Sichuan Mahjong · Cap

Earthly Hand (Di Hu) in Sichuan Mahjong: Scoring and Real Odds

In Sichuan mahjong, the earthly hand (地胡, di hu) scores the cap straight away: a non-dealer (any of the three players who aren't dealer) self-draws a win on their very first draw, and nobody has punged or konged before that. 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 earthly hand

• Only a non-dealer can have it (the dealer winning on the starting tiles is a heavenly hand)
• It's your first draw of the hand, and it self-draws a win
• Nobody has punged or konged before your draw (a claim breaks the first round)
• You can't hold your void suit

How the earthly 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).

How it relates to other hands

• Heavenly hand: the dealer wins on the starting 14 tiles — also straight to the cap.
• Self-draw: an earthly hand is always a self-draw, paid by every player still in.
• Pungs and kongs break it: once anyone pungs or kongs in the first round, non-dealers who haven't drawn yet lose the chance.

Earthly hand odds

Pure chance

After a non-dealer's first draw they hold 14 tiles — the same as drawing 14 random tiles from 108: 0.00091% of those are already a win using at most two suits, about once in 110,000 (pure chance, before the exchange).

Real play: after the exchange and the void

We let the computers play the first round of 400,000 hands (until every non-dealer had drawn once, or someone punged or konged): each non-dealer got an earthly hand on their first draw 0.031% of the time (about once in 3,270); some player had an earthly hand in 0.074% of hands, about once every 1,360 hands.

What to watch for

• Check your first draw: if you start ready, make sure the first tile hasn't already won.
• Pick the right void: holding your void suit means you can't win, even if you start ready.
• A claim ends it: once someone pungs or kongs in the first round, a later self-draw is just a normal self-draw.

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

The earthly hand in other mahjong styles

• Taiwanese mahjong: 16 tai (Taiwanese mahjong scoring)
• Japanese mahjong ("Chiihou"): yakuman (Japanese mahjong yaku list)
• Hong Kong mahjong: a limit hand (Hong Kong mahjong fan list)

FAQ

How many fan is an earthly 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.

Is winning on the dealer's first discard an earthly hand?

Not on this site — an earthly hand must be a self-draw on your own first draw. Some tables score that case separately; agree before you play.

Is there still an earthly hand if someone pungs in the first round?

No. If anyone pungs or kongs before your first draw, the earthly hand no longer counts.

How rare is an earthly hand?

Pure chance is about once in 110,000; in real play, each non-dealer gets one about once in 3,270 first draws.

Related hands

Heavenly Hand Cap The dealer wins on the starting 14 tiles: straight to the cap. Rules, who pays, 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.