A Set of Rules for Mah-Jongg

David Maze

December 25, 2004

1 Basics

1.1 The Tiles

The set has 144 tiles. Except for the pretties, there are four of each tile. There are several groups of tiles:

• Three suits; four each of one through nine of bamboo, circles, and characters. (The one of bamboo typically has a different design, in my set a bird.)

• Four winds; four each of north, south, east, and west. (These are the only tiles with letters on them.)

• Three dragons; four each of red, green, and white. (In my set these have no English character at all; the white dragon actually has an empty blue frame.)

• Two sets of pretties; one each of four flowers and one each of four seasons.

1.2 Objective

The goal of the game is to form a hand with four groups of three tiles and one pair of matched tiles. A group can be a run (chow) of three consecutive tiles within a single suit (3-4-5 of circles, for example) or a set (pung) of three identical tiles. It is also possible to form a set of four (kong); in this case, an extra tile is drawn to make the hand the right size. The extra pair of tiles is called the eyes.

When it is not your turn, you have thirteen tiles in your hand, some possibly in face-up sets. On your turn, you acquire a tile. You now have fourteen tiles; if these match the pattern described above you can declare mah-jongg and win the hand. Otherwise, you will discard a tile and the next player takes their turn.

1.3 Setup

Shuffle the tiles. Form a square wall with the tiles; it should be two tiles high and eighteen tiles on a side, with all of the tiles face down. Select a player to go first; that player is east. East will begin drawing tiles from their side of the wall, starting at the right. Roll 3d6, and separate out this number of tiles from the end of the wall. (Optionally, declare this number to always be 14 instead.) These are loose tiles. If all of the tiles aside from the loose tiles are taken and nobody has won, the hand is discarded and played again.

Starting with east and proceeding in a clockwise direction, each player takes four tiles (two pairs off the wall). This is repeated twice, and then each player in turn takes a single tile. After this each player should have thirteen tiles, all concealed. East takes one additional tile from the wall now (or draws the appropriate tile when they take their thirteenth tile: take the top tile at the end of the wall, and also take the top tile from the third pair, skipping one). This extra tile is the tile that would normally be drawn at the start of east’s first turn.

At this point, starting with east, each player has the opportunity to declare pretties and concealed kongs. If you have a flower or season, lay it face up and draw a loose tile (from the separated set at the end of the wall). If you have a set of four identical tiles, you may lay it out, then turn the middle pair of tiles over, and draw a loose tile.

1.4 Play

On your turn, you acquire a tile, then discard a tile. Normally play begins with east drawing a tile, and proceeds in a clockwise direction. You can acquire a tile on your turn by drawing the next tile from the wall. However, you may also claim the most recently discarded tile, possibly out of turn. It is conventional to state which tile you are discarding.

You may claim a tile:

• If you need it to go mah-jongg; taking this tile gives you four groups of tiles and a pair. Take the tile and lay out the group it forms face up, then reveal your remaining tiles; you have won the hand!

• If you need it for a set of four (kong), where the first three tiles are in your hand (concealed). Take the tile, lay the set of four all face-up, and draw a loose tile; it is now your turn.

• If you need it for a set of three (pung). Take the tile and lay the set all face-up; it is now your turn.

• If it would otherwise be your turn, and you need the tile for a sequence (chow). Take the tile and lay the sequence all face-up.

Otherwise, you cannot take a tile; you must draw. If the tile you draw is a pretty, lay it face up and draw a loose tile. If the tile you draw matches a set of three that is already laid out, you may add the fourth tile (an exposed kong) and draw a loose tile, though you are not compelled to. If the tile you draw matches a set of three in your hand, you may lay out the set of four and turn over the outer pair of tiles (a concealed kong) and draw a loose tile. It is also possible to declare mah-jongg at this point.

Exposed sets cannot be refactored. If you have 3-4-5 of circles exposed and draw the 2, 6, and 7, you cannot break the exposed sequence to form a new sequence, for example. Tiles in your hand can be arranged however you like, but if you go mah-jongg, your hand must have the proscribed layout.

If you have not won and it is your turn, your turn ends by discarding a tile, which other people may claim.

Robbing the kong. If another player has an exposed pung, and on their turn, they draw the fourth matching tile from the wall and use it to form an exposed kong, and if you need that tile to go mah-jongg, you may rob the kong, steal that tile, and win the hand.

