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Singaporean's Guide to Mahjong Winning Hand's Probability, Scoring and How to Mahjong

profileMing Feng
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Mahjong: Singaporean’s Favourite Pastime

Way before Crazy Rich Asians made the game of Mahjong famous by slotting it into the most important scene in the movie, some of us Singaporeans are already killing it in our self-directed “God of Gamblers” series.

Source: fareastfilm.com

Week in week out, we fully utilise the “healing power of mahjong” and how it treats senile as an excuse to gather with our friends or family members over a game on mahjong.

Mahjong is good, they say. It treats senile, they say.

That was before I lost all my taxi money and end up walking home.

With that, we compiled a Mahjong guide and find out the probability of some of these winning hands:


The Probability of Seeing These Mahjong Winning Hands

Some of us are guilty of taking Instagram stories of our tiles whenever we win with a certain hand.

Source: Sgag

We get it, you made some money, well-done!

Truth is, not all Mahjong hands are created evenly. Some of these hands have a lower chance of happening than the rest!

Based on a study done, if you were to:

  • Play 1 full game (assuming 16 rounds) of Mahjong a day
  • Starting from 1 January 2021
  • Assuming 365 days a year

Here are the dates of which you will see these Mahjong hands:

Mahjong HandWhen will you see it?Number of rounds
(Assuming 16 rounds per day)
Probability of seeing this winning Mahjong hand
All Chows without any animal or bonus tiles
(平和)
1 January 20211 Day
(16 rounds)
1 in 16 rounds
Mixed Suit
(混一色)
1 January 20211 Day
(16 rounds)
1 in 16 rounds
Pure Suit
(清一色)
2 January 20212 Days
(32 rounds)
1 in 32 rounds
Winning with a Replacement tile for bonus tiles
(花上自摸)
13 January 202113 Days
(208 rounds)
1 in 208 rounds
Robbing the Kong
(抢杠)
20 January 202120 Days
(320 rounds)
1 in 320 rounds
Little Three Dragons/Little Three Scholars
(小三元)
24 January 202124 Days
(384 rounds)
1 in 384 rounds
Thirteen Orphans/Thirteen Wonders
(十三幺)
3 June 2021154 Days
(2,464 rounds)
1 in 2,464 rounds
Little Four Winds/Little Four Blessings
(小四喜)
22 July 2021202 Days
(3,232 rounds)
1 in 3,232 rounds
Big Three Dragons/Big Three Scholars (immediate)
(大三元)
4 August 2021234 Days
(3,744 rounds)
1 in 3,744 rounds
All Honours
(字一色)
21 November 2021325 Days
(5,200 rounds)
1 in 5,200 rounds
Pure Green Suit Hand
(绿一色)
12 October 2022650 Days
(10,400 rounds)
1 in 10,400 rounds
Big Four Winds/Big Four Blessings
(大四喜)
27 November 20223,616 Days
(57,856 rounds)
1 in 57,856 rounds

Source: mahjongnews.com


Mahjong Guide For Singaporeans: Scoring

Source: Gfycat

The amount of money you win in a round of Mahjong depends on the number of Doubles (some people call them “tai” or “fan”) your combination entitles you to.

If you are having trouble remembering how many Doubles your combination entitles you to, we did a compilation to help you out!

Number of doubles
(Tai or Fan)
Combination
1 Double
一台
Seat Flower (正花/门花)

All Chows but with Animal or bonus tile (臭平和)

Pong of Dragons (箭刻)

Pong of Seat Wind (门风刻)

Pong of Round Wind (圈风刻)

Concealed Hand and self-drawn (门清)

Robbing the Kong (抢杠)

Winning with the Last Drawn Tile (海底捞月)

Winning with a Replacement tile for kongs (杠上开花)

Winning with a Replacement tile for bonus tiles (花上自摸)

Flower Set Bonus (花杠加台)

Animal Set Bonus (动物杠加台)

Any Animal Tile (动物加台)
2 Doubles
两台
All Pongs or All Pairs (碰碰和/对对和)

Mixed Suit (混一色)

Mixed Terminals and Honours (混幺九/混老头)

Little Four Winds/Little Four Blessings (小四喜)
3 Doubles
三台
Little Three Dragons/Little Three Scholars (小三元)
4 Doubles
四台
All Chows without any animal or bonus tiles (平和)

Pure Suit (清一色)
5 Doubles
(Usually the limit in Singapore context)
五台
Heavenly Win (天和)

Earthly Win (地和)

Thirteen Orphans/Thirteen Wonders (十三幺)

Big Four Winds/Big Four Blessings (大四喜)

Big Three Dragons/Big Three Scholars (大三元)

All Honours (字一色)

Pure Green Suit Hand (绿一色)

All Terminals (全幺九/清老头)

Four Concealed Pongs (self-drawn) (四暗刻/坎坎和)

All Kongs (杠杠和/十八罗汉)

Kong on Kong Win (杠上杠和)

Flower Win/Robbing the Flower (immediate) (七抢一)

Flower Win/Eight Immortals (immediate) (花和/八仙过海)

Nine Gates (九连宝灯)

Source: Singapore Sparrows


Further Reading on the Probability of These Mahjong Winning Hand

Source: Hardwarezone

Mahjong Combination: All Chows without any animal or bonus tiles (平和) and Mixed Suit (混一色)

All Chows without any animal or bonus tiles (平和) and Mixed Suit (混一色) the more common winning hands in a game of Mahjong. These two combinations have a 1 in 16 chance of happening throughout a round of mahjong.

