Riichi Book I
A Mahjong Strategy Primer
for European Players
Daina Chiba
Riichi Book I
A Mahjong Strategy Primer for European Players
Version
Daina Chiba
Copyright © 2016 Daina Chiba.
Permission is granted to copy, distribute, and/or modify this document un-
der the terms of the Creative Commons Attribution NonCommercial 3.0
Unported License, available at http://goo.gl/R9sy.
Cover photo © 2015 Katarína Mózová, Courtesy of Riichi Mahjong Slovakia.
The original form of this book is L
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X source code. Compiling this L
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source has the effect of generating a device-independent representation
of a manuscript. The L
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X source for this book is available from http:
//riichi.dynaman.net/.
About the Author
Daina (pronounced like “diner”) Chiba is a political scientist and an ap-
plied statistician working as a lecturer at University of Essex in England.
He has been playing riichi mahjong for almost 20 years. He can be reached
at daina.chiba@gmail.com.
Preface
When I moved to England in 2013, I was pleasantly surprised to
learn that riichi mahjong (modern Japanese mahjong) is quite popu-
lar in Europe. In the past two years, I have had the pleasure of play-
ing riichi in London, Guildford, Kent, Oxford, Aachen, Copenhagen,
Prague, and Vienna, along with players from Austria, China, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Italy, Japan,
the Netherlands, Poland, Russia, Slovakia, Sweden, the UK, and the
United States.
European players have been remarkably successful in organiz-
ing tournaments open to anyone who plays the game. These tourna-
ments held at least once a month somewhere in Europe are run
by local mahjong players in each country under the auspices of the
European Mahjong Association (EMA).
1
Founded in 2005, EMA has
been doing a fantastic job in maintaining common rule sets,
2
keep-
ing a player ranking system, and doing many other useful things to
promote the playing of mahjong across Europe.
Although I have come across a few good players in Europe, I came
to realize that a lot of players here are not very well-versed in the
basic principles of competitive mahjong strategies. Of course, play-
ing competitively is not the only way to enjoy the game. I am also
1
http://mahjong-europe.org/
2
EMA’s official rule book for riichi mahjong is available online at http:
//mahjong-europe.org/portal/images/docs/Riichi-rules-2016-EN.pdf
(last revised in 2016). At the time of writing this book, EMA is in the process
of revising the rule book. Explanations of EMA rules in this book are based
on the revised rules. New rules will come into effect from April, 2016.
iv PREFACE
not claiming that I know the magic formula to win because there is
no such thing. Nevertheless, there is a set of basic principles worth
learning for any aspiring players. I believe the level of sophistication
among European players could be much improved if these princi-
ples are more widely shared. Unfortunately, however, learning re-
sources currently available for non-Japanese audience are somewhat
limited.
3
I have thus decided to write a book on riichi mahjong strategies
for European players, primarily with beginners and inter mediate play-
ers in mind. I then ended up splitting the book into two volumes;
Book I is intended for beginners and intermediate players (Tenhou
rank of or below), while Book II is meant for more advanced
players. The two books are not intended for complete novices who
do not know how to play riichi mahjong.
4
The target reader is any-
one who has played riichi mahjong before and wants to improve their
skills further.
I have three main goals in preparing these books. First, I will in-
troduce a set of English terminology of riichi mahjong. “In beginning
was Word, scripture tells us. Knowing the names of particular tile
combinations, situations, and strategies will allow us to be conscious
about them and to be able to talk about them with our fellow players
after the game.
My second goal is to introduce the principles of tile efficiency.
Book I and Book II both cover tile efficiency, but at different levels.
3
There are already a few English books for beginners. There are also several
excellent blog posts on technical details about mahjong strategies. However,
there appears to be a huge gap between these two sets of resources. Introduc-
tory books do not cover strategies extensively, whereas blog posts tend to be
too advanced even for intermediate players.
4
If you want to learn how to play riichi, I’d recommend Barr (2009).
v
Book I offers an introduction to tile efficiency, covering very basic
mechanisms only. I plan to cover more advanced materials in Book
II. My third goal is to introduce a set of simple strategies regarding
critical judgements such as whether or not to call riichi, whether to
push or to fold, and whether or not to meld.
A lot of the materials covered in the books were introduced to
me through the writings of a notable Japanese mahjong player and
manga author, Masayuki Katayama. Mr. Katayama is an accom-
plished riichi player and arguably the best mahjong manga author in
the world. Some of the strategies introduced here are unabashedly
stolen from Mr. Katayamas masterpiece manga storybook Utahime
Obakamiiko ( ). I strongly encourage you to read
it yourself if you read Japanese, although I realize that you would not
be reading my book if you understood Japanese.