1.5 Simple Game

There should be enough information so far to play a round of Mah-Jongg with the objective of winning hands. After each hand, the east position shifts to the left, and that player begins the next hand.

2 Advanced Game

2.1 Winds

In the full game, there are two winds that matter. The prevailing wind begins at east, and progresses to south, west, then north; it advances when the player who was first east becomes east again. The game ends when the prevailing wind shifts back to east. The player wind is determined by your seat at the table. East takes the first play, and west sits opposite him. North and south are the opposite of normal compass directions; pretend you’re looking up through the table. Thus, south is to east’s right, and north is to east’s left.

If east wins a hand, they continue to be east for the next hand. Otherwise, the player who was previously north becomes east, possibly also causing the prevailing wind to advance. The game ends when the prevailing wind advances from north back to east.

2.2 Scoring

Hands are scored after a player goes mah-jongg. Sets of tiles are worth some number of points. Some sets of tiles also cause your score to double. All doubles are taken, one at a time, after adding up individual set scores. Thus, holding a set of winds that is both the player and prevailing wind, plus a set of dragons, this adds up to three doubles, so your end score is multiplied by eight.

Table 1 lists scores for all hands, even if you don’t win. Sequences (chows) are never worth points. Sets (pungs and kongs) are divided into major and minor sets. Sets of two through eight in a suit are minor; sets of ones, nines, winds, or dragons are major, and are worth twice as many points. A set is also worth twice as many points if it is in your hand (concealed) rather than laid out (exposed). Pairs are worth no points, unless a third tile would turn the pair into something that doubled. If your player wind is the same as the prevailing wind, a set of those winds is worth two doubles.

You get additional points for going mah-jongg; these points and doubles only apply if you win a hand. These scores are listed in Table 2. If you won by claiming another player’s discard, you get no special points; if you win by drawing a tile from the wall, you get two points; if you win by drawing a loose tile (from forming a set of four or drawing a pretty), you get a double. A hand’s score is doubled if it consists of all sets of three or four with a pair, or if the hand is worth no points aside from pretties from Table 1; this generally implies a hand of all sequences, with the pair either in a suit or from an unfavored wind.

2.3 Scoring example

Imagine a winning hand that consists of the 3, 4, and 5 of circles (exposed), three red dragons (exposed), four east winds (concealed, but still on the table, with the middle pair face down), three twos of bamboo (concealed), a pair of fives of characters (concealed), and the 1 of flowers and the 1 of seasons. Further, assume the player is east and the prevailing wind is east. Scoring for this hand would be shown in Table 3.

Exposed chow (sequence of three tiles in a suit)  0
Concealed chow  0
Exposed minor pung (set of 2-8 in a suit)  2
Concealed minor pung  4
Exposed major pung (set of 1, 9, wind, or dragon)  4
Concealed major pung  8
Exposed minor kong (set of four of 2-8)  8
Concealed minor kong  16
Exposed major kong  16
Concealed major kong  32
Pair of dragons  2
Pair of prevailing or player wind  2
Pair of prevailing and player wind  4
Pretty (flower or season, each)  4
Pung or kong of dragons  1 double
Pung or kong of prevailing wind  1 double
Pung or kong of player wind  1 double
Own flower and season (east = 1, south = 2, west = 3, north = 4)  1 double
All four flowers  1 double
All four seasons  1 double
Three concealed pungs (or kongs)  1 double
Two pungs (or kongs) of dragons, and a pair of the third (Little Three Dragons)  1 double

Table 1: Scoring for all hands

Going mah-jongg  20
Winning from the wall (drawing the winning tile)  2
Fishing the eyes (last tile makes the pair)  2
Filling the only space (only can win with one tile)  2
Winning with east’s first discard (standing hand)  100
Winning as east without drawing tiles (original hand)  3 doubles
Winning with a loose tile  1 double
Winning with the last tile from the wall  1 double
Robbing the kong  1 double
No score hand (pretties are okay)  1 double
All pungs or kongs  1 double
All major pungs or kongs (no 2-8)  1 double
Only one suit, with 1 or 9 (winds and dragons okay)  1 double
Only one suit, with 1 or 9 (no winds or dragons)  3 doubles

