Chinese Official Mahjong · 88 pt

Thirteen Orphans in Chinese Official Mahjong (MCR): Points, the 13-Sided Wait, Odds

In Chinese Official Mahjong, Thirteen Orphans (十三幺) is worth 88 points: you win holding one of each of the thirteen terminals and honors — 1 and 9 characters, 1 and 9 dots, 1 and 9 bamboo, East, South, West, North, Red, Green and White — plus a second copy of any one of them as the pair, 14 tiles in all. It isn't four sets and a pair; it's one of MCR's three special winning shapes (the others are Seven Pairs and Knitted).

The rules for Thirteen Orphans

• Thirteen kinds: 1 and 9 characters, 1 and 9 dots, 1 and 9 bamboo, East, South, West, North, Red, Green, White — at least one of each
• One of them twice (the pair), 14 tiles in all
• Always concealed: no chows, pungs or kongs
• Self-drawn or on a discard

The 13-sided wait and the single wait

• Holding one of each of the thirteen, any of the thirteen tiles wins — the 13-sided wait
• With a pair already and one kind missing, only that kind wins

Either way, Single Wait is not scored.

What Thirteen Orphans does not combine with

Under the non-repeat rule, Thirteen Orphans already includes these fan, so they are not counted:

• All Types (6 points): all five types are always there
• Concealed Hand (2 points) and Fully Concealed Hand (4 points): it is always concealed
• Single Wait (1 point)

Thirteen Orphans isn't All Terminals and Honors either: that fan is made of pungs and a pair, which this hand doesn't have.

Fan that still stack: Self-Drawn (1 point — Fully Concealed Hand is out, so its "no Self-Drawn" rule doesn't apply), Last Tile, Robbing the Kong, Last Tile Draw, Last Tile Claim and flowers.

How Thirteen Orphans is scored

The hands below are scored live by the same code the game uses, including the fan left out under the non-repeat rule.

How it relates to other fan

• All Terminals and Honors: also only terminals and honors, but as four pungs and a pair; Thirteen Orphans doesn't score it.
• Greater Honors and Knitted Tiles and Lesser Honors and Knitted Tiles: the other "unconnected tiles" special hands — with lots of honors and few connections, weigh all three.
• All Types: Thirteen Orphans always has all five types, so All Types isn't counted.

Thirteen Orphans odds

How many orphan kinds in the opening hand

Thirteen Orphans counts kinds, not tiles: how many different terminals and honors are in the 13-tile opening hand. 7 or more kinds about 6.2% of the time, 8 or more about 1.2%, 9 or more only about 0.15%:

Source: 1,000,000 random 13-tile deals (flowers already replaced).

Counting a pair among them as one more (kinds plus one if paired), 10 or more — at most three useful tiles from being ready — happens about 0.08% of the time.

14 random tiles

Drawing 14 random tiles from the 136, the chance they are exactly Thirteen Orphans is about one in 3,200,000,000. Real play draws one tile at a time and you choose what to keep, so this only shows how hard it is to get by accident.

In 4,000 hands of normal computer play on this site (3,849 wins), Thirteen Orphans came up 3 times — far too small a sample for an 88-point hand.

Which hands can go for Thirteen Orphans

• 9 or more orphan kinds at the start is when it's worth considering; with 7 or 8, the same tiles usually suit Knitted, Greater Honors and Knitted Tiles or Half Flush better.
• Throw the simples first: 2–8 tiles are useless for Thirteen Orphans.
• Watch the discards: if three of the kind you're missing are out, only one is left; all four out and it's dead.
• Opponents notice: discarding simples while keeping terminals and honors is easy to read, and late in the hand they will hold those tiles back. Know when to fold.

Want to try? Open a table of Chinese Official Mahjong online — the computers play with you and the scoring is done for you.

Thirteen Orphans in other mahjong styles

• Japanese mahjong: Kokushi Musou, a yakuman (Japanese mahjong yaku list)
• Hong Kong mahjong has Thirteen Orphans too (Hong Kong mahjong fan table)

FAQ

How many points is Thirteen Orphans?

In Chinese Official Mahjong Thirteen Orphans is worth 88 points, and it no longer counts All Types, Concealed Hand, Fully Concealed Hand or Single Wait.

Which thirteen tiles are they?

1 and 9 characters, 1 and 9 dots, 1 and 9 bamboo, plus East, South, West, North, Red, Green and White — one of each, with one of them doubled as the pair.

Can you claim tiles for Thirteen Orphans?

No. Thirteen Orphans has no chows or pungs at all, so it is always concealed.

How much is a self-drawn Thirteen Orphans?

Thirteen Orphans (88) plus Self-Drawn (1); Fully Concealed Hand isn't counted. If the winning tile is the last of its kind, add Last Tile (4).

Related fan

All Terminals and Honors 32 pt Only 1s, 9s and honors for 32 points: the pung and seven-pairs forms, what it doesn't combine with, and the All Types and Triple Pung it often brings. Greater Honors and Knitted Tiles 24 pt The knitted hand with all seven honors, 24 points: examples, the difference from the Lesser version, what it doesn't combine with, how often it shows up. Lesser Honors and Knitted Tiles 12 pt Fourteen unconnected tiles for 12 points: the knitted tiles plus honors, how it waits, how it stacks with Knitted Straight, how often it shows up.