Here’s what an “All Chows without any animal or bonus tiles (平和)” combination looks like:

Source: mahjongstudio.com

It is a winning hand which consists only of consecutive numbers in sets of three. The set should not have any flowers, animals, own wind or dragon tiles in it.

Here’s what a Mixed Suit (混一色)combination looks like:

Source: mahjongstudio.com

For Mixed suit, it is a combination made up of tiles of the same suit and includes Winds or Dragons tiles.

Mahjong Combination: Pure Suit (清一色)

A Pure Suit (清一色) winning hand has a 1 in 32 chance of occurring.

Source: mahjongstudio.com

A Pure Suit is a combination made up of tiles from the same suit (eg. Bamboo, Circles or Characters).

Mahjong Combination: Winning With a Replacement Tile for Bonus Tiles (花上自摸)

For every 208 rounds of Mahjong game, there is a chance of players winning the game, with a hand completed by a replacement card. This is after receiving a flower or animal tile.

Mahjong Combination: Robbing the Kong (抢杠)

A winning hand that is completed by snatching a declared Kong from other players. There is a 1 in 320 chance of this happening.

Mahjong Combination: Little Three Dragons/Little Three Scholars (小三元)

Little Three Dragons/Little Three Scholars is a hand made up of 2 sets of Dragon tiles and the remaining Dragon set as the eye.

Source: Mahjongstudio.com

There is a 1 in 384 chance of this happening.


Now, to some of the hardest combinations. These are the only type of winning hands worth putting on your social media.

Source: giphy

Mahjong Combination: Thirteen Orphans/Thirteen Wonders (十三幺)

This is, in my opinion, one of the hardest combinations to get, but I was wrong.

Turns out, the Thirteen Orphans/Thirteen Wonders is actually the easiest when compared to the rest of the special combinations. There is a 1 in 2,464 chance of it happening.

Source: mahjongstudio.com

This combination requires each of the four Winds tile, each of the three Dragons tile, the number one and number nine of the three suits (Bamboo, Circles or Characters).

Mahjong Combination: Little Four Winds/Little Four Blessings (小四喜)

We are now down to some of the rarer winning hands in mahjong.

Source: mahjongstudio.com

The Little Four Winds/Little Four Blessings is made up of three of the Winds (in a pong or Kong)with one pair of the remaining Wind. This combination has a 1 in 3,232 chance of happening.

Mahjong Combination: Big Three Dragons/Big Three Scholars (大三元)

Unleash the Dragons!

Source: mahjongstudio.com

If you have three of the Dragons (in a pong or kong), you are winning the game with the Big Three Dragons/Big Three Scholars combination.

There is only a 1 in 3,744 chance of you getting it.

Mahjong Combination: All Honours (字一色)

If you have a hand made up of either the four Winds or three Dragons, you have an All Honours winning hand.

Source: mahjongstudio.com

This combination only appears once every 5,200 round.

Mahjong Combination: Pure Green Suit Hand/ The Green Bamboo (绿一色)

We are down to the second rarest combination. The Pure Green Suit Hand has a 1 in 10,400 chance of happening.

Source: mahjongstudio.com

The reason that this hand got its name lies in the colour of all the tiles in this winning hand. Made up of only Bamboo tiles and the ‘Fa’ tile, this winning hand is hard to come by.

Mahjong Combination: Big Four Winds/Big Four Blessings (大四喜)

No prize for guessing, but the Big Four Winds/Big Four Blessings winning hand has the lowest probability in a game of mahjong. With a rare 1 in 57,856 chance of happening, this combination definitely needs to go onto your Instastory!

Source: mahjongstudio.com

This winning hand requires all the Winds (be it pong or kong) to be in the combination.


How To Play Mahjong

There are a total of 148 tiles in a Singaporean Mahjong set.

The tilesets are:

The Circles Suit (筒子)

Source: wikipedia

There are 4 of each tile in a Singaporean Mahjong set.

The Bamboo Suit (索子)

Source: wikipedia

There are 4 of each tile in a Singaporean Mahjong set.

The Character Suit (万子)

Source: wikipedia

There are 4 of each tile in a Singaporean Mahjong set.

The Wind Tiles (四风牌)

Source: wikipedia

There are 4 of each tile in a Singaporean Mahjong set.

The Dragon Tiles (三元牌)

Source: wikipedia

There are 4 of each tile in a Singaporean Mahjong set.

The Flower and Animals Tiles

Source: wikipedia
Source: wikipedia

There is only one of each per set.

How To Win Mahjong

Over a game of mahjong, tiles are distributed to the players and the game is played.

The game ends when one of the players managed to assemble a winning hand or when the unused tile runs out. In the case when the unused tile runs out, the game is considered a draw.

What Happens Next After A Win?

When someone wins the game, the banker position is passed on to the player on the right of the current banker. Each time, the banker position completes its cycle on all the four players, the “Wind” of the game changes.

A mahjong round is completed when all four “Winds” are completed.

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About Ming Feng
A stint in Bloomberg gifted me with a beer belly, which only grew larger when I moved on to become a Professional Trader. Now I turn caffeine into digestible finance-related content.
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