Another Japanese author whose work has been influential in the
writing of Book I is Makoto Fukuchi. Mr. Fukuchi is also a distin-
guished riichi player and the best-selling author of mahjong strategy
books. A part of the exposition of t he five-block method in Chapter
4 is based on Mr. Fukuchi’s skillful explanation in his books.
I am also indebted to a lot of friends I have acquainted with through
mahjong in Europe. Philipp Martin has read an early draft of the
book and provided me wit h valuable comments and encouragement.
I am also grateful to Gemma Sakamoto, who has been hosting a monthly
mahjong get-together in London. Finally, my thanks go to Ian Fraser,
one of the founders of the UK Mahjong Association. Without the ef-
forts of Ian and his team, I would not have been able to get to know
so many fellow players in the UK and in Europe.
The cover photo (© Katarína Mózová) is from the 2015 Bratislava
vi PREFACE
Riichi Open Tournament. I thank Katarína and Riichi Mahjong Slo-
vakia (especially Matej Labaš) for giving me their permission to use
it.
After I made the book publicly available in January 2016, a lot
of people have given me feedback on various aspects of the book.
Based on their feedback, I corrected some terminology inconsisten-
cies and typos. In particular, I thank David Clarke, Aaron Ebejer,
Nicolas Giaconia, Grant Mahoney, Ting, and Chris Rowe for their
valuable inputs.
Daina Chiba
London, UK
10 January, 2016
(updated on 10 April, 2017)
vii
Plan of the book
To improve your mahjong skills, you need not only to learn the
theories but also to practice what you learn by playing lots of games,
preferably with players who are stronger than yourself. Before the
advent of online mahjong platforms, however, doing so was not very
easy if you live outside of Japan.
Thanks to the recent development of online mahjong platforms, it
is now feasible for you to play hundreds or thousands of games with
serious opponents while living outside of Japan. On these websites,
you can easily find fellow players to play with 24/7. Most platforms
keep the record of all t he games players have played, and a replay
function would allow you to reflect on your past plays. You can also
take a look at player statistics data, which gives you important clues
as to what skills you need to work on.
I thus recommend you practice mahjong skills by playing online
while you study the strategy principles with this book. You do not
need to wait until you finish reading everything covered in the book
before you start playing. Go ahead and play games first, then come
back to the book and study the relevant parts of the book.
This book is divided into four parts. Part I provides an introduc-
tion to an online mahjong platform called Tenhou ( ). The website
is in Japanese, but I will walk you through the account registration
process and show you how to play games in Chapter 1. There al-
ready exist several excellent online resources that explain how to play
Tenhou, including:
Arcturus’s Tenhou Documentation
http://arcturus.su/tenhou/
viii PREFACE
Complete Beginner’s Guide to Online Mahjong (Osamuko)
http://goo.gl/F5sJvO
Playing Online: Tenhou (Reach Mahjong of New York)
http://goo.gl/Oc1eNe
If you have already read either of the three before, you can skip Chap-
ter 1 of this book, for there is not much new information there for
you. Chapter 2 explains some advanced features of Tenhou, which
you can also skip when you read this book for the first time.
Parts II and III are the “meat” of the book. Part II covers basic
tile efficiency t heories that allow you to maximize the speed and/or
hand value of your hand. After introducing basic terminology in
Chapter 3, I discuss the five-block method in Chapter 4 and provide
some tips on how to pursue several yaku in Chapter 5. Part III cov-
ers strategy principles, including score calculation methods (Chap-
ter 6), riichi judgement (Chapter 7), defense judgement (Chapter 8),
melding judgement (Chapter 9), and so called “grand strategies” to
win a game (Chapter 10). Finally, Appendices include a chapter on
etiquettes for offline playing (Chapter A) and another chapter on fur-
ther readings (Chapter B).
Numbers and letters shown in this color as well as each entry in
the Contents section below are hyperlinked; clicking on one will take
you to the pertinent page.