Table 2: Scoring for winning hands

3C-4C-5C  Exposed chow  0
RD-RD-RD Exposed pung of majors  4
EW-XX-XX-EW Concealed kong of majors 32
2B-2B-2B  Concealed pung of minors 4
5K-5K  Eyes  0
1F  Pretty  4
1S  Pretty  4
Going mah-jongg  20
Total points:  68
RD-RD-RD Pung of dragons  double
EW-XX-XX-EW Kong of player wind  double
EW-XX-XX-EW Kong of prevailing wind  double
1F-1S Own flower and season double
Total hand score:  1088

Table 3: Scoring the sample hand

This scoring assumes that the player won by, say, claiming a red dragon to form the exposed set of three. If they won by drawing the fourth east wind from the wall, laying out the kong, drawing a loose tile, and then getting the 5K for the eyes, they would get 2 extra points for fishing the eyes and filling the only space (for 72), plus an extra double for winning from the wall, for a total score of 2304. These are exceptionally good hands; winning hands will frequently score around 30 points, perhaps adding one or maybe two doubles.

2.4 Settling

The final phase of the hand involves the exchange of points (or money). First, each player gives the winning player the value of the winning player’s hand. Then, the losing players settle with each other; the player with the most points of the losers collects the difference between the score of their own hand and the two remaining players, then the losing player with the second-most points collects the difference between his hand and the hand of the losing player with the fewest points.

Any transaction involving east is doubled in value. Thus, if east wins the hand, he collects twice the value of his hand from each player, for a total of six times the value of the hand. Otherwise, the winning player collects twice the value of his hand from east and the value of the hand from the two other players, for a total of four times the value of the hand. Settlements involving east are similarly doubled if east does not win the hand.

It is therefore impossible for the winning player to lose money on the hand, even if they have fairly few points. It is similarly possible to make money on a good hand even without winning. An example is shown in Table 4. In this hand, north wins a hand and scores 64 points; west doesn’t win but has 72 points; south has 8 points, and east has no points. Note that all scoring involving east is doubled: south pays west the difference in their hands (56 points), but east pays south and west twice the respective differences. Since north won, he collects four times the value of his hand, and pays nothing to anyone, even though west’s hand is worth more than his.

It is generally desirable to set a limit on the value of a hand. 3000 points is a typical limit; a hand worth more than 3000 is worth 3000 for purposes of settlement. If playing for money, lower

East South West North
Hand scores:  0  8  72  64
1. All players pay winner -128 -64  -64 +256
2. Losers settle with west -144 -64 +208
3. East settles with south -16 +16
Totals:  -288 -112 +144 +256

Table 4: Example of settling hands

limits may be desirable; with a 250-point limit in a penny game, east can only lose (or win) $15 in a single hand. Lower limits make the game less interesting.

2.5 Limit Hands

(This section can be safely ignored.) A number of odd hands are actually worth points, if you manage to accumulate them in your hand. These are generally mostly concealed hands; if you collect one, you may declare mah-jongg, and your hand scores the agreed-upon limit.

• Four of each dragon, plus a pair of the player’s wind. The sets of dragons must not be laid out, even as normal concealed kongs. (Imperial Mah Jongg) Alternatively, this hand may be collected as three pungs of dragons (possibly exposed) plus one of each dragon plus a pair of the player’s wind. (Mah Jongg of the Crazy Monkey)

• Four each of three winds, plus a pair of the fourth. The sets of winds must not be laid out, even as normal concealed kongs. (Mah Jongg of the Mandarin)

• A pung or kong of each wind, plus a pair of dragons. (The Fourfold Homely Happiness)

• Within a single suit, 1-1-1-2-3-4-5-6-7-8-9-9-9, plus one more tile from that same suit. (Calling Nine Tile Hand)

• One of each dragon and wind, plus one of the one and nine of each suit, plus one more tile from this set. (Thirteen Wonders of the Ancient World)

• Pungs or kongs of either all three nines or all three ones, a pung of dragons, and a pair of the player’s wind. (Three Adopted Sons of the Dragon)

• Four consecutive pungs within a single suit, plus a pair of winds or dragons. (Four Siamese Sisters)

• All pungs or kongs and a pair, all of winds or dragons.

• Seven pairs.

• Form a kong (set of four). Draw a loose tile, and with that, form a second kong. Draw another loose tile, and go mah-jongg normally using that tile.

Other limit hands are known to exist; see a more canonical set of rules.