In Hong Kong mahjong, when a player declares a winning hand, scoring proceeds in two stages. First, the winning hand is awarded a number of "faan"—a unit from the Cantonese term 番 (pinyin: fān / jyutping: faan1).
Second, faan are converted into scores for each player. When gambling with mahjong, these scores represent money. In this article, "points" refer exclusively to these scores (and not faan).
Most Hong Kong mahjong games require that players declaring a win to have 3 faan, but other minimums are possible. This generally increases the length of each game and allows more strategizing around discarding and forming melds.
Counting faan
In Hong Kong mahjong, 13 faan is considered the absolute limit for faan, but players can set a lower ceiling to reduce stakes (e.g., 8 faan).
The general equation for the total faan of a winning hand is:
<math>\text{Total Faan} = \begin{cases} \min(13, \text{Hand} + \text{Winning Condition}), \text{if hand is a limit hand,} \\ \min(13, \text{Hand} + \text{Wind and Dragon} + \text{Flower} + \text{Winning Condition}), \text{if otherwise.} \end{cases}</math>
High-scoring hands (, translated to "limit hands" in this article) are only scored based on the hand and winning conditions, but not winds, dragons, or flowers.
Hand Faan
The contents of the hand are most important for awarding faan. Typically, a rarer hand is worth more points, but this may not be the case.
If multiple criteria are satisfied, the points awarded under each criterion are stacked together.
The tables following list the criteria for scoring the contents of the hand.
{| class="wikitable"
|+
|-
! English !! Cantonese !! Faan !! Description
|-
! rowspan=2 | Common Hand (i.e., all sequences)
| || 1 || Every meld is a Chow
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | All in Triplets
| || 3 || Every meld is either a Pong or Kong
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Mixed One Suit
| || 3 || Only honor tiles and tiles from one suit
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | All One Suit
| || 7 || All tiles from one suit
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Mixed Orphans
| || 1 || Hand containing Pongs/Kongs of Ones, Nines, or Honor Tiles only (implies All in Triplets, which adds another 3 faan)
|-
| colspan="3" | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Small Dragons
| || 3 || Melds of 2 dragons and a pair of the 3rd dragon. The faan of the 2 dragon triplets will be counted also, such that the dragon tiles will add 5 faan.
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Great Dragons
| || 5 || Melds of all 3 dragons. The faan of the 3 dragon triplets will be counted also, such that the dragon tiles will add 8 faan.
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Small Winds
| || 6 || Melds of 3 winds and a pair of the 4th wind. Bonuses for seat or round wind can result in even higher faan.
If the remaining meld is from a suit, this hand will satisfy Mixed One Suit (which adds another 3 faan). Thus, a hand that satisfies Small Winds will grant at least 9 faan in practice.
|-
| colspan=3 | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan=2 | Seven Pairs (played by some variants)
| || 4 || Hand consists of seven pairs. Can stack with All Honor Tiles, Mixed One Suit and All One Suit.
In some variants, Kongs are not permitted in this hand.
|-
| colspan=3 | 45px45px-45px45px-45px45px-45px45px-45px45px-45px45px-45px45px
|}
Limit Hands
Certain high-scoring hands are "limit hands" that are ineligible for additional faan awarded based on winds, dragons, or flowers. Even if the limit hand satisfies other hand criteria (e.g., all honor tiles must also be all triplets), the faan from the other criteria are not counted.
Various sources classify limit hands differently and assign them different scores (e.g., the Hong Kong Mahjong Assoication sets a maximum faan of 10, such that 13 Orphans is only awarded 10 faan). This section is written to conform with the Cantonese version of this article.
If a winning hand satisfies more than one capped hand criterion (e.g., great winds where the pair is dragons, therefore also an all honor tile hand), only the criterion with the highest score applies.