Contents
Preface iii
I Playing Riichi Online 1
1 Introduction to Tenhou ( ) 3
1.1 Why play online? . . . . . . . . . . . . . . . . . . . . . 3
1.2 Setting up an account . . . . . . . . . . . . . . . . . . . 4
1.3 The main page . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Playing a game . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . 26
1.6 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Advanced features of Tenhou 30
2.1 Rank and rating . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Four rooms . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3 Reading t he statistics . . . . . . . . . . . . . . . . . . . 37
2.4 Viewing games . . . . . . . . . . . . . . . . . . . . . . 43
II Basic Tile Efficiency 46
3 Riichi mahjong basics 48
3.1 Learning strategies . . . . . . . . . . . . . . . . . . . . 48
3.2 Basic building blocks . . . . . . . . . . . . . . . . . . . 50
3.3 Complex shapes . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Waits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
ix
x CONTENTS
3.5 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 The five-block method 84
4.1 Finding a redundant tile . . . . . . . . . . . . . . . . . 85
4.2 Alternative configurations . . . . . . . . . . . . . . . . 88
4.3 Selecting tile blocks . . . . . . . . . . . . . . . . . . . . 97
4.4 Building a block . . . . . . . . . . . . . . . . . . . . . . 104
5 Pursuing yaku 110
5.1 How to get sanshoku . . . . . . . . . . . . . . . . . . . 111
5.2 How to get ittsu . . . . . . . . . . . . . . . . . . . . . 120
5.3 How to get pinfu . . . . . . . . . . . . . . . . . . . . . 125
5.4 How to get honitsu . . . . . . . . . . . . . . . . . . . . 128
5.5 How to get toitoi / chiitoitsu . . . . . . . . . . . . 134
III Strategy Principles 138
6 Scoring 140
6.1 Three steps in score calculation . . . . . . . . . . . . . 140
6.2 Basic scoring . . . . . . . . . . . . . . . . . . . . . . . . 142
6.3 Advanced scoring . . . . . . . . . . . . . . . . . . . . . 153
6.4 Scoring tables . . . . . . . . . . . . . . . . . . . . . . . 161
7 Riichi judgement 163
7.1 To riichi or not to riichi? . . . . . . . . . . . . . . . . . 163
7.2 Insta-riichi . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.3 When not to riichi . . . . . . . . . . . . . . . . . . . . . 176
7.4 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Defense judgement 189
8.1 To push or to fold? . . . . . . . . . . . . . . . . . . . . 189
CONTENTS xi
8.2 Defense basics . . . . . . . . . . . . . . . . . . . . . . . 193
8.3 Defense against riichi . . . . . . . . . . . . . . . . . . . 204
8.4 Defense against open hands . . . . . . . . . . . . . . . 208
8.5 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . 215
9 Melding judgement 216
9.1 To meld or not to meld? . . . . . . . . . . . . . . . . . 216
9.2 Melding choice: examples . . . . . . . . . . . . . . . . 219
9.3 Calling kan . . . . . . . . . . . . . . . . . . . . . . . . . 225
9.4 Miscellaneous tips for melding . . . . . . . . . . . . . 231
10 Grand strategies 235
10.1 What do do in South-4 . . . . . . . . . . . . . . . . . . 235
10.2 What to do by South-3 . . . . . . . . . . . . . . . . . . 244
10.3 Tables for induced point differences . . . . . . . . . . 247
Appendices
A Manners for offline playing 250
A.1 Dealing tiles . . . . . . . . . . . . . . . . . . . . . . . . 250
A.2 Drawing and discarding . . . . . . . . . . . . . . . . . 252
A.3 Calling . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
A.4 Winning a hand . . . . . . . . . . . . . . . . . . . . . . 255
B Further readings 260
B.1 Books on riichi mahjong . . . . . . . . . . . . . . . . . 260
B.2 Online resources . . . . . . . . . . . . . . . . . . . . . 262
Part I
Playing Riichi Online
1
Chapter 1
Introduction to Tenhou ( )
1.1 Why play online?
Playing mahjong online is an excellent way to practice your mahjong
skills. You don’t need any mahjong equipment to play; you dont
need to coordinate with your mahjong friends to find the time and
place t hat work for the all four of you. You can simply open your
computer and access one of many online mahjong platforms. As long
as you have an internet connection, you can play mahjong any time,
anywhere, and for any length of time.
Another advantage of online playing is that you can easily keep
the record of your playing history and obtain detailed statistics from
all the games you play. Analyzing these statistics will help you iden-
tify what skill sets you need to work on. You can also show your
game record to your friends and ask for their opinions about partic-
ular choices you’ve made in a game.
(Tenhou) is arguably the
most popular online mahjong plat-
form in the world. As of December,
2015, there are over three hundred
thousands active players on Tenhou.
1
A lot of professional mahjong play-
ers from Japan now play Tenhou.
There are also some Tenhou players who have later become profes-
sional after practicing their skills on Tenhou. It has become a common
1
To be exact, it has 304,534 active players and 3,566,353 registered players as of
20 December, 2015.
4 CHAPTER 1. INTRODUCTION TO TENHOU ( )
understanding among players in Japan that your rank and rating on
Tenhou are one of the most reliable indicators of your mahjong skill
levels. To get you started, this chapter explains how to set up an ac-
count on Tenhou and provides some basic operation manual.
1.2 Setting up an account
One of the challenges for European players in setting up an ac-
count on Tenhou would be that almost everything is written in Japanese.
However, you will only need a minimal level of Japanese to get by,
and this chapter will walk you through the process.
First, go to the Tenhou webpage (http://tenhou.net/).
Scroll down and click either the PLAY button (to play in a pop-up
window) or a link just below the button (to play in the current win-
dow) that reads .
Click here to play
in a pop-up
window.
Click this link to
play in the
current window.
