Sichuan Mahjong · Cap

Heavenly Hand (Tian Hu) in Sichuan Mahjong: Scoring and Real Odds

In Sichuan mahjong, the heavenly hand (天胡, tian hu) scores the cap straight away: after the three-tile exchange and the void, the dealer's 14 tiles are already a winning hand before a single discard. Whatever the pattern, it scores the cap of 4 fan: each player pays 16 units, plus the 1-unit self-draw bonus.

The rules for the heavenly hand

• Only the dealer can have it (only the dealer starts with 14 tiles)
• After the exchange and the void, before any discard, the 14 tiles are a winning hand
• None of the 14 may be from the void suit, so a heavenly hand uses at most two suits
• It counts as a self-draw: all three other players pay

How the heavenly hand is scored

The pattern doesn't matter — it goes straight to the cap. The two hands below are scored live by the same code the game uses (the self-draw bonus comes on top).

You can change the cap in settings (3–6 fan), and the heavenly hand always follows it.

How it relates to other hands

• Earthly hand: a non-dealer self-draws on their very first draw — also straight to the cap.
• Self-draw: the heavenly hand is a self-draw paid by all three; with the self-draw fan option it's already at the cap, so nothing more.
• Pattern fan: pure one suit, seven pairs, All Pungs, roots… none of them matter in a heavenly hand — the result is the cap.

Heavenly hand odds

How rare is it? We measured it two ways:

Pure chance: any 14 tiles

Drawing 14 random tiles from 108, 10,000,000 times: 0.0054% were already a winning hand (four sets and a pair, or seven pairs); adding Sichuan's "two suits at most" condition leaves 0.00091% — about once in 110,000.

Real play: after the exchange and the void

Real hands have the three-tile exchange: the dealer can pass on the three least useful tiles, often clearing out the third suit. We let the computers play the first round of 400,000 hands: the dealer had a heavenly hand 0.041% of the time — about once every 2,440 hands.

What to watch for

• Dealer, check first: after the exchange and the void, make sure your 14 tiles aren't already a win before choosing a discard.
• Pick the right void: you can only win with two suits; a third-suit tile among the 14 rules out the heavenly hand.
• It collects the cap: change the cap in settings and the heavenly hand changes with it.

To try it, open a table of online Sichuan mahjong — the computers play blood battle with you and count the fan for you.

The heavenly hand in other mahjong styles

• Taiwanese mahjong: 24 tai (Taiwanese mahjong scoring)
• Japanese mahjong ("Tenhou"): yakuman (Japanese mahjong yaku list)
• Hong Kong mahjong: a limit hand, straight to the maximum (Hong Kong mahjong fan list)

FAQ

How many fan is a heavenly hand?

The pattern doesn't matter; it scores the cap: 4 fan by default, so each player pays 16 units plus the 1-unit self-draw bonus.

Can a non-dealer get a heavenly hand?

No. Only the dealer starts with 14 tiles; a non-dealer self-drawing on their first draw is an earthly hand, also at the cap.

How rare is a heavenly hand?

Random 14 tiles make a Sichuan win about once in 110,000; with the exchange, real play gives a heavenly hand about once every 2,440 hands.

Do pure one suit or roots add to a heavenly hand?

No. A heavenly hand goes straight to the cap; pattern fan don't add on top.

Related hands

Earthly Hand Cap A non-dealer self-draws on their first draw: straight to the cap. Rules, local definitions, and the real odds. Self-Draw 1 fan Everyone pays on a self-draw: the +1-unit bonus versus the +1-fan option, and how often wins are self-drawn.