{| class="wikitable"
|+
|-
! rowspan="2" | All Honor Tiles
| || 10 || All honor tiles
|-
| colspan="3" | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan="1" | Self Triplets
| <br />|| 10 || Every meld is either a concealed (unmelded) Pong or concealed Kong. The bonus can only be won either (a) by self-pick or (b) from a discarded winning tile that forms the pair, i.e., the discard cannot form the melds.
|-
! rowspan="2" | Orphans
| || 10 || Hand containing Pongs/Kongs of Ones and Nines only
|-
| colspan="3" | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan="2" | Nine Gates
| || 10 || Hand in any one suit consisting of 1112345678999, must be totally concealed.
|-
| colspan="3" | 45px45px45px-45px45px45px45px45px45px45px-45px45px45px + any tile in the set
|-
! rowspan="2" | Great Winds
| || 13 || Melds of all 4 winds
|-
| colspan="3" | 45px45px45px-45px45px45px-45px45px45px-45px45px45px-45px45px
|-
! rowspan="2" | All Kongs
| <br /><br /> || 13 || Hand containing four Kongs (and a pair)
|-
| colspan="3" | 45px45px45px45px-45px45px45px45px-45px45px45px45px-45px45px45px45px-45px45px
|-
! rowspan="2" | Thirteen Orphans
| || 13 || One of each one, nine, wind, and dragon, and a 14th tile (any other terminal or honor tile)
|-
| colspan="3" | 45px45px-45px45px-45px45px-45px45px45px45px-45px45px45px + any tile in the set
|}
;Notes
Wind and Dragon Faan
{| class="wikitable"
|+
|-
! English !! Cantonese !! Faan !! Description !! Example
|-
| Seat Wind || 門風 (mun4 fung1) || 1 || A meld of the winner's seat wind ||20px20px20px /20px20px20px /20px20px20px /20px20px20px
|-
| Prevailing Wind || 圈風 (hyun1 fung1) || 1 || A meld of the prevailing wind ||20px20px20px /20px20px20px /20px20px20px /20px20px20px
|-
| Red Dragon || 紅中 (hung4 zung1) || | 1 || A meld of the red dragon ||20px20px20px
|-
| Green Dragon || 發財 (faat3 coi4) || | 1 || A meld of the green dragon|| 20px20px20px
|-
| White Dragon || 白板 (baak6 baan2) || | 1 || A meld of the white dragon || 20px20px20px
|}
A double wind, where a certain wind is both the winner's seat wind and the prevailing wind, counts as 2 faan.
Flower Faan
Some criteria for faan are based on "bonus tiles"—the flowers and the seasons (which are also collectively called flowers).
{| class="wikitable"
|+
|-
! English
!Cantonese!! Faan !! Description !! Example
|-
| No Flowers or Seasons
|无花 (mou4 faa1)|| | 1 || No flower or season bonus tiles ||
|-
| Flower of Own Wind
|正花 (zing3 faa1)|| 1 || A flower of the winner's seat wind ||24x24px / 24x24px / 24x24px / 24x24px
|-
| Season of Own Wind
|正花 (zing3 faa1)|| 1 || A season of the winner's seat wind ||24x24px / 24x24px / 24x24px / 24x24px
|-
| All Flowers
|一台花 (jat1 toi4 faa1)|| | 2 || All flower bonus tiles (does not stack with Flower of Own Wind) ||24x24px24x24px24x24px24x24px
|-
| All Seasons
|一台花 (jat1 toi4 faa1)|| | 2 || All season bonus tiles (does not stack with Season of Own Wind)|| 24x24px24x24px24x24px24x24px
|}
Under certain custom rules, a player who draws 7 bonus tiles can declare a win worth 3 faan on the spot; a player who draws all 8 bonus tiles can declare a win worth 13 faan.
Winning Condition Faan
Other scoring criteria are based on the winning condition—how the winner won.
{| class="wikitable"
|+
|-
! English !! Cantonese !! Additional Faan !! Description
|-
| Self-Pick || 自摸 (zi6 mo1) || 1 || The winning tile is from the wall
|-
| Win from Wall (i.e., fully concealed hand) || 門前清 (mun4 cin4 cing1) || 1 || Awarded when the entire hand remains concealed (no open melds exposed) until the winning tile is either self-drawn or claimed from a discard.