1.2. SETTING UP AN ACCOUNT 5
Then, on the next page (either in a pop-up window or in the cur-
rent window), you’ll see something like the following:
Flash version Web version
The bottom line will initially read LOADING... / , but
in a few seconds it will change into »Flash | Web
β . Then, click on the Flash link if you are
accessing from a flash-capable device such as your PC; alternatively,
click on the Web β link if you are accessing from a
smart phone or tablet. If it doesn’t change into »Flash
| Web β within 10 seconds or so, you may want
to click on the link right next to LOADING, which will
prompt the browser to reload the page. Clicking on either of the
Flash/Web links will take you to the log-in entrance of
Tenhou. Explanations below are based on the Flash version.
6 CHAPTER 1. INTRODUCTION TO TENHOU ( )
Registration ID field (likely to be blank at first)
When you first visit this page, the ID field right next to the
ID button is likely to be blank, as shown in the picture above.
This is because you havent registered an account. In order to create
an account, click on the ID (New ID Registration) button
on the left.
A pop-up message will show up, warning you that whatever ID
that is currently shown in the ID field (if any) will be overwritten
with a new ID and that you may want to copy and paste the current
ID (if any) into some text file or similar. Do so if you do see an old
ID in the ID field, just to be safe. If the ID field is blank, just click the
Yes button, which will open yet another pop-up message.
1.2. SETTING UP AN ACCOUNT 7
It is telling you the following:
You can create a player ID for free, and doing so is necessary if
you want to earn a rank (kyu / dan) and rating.
Some characters or character combinations are not allowed in
player names.
Once you register, you cannot register another account for a
given period (7 days).
If you don’t play for 180 days, your ID may be deleted.
A player name must have 1-8 characters.
Type in a player name youd like to have (8 characters or fewer)
into the blank field at the bottom and click OK. You cannot change
your player name later, so choose wisely. If the player name you type
in is already taken by another player, it gives you an error message,
as follows:
This player name is taken.
Click OK, and type in another name. If successful, you’ll see a
new message asking you to confirm that you want to register an ac-
count with the player name provided.
8 CHAPTER 1. INTRODUCTION TO TENHOU ( )
Click Yes and you’ll see another message as follows:
The 19-digit alpha-numeric code that starts with “ID” (shown in
white on a black background) is your unique player ID (it is ID12345678-
ABCDEFGH in the picture above). I suggest you save your ID in a
text file or something so that you don’t lose it. They cannot re-issue
your player ID (unless you have a paid membership and hold a rank
of or higher).
Clicking OK will take you back to the log-in entrance page, but
this time you should see your player ID in the ID field.
1.2. SETTING UP AN ACCOUNT 9
Your player ID
Choose (male voice) or (female voice)
Can choose
or
.
You can make several choices before entering the main page. First,
you can choose male or female voice (for pon / chii / riichi, etc.) by
clicking on the button right next to the ID field. You can choose a
different gender each time you log in to the main lobby. Second, you
can choose (premium) or (economy) version.
The premium version has better graphics, so I suggest you choose
the premium version.
If you are happy with your choices, you can enter the main page
by clicking on the OK button on the right.
10 CHAPTER 1. INTRODUCTION TO TENHOU ( )
1.3 The main page
Here is what the Tenhou main page looks like when you first log
on in. The right half of the main page shows your statistics (currently
all the fields are blank because you haven’t played any games), and
the left half shows the games you can play and some other features.
Menu Cancel (to cancel a reservation)
Main tabs
Sub tabs
In the second line of the left hand side, you see three numbers. In
the example above, they are 1857, 915, and 118 (the numbers will be
different on your screen). These numbers show that 1857 players are
currently online, 915 players are waiting, and 118 players are about
to finish their games.
Below these three numbers, there are six main tabs, which read
, β, β, , , and . The tab is the main
lobby where we play games ( reads dan-i-sen in Japanese; it
means ranking matches). Under the tab, there are four sub-
tabs, which read , , , and , corresponding to four
1.3. THE MAIN PAGE 11
different rooms. At first you can only play at tables in the room.
Let’s first go to the tab, and choose the sub-tab.
Making reservations
In each of the four rooms (i.e., , , , and ), there are
12 different variants of riichi mahjong games you can choose from.
Games in the left column (under tonpusen) are East-only
games,
2
and games in the right column (under tonnansen)
are more standard East-South games that have both East and South
rounds.
3
Closed tanyao
Open tanyao
With red fives
Fast
Three-player
Fast (3p)
East-only East–South
1 player waiting
44 players playing
Games in the first row ( kuitan nashi) are unusual games
where open tanyao (All Simples) is not allowed; you have to have a
concealed hand to claim tanyao.
4
There is no red five in these games,
either. Open tanyao is allowed in all the other games. Games in t he
2
In a special circumstance where no player gets 30000 or more points by the end
of East-4, the game continues into the South round.
