Hong Kong Mahjong · Limit
Nine Gates (九子連環) in Hong Kong Mahjong: Limit Hand, 9-Sided Wait and Odds
In Hong Kong mahjong, Nine Gates (九子連環) is a limit hand, scored Limit: with a fully concealed hand — no chows, pungs or kongs — your 13 tiles are 1112345678999 of one suit (three 1s, one each of 2 to 8, three 9s). Any tile of that suit from 1 to 9 now completes the hand, and winning on it is Nine Gates, scored at the 10-fan cap.
Nine Gates is always Pure One Suit too, already 7 fan; but a limit hand isn't added up, it's simply Limit.
On this page
The rules for Nine Gates
- Before the winning tile, your 13 tiles are 1112345678999 of one suit — characters, dots or bamboo
- The winning tile is any tile of that suit, 1 to 9
- Fully concealed: no chows, pungs or exposed kongs — not even a concealed kong
- You can win by self-draw or on a discard
The 9-sided wait
Add any tile of the same suit to 1112345678999 and it splits into four sets and a pair, so all nine tiles 1 to 9 win:
| Winning tile | Split |
|---|---|
| 1 | 111 + 123 + 456 + 789 + pair 99 |
| 2 | 111 + pair 22 + 345 + 678 + 999 |
| 3 | pair 11 + 123 + 345 + 678 + 999 |
| 5 | 111 + 234 + pair 55 + 678 + 999 |
| 9 | pair 11 + 123 + 456 + 789 + 999 |
4, 6, 7 and 8 split just as neatly — hence the 9-sided wait.
How Nine Gates is scored
A limit hand isn't added up item by item. The fan below are computed live by the same scoring code the game uses.
Won on a discard
| Nine gates (九子連環) | Limit |
| Total | 10 fan · Limit |
|---|
Anything over 10 fan scores 10 (the limit).
Self-drawn
| Concealed hand (門前清) | 1 |
| Self-drawn (自摸) | 1 |
| Pure one suit (清一色) | 7 |
| No flowers (無花) | 1 |
| Total | 10 fan · Limit |
|---|
Anything over 10 fan scores 10 (the limit).
| Situation | Fan |
|---|---|
| Nine Gates | Limit |
| One suit but not 1112345678999 (Pure One Suit) | 7 fan |
| Pure One Suit + concealed hand + self-draw | 9 fan |
How it relates to other hands
- Pure One Suit: Nine Gates is always Pure One Suit; without the exact shape you score Pure One Suit, and concealed plus self-draw plus No Flowers still hits the limit.
- Thirteen Orphans: the other concealed limit hand with a many-sided wait, built from terminals and honours.
- Heavenly Hand: if the dealer's first 14 tiles are already Nine Gates, it's a Heavenly Hand — a limit counted once.
- Concealed hand: Nine Gates is always concealed, but a limit hand doesn't add concealed or self-draw on top.
Nine Gates odds
How many tiles of one suit in the opening hand
Nine Gates needs all 14 tiles from one suit. A 13-tile opening hand has 9 or more of one suit only 0.25% of the time, and 10 or more 0.028%.
| Most tiles of one suit in the opening hand | Chance |
|---|---|
| 5+ tiles | 65% |
| 6+ tiles | 27% |
| 7+ tiles | 7.8% |
| 8+ tiles | 1.6% |
| 9+ tiles | 0.25% |
| 10+ tiles | 0.028% |
Source: 1,000,000 random 13-tile deals (flowers already replaced).
Fourteen random tiles that are already Nine Gates
Counting combinations exactly: 14 random tiles from the 136 (flowers excluded) form 1112345678999 of one suit plus one more of that suit with probability 0.0000000002% — about once in 490,000,000,000, rarer still than Thirteen Orphans at once in 3,200,000,000. In play you draw and discard, but you still have to reach that exact shape without claiming a single tile.
How often it happens in play
In 100,000 hands of computer play on this site, Nine Gates came up 0 times; Pure One Suit, in the same games, was 0.83% of wins.
When Nine Gates can happen
Nobody plans Nine Gates from the deal. It usually appears when a concealed Pure One Suit is nearly done and the shape happens to fit:
- Already ready with a concealed one-suit hand: if you hold three 1s and three 9s, check whether 2 to 8 are all there.
- Don't kong your 1s or 9s: a concealed kong ends Nine Gates — keep four 1s or four 9s in hand.
- Don't give up Pure One Suit for it: a concealed, self-drawn Pure One Suit is already at the limit; Nine Gates is a bonus.
To practise concealed one-suit hands, open a table of online Hong Kong mahjong — the computers play with you.
Nine Gates in other mahjong styles
The same shape is a big hand in Japanese, Taiwanese and Chinese Official (Guobiao) mahjong, but the name, the score and whether the waiting shape matters vary: Japanese mahjong yaku list, Taiwanese mahjong tai table, Guobiao fan table.
FAQ
How many fan is Nine Gates?
In Hong Kong mahjong Nine Gates is a limit hand: Limit, the 10-fan cap, with nothing else added.
Can Nine Gates include a concealed kong?
No. This site requires no declared sets at all; even a concealed kong turns it back into an ordinary Pure One Suit.
Does Nine Gates have to be self-drawn?
Not on this site — winning on a discard counts the same. Some tables require a self-draw, so ask before you play.
Related hands
Pure One Suit 7 fan
Every tile from a single suit — 7 fan, one step from the limit. Examples, Mixed vs Pure One Suit, and how many suited tiles you need to go for it.
Thirteen Orphans Limit
One of each of the thirteen terminals and honours plus a pair: a limit hand, no claims allowed, with up to a 13-sided wait.
Heavenly Hand Limit
The dealer's 14 opening tiles are already a win: limit hand. The rules, Earthly and Human hands compared, and the real odds.
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.