Hands that are strictly concealed by definition (e.g., Seven Pairs, Thirteen Orphans, Self Triplets, Nine Gates) do not receive this additional point.
|-
| Robbing Kong || 搶槓 (coeng2 gong3) || 1 || When the tile used by player A to make a Kong is player B's winning tile, player B can declare a win (and obtain this bonus).
|-
| Win by Last Catch || 海底撈月 (hoi2 dai2 lau4 jyut6)|| 1 || The winning tile is either the last tile from the wall or the last discard
|-
| Win by Kong || 槓上開花 (gong3 soeng5hoi1faa1) || 1|| The winning tile is from a replacement tile due to a Kong or a Bonus Tile. Implies self-pick (which adds 1 additional faan).
|-
| Win by Double-Kong || 槓上槓 (gong3 soeng5gong3) || 8|| Similar to 'Win by Kong', except that the tile used to make the Kong was itself an extra tile from declaring a Kong. Implies self-pick (which adds 1 additional faan).
|-
| Heavenly Hand || 天糊 (tin1 wu4*2) || 13 || East wins with initial hand
|-
| Earthly Hand || 地糊 (dei6 wu4*2) || 13 || Non-East player wins on East's first discard
|}
Converting faan to score
Faan is converted score in an exponential manner (i.e., each additional faan is worth more than the last). When gambling with mahjong, these scores represent money, e.g., 8 points is 8 Hong Kong dollars.
Faan-to-score table
In typical Hong Kong mahjong (also known as Hong Kong New Style), there are two common ways to translate faan: "full spicy" and "half spicy". Players can also forgo both and agree on a custom table.
Full spicy
In "full spicy", the points awarded for a hand are 2 to the power of the number of faan, i.e., <math>2^{\text{faan</math>.
{| class="wikitable"
|+
!Faan
!Points
!Formula
|-
|0
|1
|<math>2^0 = 1</math>
|-
|1
|2
|<math>2^1 = 2</math>
|-
|2
|4
|<math>2^2 = 2 \times 2 = 4</math>
|-
|3
|8
|<math>2^3 = 2 \times 2 \times 2 = 8</math>
|-
|4
|16
|<math>2^4 = 16</math>
|-
|5
|32
|<math>2^5 = 32</math>
|-
|6
|64
|<math>2^6 = 64</math>
|-
|7
|128
|<math>2^7 = 128</math>
|-
|8
|256
|<math>2^8 = 256</math>
|-
|9
|512
|<math>2^9 = 512</math>
|-
|10
|1024
|<math>2^{10} = 1024</math>
|-
|11
|2048
|<math>2^{11} = 2048</math>
|-
|12
|4096
|<math>2^{12} = 4096</math>
|-
|13
|8192
|<math>2^{13} = 8192</math>
|}
Half spicy
"Half spicy" mitigates how quickly points increase with each additional faan.
It starts the same as full spicy, but from 4 faan onward, points double every two faan instead of every one. An odd-numbered faan above 4—e.g., 5 faan—is always 1.5 times the points of the previous faan.
{| class="wikitable"
|+
!Faan
!Points
!Formula
|-
|0
|1
|<math>2^0 = 1</math>
|-
|1
|2
|<math>2^1 = 2</math>
|-
|2
|4
|<math>2^2 = 4</math>
|-
|3
|8
|<math>2^3 = 8</math>
|-
|4
|16
|<math>2^4 = 16</math>
|-
|5
|24
|<math>1.5 \times 2^4 = 24</math>
|-
|6
|32
|<math>2^5 = 32</math>
|-
|7
|48
|<math>1.5 \times 2^5 = 48</math>
|-
|8
|64
|<math>2^6 = 64</math>
|-
|9
|96
|<math>1.5 \times 2^6 = 96</math>
|-
|10
|128
|<math>2^7 = 128</math>
|-
|11
|192
|<math>1.5 \times 2^7 = 192</math>
|-
|12
|256
|<math>2^8 = 256</math>
|-
|13
|384
|<math>1.5 \times 2^8 = 384</math>
|}
Which player pays
Suppose player A wins with 3 faan, their winning tile is from player B, and discarder pays all. Under either the full or half spicy table, that translates to 8 points.
When player A gains 8 points, because player B is the discarder, the latter loses 8 points.
{| class="wikitable"
! !! Player A !! Player B !! Player C !! Player D
|-
| Before || 0 || 0 || 0 || 0
|-
| Game 1 || +8 || −8 || 0 || 0
|}
The total points in a mahjong game always sum to zero.