3
Just like East-only games, when there is no player who has 30000 or more points
by the end of South-4, the game continues into t he West round.
4
kuitan means “open tanyao and kuitan nashi means “without kuitan in
Japanese.
12 CHAPTER 1. INTRODUCTION TO TENHOU ( )
second row are more standard games with open tanyao, but they do
not have red fives. Games in the third row have three red fives. This
is arguably the most standard type of riichi mahjong game played in
Japan as of now. Games in the fourth row have the same r ule as those
in the third, but the time limit on each action is more strict. Games in
the fifth and sixth rows are three-player games, where open tanyao
and red fives are both allowed.
The set of numbers delimited by a colon in each cell represent
the numbers of players currently waiting and playing the game, re-
spectively. For example, the first row in the left column shows 3:24,
which means that 3 players are waiting in queue after signing up for
a game, and 24 players are currently playing East-only, closed tanyao
games. As it happens, East-South games with red fives are usually
the most popular on Tenhou, followed by East-only, fast games.
To sign up for a game, click on the (reservation) button in
the corresponding cell. You can make as many reservations as you
want; you will be given a seat at a table that first becomes available. If
you make multiple reservations, other reservations will be automat-
ically canceled when you start playing at another table. To cancel all
the reservations at once, click on the (Cancel) button at
the bottom right of the left-hand side of the main page. The cancel
button becomes active (clickable) only after you make a reservation.
1.4. PLAYING A GAME 13
1.4 Playing a game
Once a slot becomes available for
you, you will be taken to a game ta-
ble along with three other players. A
black pop-up screen (see right) will
appear. The game will start in 10 sec-
onds (if all t he four players click on
the OK button, the game will start
immediately). Each player is ran-
domly assigned to East, West, South, or North. In the example below,
my initial seat wind is North ( ).
The Tenhou interface is quite intuitive so you wont need much
instruction. Once a hand begins, tiles are dealt automatically. You
also automatically draw a tile when your turn comes. In each turn,
click on the tile you want to discard.
Each action is timed. At a standard (non fast) table, you have 5
seconds to discard a tile. In addition, you are given a total allowance
of 10 seconds in each hand. That is, even when you use up the 5
14 CHAPTER 1. INTRODUCTION TO TENHOU ( )
seconds allocated to you in a particular turn, you will be given the
maximum of additional 10 seconds (minus the seconds you have al-
ready used up in previous turns in the hand). For example, when
you use 5 + 4 seconds in the first turn, t he remaining allowance re-
duces to 104 = 6 seconds in this hand. Therefore, the next time you
use up the first 5 seconds, you will be given only 6 more seconds. The
allowance will increase by 1 second (up to 10 seconds) each time you
make your discard choice in less than 1 second. The allowance will
revert to 10 seconds when the next hand begins. At fast tables, each
action must be done in 3 seconds, with a total allowance of 5 seconds.
1.4.1 Calling / melding
When a call becomes available, a box with a call name will show
up to prompt your reaction. The call prompts are written in Japanese.
The good news is that they are relatively simple and easy to guess
from the context. It would be enough to memorize the following
eight mahjong words in Japanese.
1. riichi [r´I:tS]
You can call riichi when you have (1) a closed ready hand, (2) at
least 1000 points left, and (3) at least one turn left to draw. When all
of the t hree conditions are met, a translucent box that reads
in white letters will pop up in your tur n.
If you want to riichi, you must click on the box first, then click
on the tile you want to discard. Once you click on the box, you
cannot call it off. Clicking on the box also makes it impossible
to discard a tile that does not make the hand ready. In the above ex-
1.4. PLAYING A GAME 15
ample, tiles other than ıȷfi” will become unclickable once you
click on the box. If you do not want to call riichi, just click on
the tile you want to discard.
2. ron [r´ON]
A box will pop up whenever you can legitimately declare
ron on an opponent’s discard. In other words, chombo is made im-
possible on Tenhou. For example, when you are furiten, a box
will not pop up because you cannot legally ron with a furiten hand.
Whenever your hand is in a furiten status, it is indicated with a
(furiten) sign in small translucent letters below your hand
that looks like: . If you don’t click on the box in time
(i.e., in 5 or 3 seconds + allowance), it is assumed that you pass.
3. Pass (do nothing)
Whenever a box pops up, another box that reads (pass)
will accompany it.
Click on the box immediately if you don’t want to declare ron
on a discard. You would not want to pause for too long because t hat
can look suspicious. A box will also pop up when other calling
actions become available.
4. tsumo [ts´umo]
A box will pop up when you can legitimately declare tsumo
with your draw.
