Hong Kong Mahjong · Limit
Heavenly Hand (天糊) in Hong Kong Mahjong: Fan, Rules and Real Odds
In Hong Kong mahjong, the Heavenly Hand (天糊) is a limit hand, scored at Limit: after the opening flower replacement, the dealer's 14 tiles already form a complete hand, and the dealer wins before discarding a single tile.
Limit hands score the limit straight away (10 fan on this site) without counting anything else — a chicken hand or a Pure One Suit, it's the same.
On this page
The rules for the Heavenly Hand
- Only the dealer can have it — only the dealer starts with 14 tiles
- Opening flowers are replaced as usual; if the 14 tiles are complete afterwards, it counts
- It must be declared before the first discard
- If the dealer first declares a concealed kong and then wins on the replacement, it's not a Heavenly Hand (the tiles have moved) — just Win on a Kong and the other fan
- Any complete hand counts, Thirteen Orphans included
How the Heavenly Hand is scored
The fan below are computed live by the same scoring code the game uses.
Self-drawn
| Heavenly hand (天糊) | Limit |
| Total | 10 fan · Limit |
|---|
Anything over 10 fan scores 10 (the limit).
It's paid as a self-draw: each of the other three pays one share at the limit.
Heavenly, Earthly and Human hands
| Limit hand | Who | When | How |
|---|---|---|---|
| Heavenly Hand | Dealer | Opening, before discarding | Self-draw |
| Earthly Hand | Non-dealer | First draw, no claims before | Self-draw |
| Human Hand | Non-dealer | Dealer's first discard | Win on discard |
All three are limit hands, all scored at Limit.
How it relates to other hands
- Self-drawn: the Heavenly Hand is a self-draw, but a limit hand adds no Self-drawn fan.
- Nine Gates, Thirteen Orphans: if the opening hand is one of these, it's still just the limit; limit hands don't stack.
- Earthly Hand, Human Hand: the other first-round limit hands, see the table above.
Heavenly Hand odds
Random 14 tiles that are already complete
The dealer's 14 tiles after flower replacement are effectively 14 random tiles from the 136 non-flower tiles. We drew 40,000,000 such hands; 0.00026% were already complete (a normal hand or Thirteen Orphans) — roughly once every 390,000 deals.
The first round of computer play
We also let four of this site's computers (Normal level) play 400,000 hands, each one only through the first round: the Heavenly Hand came up 0 times — in line with the odds above, hundreds of thousands of hands may not show a single one. You're the dealer only one hand in four, so for any single player it's four times rarer still.
There's no way to aim for it — it's all in the deal. You may play a lifetime without seeing one; if it happens, declare it before you discard. To look at some opening hands, open a table of online Hong Kong mahjong.
The Heavenly Hand in other mahjong styles
- Sichuan mahjong: the Heavenly Hand scores the cap directly (Sichuan mahjong Heavenly Hand)
- Taiwanese and Japanese mahjong also have a heavenly hand, scored differently: see the Taiwanese mahjong tai list and the Japanese mahjong yaku list
- Chinese Official (Guobiao): see the Guobiao fan list
FAQ
How many fan is the Heavenly Hand?
It's a limit hand: Limit straight away (10 fan on this site), with no other fan added.
Can a non-dealer get a Heavenly Hand?
No. Non-dealers start with 13 tiles; a self-draw on their first draw is the Earthly Hand.
Does a dealer's concealed kong followed by a win count?
No. Declaring the kong has moved the tiles, so it's only Win on a Kong plus the hand's other fan.
How rare is the Heavenly Hand?
About 0.00026% of random 14-tile hands are already complete — roughly once every 390,000 deals.
Related hands
Earthly Hand Limit
A non-dealer wins on their first draw: limit hand. The rules, how tables define it differently, and the real odds.
Human Hand Limit
A non-dealer wins on the dealer's first discard: a limit hand here. The rules, who pays, tables that don't allow it, and the real odds.
Self-Drawn 1 fan
Drawing your own winning tile adds 1 fan: open hands count, who pays, stacking with Concealed and Win on a Kong, and how often it happens.
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.