How to handle self-pick
When a player self-draws their winning tile, all players pay. The points awarded are 1.5 times the table amount, which also ensures the winner's total is divisible by three.
Building on the previous example, suppose player C wins with 3 faan and their winning tile is self-drawn. Under either the full or half spicy table, that translates to 8 points. The self-pick means player C is awarded <math>1.5 \times 8 = 12</math> points instead.
{| class="wikitable"
! !! Player A !! Player B !! Player C !! Player D
|-
| Before || +8 || −8 || 0 || 0
|-
| Game 2 || −4 || −4 || +12 || −4
|-
| Total|| +4|| −12|| +12|| −4
|}
Common modifications
Discarder-pays-all or -half
There are two ways to handle payment when the winning tile comes from a discard.
In discarder-pays-all, the discarder pays the winner the full points.
In discarder-pays-half, only half the awarded points are paid the discarder; the other half is split evenly between and paid by the two remaining players.
Faan maximum
To reduce the stakes, a common modification is to cap the number of faan recognized. Typically the cap is set at 10 faan. That would mean, for example, that a 12-faan win is still awarded the points for 10 faan.
Divide by a constant
To reduce the stakes, players can also agree to divide all points by a constant, e.g., 16. This would make a 3-faan hand worth <math>{8 \div 16 = 0.5}</math> point. This can also scale point values when settling in a currency that is more valuable than Hong Kong dollars.
For round numbers, the constant should be a multiple of 2.
Old-style scoring
There's also documentation of more archaic scoring systems, commonly referred to as Hong Kong Old Style. These can be viewed here.
Penalties
{| class="wikitable"
|-
! English !! Cantonese !! Description
|-
| False win || 詐糊|| If a player declares a winning hand that doesn't meet the faan minimum, they pay all players the points for the maximum faan, i.e., the player loses <math>384 \times 3 = 1152</math> points under the half spicy table.
|}
Penalties that apply under discarder-pays-half system
{| class="wikitable"
|-
! English !! Cantonese !! Description
|-
| 9 Pieces Penalty || 九張包 || Discarder pays all losses for enabling winner to go out with Pure Hand after winner had already melded 3 sets (9 tiles) of the same suit
|-
| 12 Pieces Penalty || 十二張包自摸 || Winner goes out with Self-Picked Pure Hand after discarder has allowed them to meld a 4th set of the same suit; Discarder pays all losses
|-
| Fifth Tile Penalty || 五子包生 || Discarder pays all losses for discarding a "fresh" (previously unseen anywhere on the table) tile when there are 5 or less tiles left in the wall, allowing winner to go out
|}
Use of poker chips
Poker chips can be used to keep score. When used, all players must agree upon how many points one chip is worth.
There is no universally followed rule for what happens when a player runs out of points (i.e. their total points goes below zero). In some circles, the match is immediately aborted, with the player furthest ahead in score declared the winner, while in others, a player out of poker chips continues to play without risk of further losses. The loser can also pay cash to buy back the chips from the winners and the game continues.
Hand progress terminology
The following is a list of terms describing the progress of one's hand:
- 獨聽 (duk6 teng1) - Known in English typically as a one-shot win or a last-chance win, this occurs if the winner was looking for one and only one tile to win the hand (e.g., the middle tile in a Chow). In some variations, this may extend to cases where two or more tiles could win the hand, but all but one were previously discarded.
- 雞糊 (gai1 wu2) - Also known in some circles as 推倒胡 (tuī dǎo hú/teoi1 dit3 wu4) or 雞胡 (ji hú/gai1 wu4 "Chicken Hand"), this is used to describe a winning hand worth zero faan, or no points. For games with a minimum faan score, this can also describe those with insufficient faan.
- 詐糊 (zaa3 wu2) - Known in English literally as a trick hand, used to describe a "false alarm" when a player claims to have won the amount claimed but in fact has not.
- 食糊 (sik6 wu2) - Winning off another player's discard.
- 叫糊 (giu3 wu2) - A "ready" or "waiting" hand, one tile away from winning.
References
External links
- Game that implements HK scoring rules