16 CHAPTER 1. INTRODUCTION TO TENHOU ( )
5. pon [p´ON]
When calling pon becomes available, a box will pop up right
above the tiles in your hand with which to call pon. A box will
also pop up. If you want to call pon, mouseover the tiles in your
hand with which to call pon. Then the candidate tiles will stick out,
as follows:
Click on them to call pon. If you click on the box or don’t do
anything in time, it is assumed that you pass.
6. chii [tS´I:]
Chii calls are done in a similar way. When it becomes available,
a small sign that reads will pop up right above the tiles in your
hand with which to call chii.
When you have multiple sets of tiles with which to chii, as is the
case in the above picture, mouseover the candidate tiles to choose. In
the picture above, the left player discarded a and you can chii it
with either ¸˛or ˛‹. If you want to chii it with ¸˛, mouseover
the ¸ then the ¸ and a ˛ will stick out so you can click on them. If
you want to chii it with ˛‹, mouseover the then a ˛ and the
will stick out so you can click on them.
1.4. PLAYING A GAME 17
7. kan [k´2N]
Calling kan on a discard is similar to calling pon. To build a melded
kan by extending a melded pon, you need to mouseover the melded
pon until a small sign that reads appears below the pon. To call
a concealed kan, mouseover the four tiles you want to kan then the
tiles will stick out, accompanied by a small sign that reads below
them. Click on them to call kan.
8. Kyushu Kyuhai
When you have nine different terminals and honors after the first
draw in an uninterrupted first set of turns, you can declare an abortive
draw. When this becomes available, a box that reads will
pop up. Click on it if you want to declare an abortive draw. If you
wish to continue with the hand, just click on t he tile you want to dis-
card.
Multiple boxes
Sometimes you have multiple choices as to what to do with a
given discard of your opponent. In the following example, you have
a ready hand waiting for -ı, and the left player discarded a ı.
You will be given the following three choices:
Ron Pass
Chii
Call ron
Call chii
Pass (do nothing)
18 CHAPTER 1. INTRODUCTION TO TENHOU ( )
To call ron on the discarded ı, click on the (ron) box that pops
up above your hand. If you want to do nothing, click on the
(pass) box right next to the box. Alternatively, if you want to
call chii, mouseover the two tiles you want to chii with (in t his case
‰) and click on them.
1.4.2 Buttons
The buttons at the bottom right corner allow you to toggle on/off
some calling-related features. Each feature is turned off at the begin-
ning of a new hand.
Auto call win
Auto discard draw
No call Picture ( )
Sound ( )
(Auto call win)
If you turn this on, you will automatically win a hand when possi-
ble without clicking on or boxes. In other words, the option
of passing is unavailable when this is turned on. Keep in mind that
this can be problematic at times when you intend not to win your
hand from a particular opponent or on a particular tile. When t his
is turned on, the word is shown in white; when it is turned
off, it is translucent. In the picture above, it is turned on.
(Auto discard draw)
If you turn this on, you will automatically discard whatever tile
you draw. Turn this on when you have to go to toilet or somewhere
but don’t want to quit the game entirely. When you riichi, this feature
is automatically (and implicitly) turned on. In the picture above, it is
turned off.
1.4. PLAYING A GAME 19
(No call)
If you turn this on, you will not be prompted to call chii, pon, or
kan. This feature is useful for hiding information about your hand’s
tile composition from your opponents. If you pause every time some-
one discards a certain tile you can call, your opponents might be able
to guess what pairs of tiles you have and dont have. Drawing a de-
duction from such time lags constitutes an important skill in Tenhou.
However, in order not to disadvantage players waiting to call chii /
pon too much, time lags will also occur randomly (i.e., even when no
one can call pon / chii on the discarded tile).
(Picture) and (Sound effect)
You can change the appearance of the tiles and/or mat or resize
the window with the Picture button. You can turn on/off t he sound
effect (for riichi, chii, pon, etc.) with the Sound button.
20 CHAPTER 1. INTRODUCTION TO TENHOU ( )
1.4.3 Scoring
When a player wins a hand, the score will be calculated auto-
matically. A scoring board will pop up that shows the hand, dora
(and ura dora if riichi was declared), yaku names and the associated
number of han, minipoints, and the total hand value.
In the example above, the left player dealt into my hand that is worth
60 (fu; minipoints) 13 (han) = 32000 (points). Yaku names will
be shown in Japanese along with han counts. Table 1.2 at the end of
this chapter lists all the yaku names Tenhou recognizes.
1.4. PLAYING A GAME 21
1.4.4 Indicators
The black rectangular board in the middle of the screen provides
information about the proceeding of the game.
Number of
riichi bets
Counter
We can see that this is South-4, there is 0 counter and 0 riichi bet,
and it is the North player’s turn. The West player is leading (44000
points), followed by the East player (26800), the North player (17400),
and the South player (11800). Player’s rank (kyu / dan) is shown
right next to their points.
