Three Dragons; with any other pair you only score the two dragon pungs, 1 fan each.
What's the difference between Small and Great Three Dragons?
Small Three Dragons is two pungs and a pair, 5 fan; Great Three Dragons is pungs of all three, 8 fan.
Related hands
Great Three Dragons 8 fan
Pungs of Red, Green and White — an 8-fan big hand: examples, the difference from Small Three Dragons, when it hits the limit and how many dragons you need.
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.
Mixed One Suit 3 fan
One suit plus honours — 3 fan, enough to win by itself. Examples, the difference from Pure One Suit, combos and how many tiles you need to go for it.
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.