If you mouseover the middle board, you will see the current point
differences between you and each of your opponents. In the present
example, the West player has 44000 26800 = +17200 more points
than I do. If you are leading against another player, the point differ-
ence will be negative. For example, the Sout h player has 11800 so the
point difference is 11800 26800 = 15000.
22 CHAPTER 1. INTRODUCTION TO TENHOU ( )
It is important to pay a close attention to these point differences,
especially in the South round or when one of your opponents is at
the risk of bankruptcy. In the current example, if the East player wins
a 12000 hand from the South player, South will go bankrupt and the
game is terminated. Notice that East is currently ranked second, hav-
ing 17200 points fewer than West. In this case, winning a 12000 from
South is not ideal for East because East will still be ranked second
and the game is over.
5
You can also see the type of game you are currently playing on
the board. Just below the wall opposite to you is an indicator that
looks like this: .
The first letter indicates t he room: for (ippan), for
(joukyu), for (tokujou), for (houou). See
Chapter ?? for explanations of these.
The second letter indicates if it is an East-only game ( ) or an
East–South ( ) game.
The third letter indicates if open tanyao is allowed: (with
open tanyao) or (without open tanyao)
A fourth letter ( ) is added if there are red fives.
A fifth letter ( ) is added if it is a fast game.
5
As we will see later, avoiding the fourth place is very important in Tenhou rules
than it is in other rules. However, this does not mean that it is your only priority;
you would still want to improve your placement in a game when doing so is a
realistic possibility.
1.4. PLAYING A GAME 23
1.4.5 Ending of a game
A game can end in several different ways.
One or more player goes bankrupt (below 0 points).
South-4 (East-4 in East-only games) ends and at least one player
has 30000 or more points.
West-4 (South-4 in East-only games) ends.
At any point in the West round (South round in East-only games),
at least one player has 30000 or more points.
When a game ends, final scores are calculated as follows.
In cases of a tie, the player sitting closer to the first dealer wins.
Oka (winning premium) is 20000. That is, although every player
is allocated 25000 points at the beginning of a game, they have
to return 30000 at the end of the game, meaning that 30000 will
be subtracted from the final raw scores. The residual points of
20000 = (30000 25000) × 4 are awarded to the winner of the
game.
Uma (placement bonus) is 10-20. That is, 1st player gets +20000,
2nd player gets +10000, 3rd player gets 10000, and 4th player
gets 20000.
Each score is then scaled by dividing it by 1000 and rounding it
off.
It appears that European players are not very familiar with the
oka system (possibly because there is no oka in EMA rules), so let
me explain this with an example. Suppose that players A, B, C, and
24 CHAPTER 1. INTRODUCTION TO TENHOU ( )
Table 1.1: Final score calculation on Tenhou
Player Raw score Before uma After uma After oka
A 39000 9000 29000 49000
B 25100 4900 5100 5100
C 22900 7100 17100 17100
D 13000 17000 37000 37000
D hold the following raw points at the end of a game; 39000, 25100,
22900, and 13000, as shown in Table 1.1 below.
The first numerical column shows the raw scores. Then, 30000 is
subtracted from each of the raw scores (second column). Then, we
add uma to each score based on placements (third column). Finally,
we add oka to the winner’s score to obtain the final scores (fourth
column).
The final scores after adding
uma and oka and scaling will be
displayed along with the place-
ments and raw scores. In the ex-
ample to the right of this text, I (
means “me”) came in 1st, earning
50100 points (60.0 with uma and
oka), 2nd player (C , which
reads Mr. C) earns 46000 points
(+ 26.0 with uma), 3rd player earns
6700 points (33.0 with uma), and
4th player went bankrupt (2800 points, 53.0 with uma).
1.4. PLAYING A GAME 25
bababababababababababababababab
Notes on placement
It is important to keep in mind that your rank and rating on Tenhou
depend solely on the placement in a game and not on how many
points you earn in a game, before or after adding uma and oka.
In other words, there is absolutely no difference between getting
1st place with 30000 points and getting 1st place with, say, 80000
points in terms of their contributions to your rank and rating.
a
This feature adds an interesting strategic element to the game.
That is, it makes it clearer that the goal of mahjong is not to win
a hand per se but to have a better placement at the end of a game.
Winning a hand is just one of several means to securing a good
placement. On occasion, you may find it beneficial to assist one
of your opponents instead of trying to win a hand yourself. Inten-
tionally dealing into an opponent’s hand can sometimes be a good
tactic when it serves the purpose of securing your own placement.
In my impression, many European players are lacking the appreci-
ation of this aspect of mahjong. I hope you will learn to appreciate
it through playing lots of games on Tenhou.
a
You might wonder why they still calculate the final scores with uma
and oka in Tenhou if they are irrelevant; I honestly have no idea.
26 CHAPTER 1. INTRODUCTION TO TENHOU ( )
1.5 Troubleshooting
At times, you may get disconnected from the Tenhou server (pos-
sibly because of poor internet connection on your end or problems
on the server).
6
When a player gets disconnected from the server
during a game, the game still continues. The “auto discard draw”
will be turned on for the disconnected player, so they will be simply
discarding anything they draw until they return. The player name
will turn into dark red once a player is disconnected.
When you get disconnected,
you may get a warning mes-
sage shown above, asking you
if you would like to get con-
nected again. Click Yes if you
want to. However, a warning
message does not always show up when you get disconnected. When
a screen freezes during a game for more than 15 seconds, you should
suspect that you are disconnected. You may want to hit the refresh
button on your browser to get connected to the server again.
You can create more than one accounts on Tenhou, but you will
have to wait for 7 days unless your IP address changes. If you at-
tempt to create a second account from the same IP address within
7 days, you will get an error message shown below, telling you that
you cannot create a new account from your IP address in 7 days.
6
You will notice that players sometimes get disconnected on purpose to quit
playing, especially when they are losing badly.
1.6. RULES 27
1.6 Rules
Here is a summary of the rules on Tenhou.
Three red fives (one in each suit) in games with red fives.
No kuikae (swap-calling). That is, you cannot discard an iden-
tical tile after pon or chii. You cannot discard the tile from other
end of the run, either.
“Sudden death” rule when no player has 30000 or more points
after South-4 (East-4 in East-only games).
A game is terminated when a player goes bankrupt.
Automatic agariyame rule (i.e., the game is automatically ter-
minated if the dealer is leading after the end of Sout h-4, even if
he won a hand in South-4).
One-han minimum all the time (i.e., no two-han minimum even
after five counters).
Abortive draw in the following situations
(nine terminals / honors)
(four riichi’s)
(three players call ron on a discard)
(four players discard the same wind)
(four kan by different players)
(nagashi mangan) is allowed. You can declare it even
when you have called pon / chii. You cannot declare it if one
or more of your discards has been called by others.
28 CHAPTER 1. INTRODUCTION TO TENHOU ( )
Up to two players can win on a discard. riichi bets and counter
bonus go to the player sitting closer to the player who discarded
the winning tile. The dealership remains if the dealer is one of
the winners.
The following are recognized as yakuman: (Tenhou; Bless-
ing of Heaven) / (chihou; Blessing of Earth) / (daisangen;
Big Three Dragons) / (su anko; Four Concealed Pungs)
/ (su anko tanki; Single-Wait Four Concealed Pungs)
/ (tsuiisou; All Honors) / (ryuiisou; All Green)
/ (chinroutou; All Terminals) / (kokushi muso;
Thirteen Orphans) / 13 (Thirteen-wait Thirteen Or-
phans) / (daisushi; Big Four Winds) / (shosushi;
Little Four Winds) / (su kantsu; Four Kongs) /
(churenpoutou; Nine Gates) / (junsei churenpoutou;
Nine-wait Nine Gates).
Yakuman can be combined. For example, (Big Three Drag-
ons) can be combined wit h (All Honors), (Four
Concealed Pungs), and either of (Four Kongs), (Bless-
ing of Heaven) or (Blessing of Earth), producing a quadru-
ple yakuman (128000 points).
There is no double yakuman unless different yakuman are com-
bined. For example, (Thirteen Orphans) and
13 (Thirteen-wait Thirteen Orphans) are both single yakuman .
You cannot call pon / chii / kan on the last discard in a hand.
Sekinin barai: a player who feeds the third Dragon pon / kan
to an opponent with two melded Dragon pon / kan must pay
the full value of the hand in case Big Three Dragons is made on
a self-draw. In case another player deals into it, the two share
1.6. RULES 29
the payment equally. The same rule applies to Big Four Winds,
but not to rinshan kaihou (After a Kong).
Table 1.2: List of yaku names
Yaku Pronunciation EMA name Han (open)
(menzen-) tsumo Fully Concealed Hand 1 (NA)
riichi Riichi 1 (NA)
ippatsu Ippatsu 1 (NA)
chankan Robbing the Kong 1
rinshan kaiho After a Kong 1
haitei (-moyue) Under the Sea 1
houtei (-raoyui) Under the River 1
jikaze Seat Wind 1
bakaze Prevailing Wind 1
yakuhai / fanpai Dragon Pung 1
tanyao All Simples 1
iipeiko Pure Double Chow 1 (NA)
pinfu Pinfu 1 (NA)
chanta Outside Hand 2 (1)
ittsu Pure Straight 2 (1)
sanshoku (-doujun) Mixed Triple Chow 2 (1)
sanshoku doukou Mixed Triple Pungs 2
double riichi
Double Riichi
2 (NA)
san kantsu Three Kongs 2
toitoi All Pungs 2
san anko Three Concealed Pungs 2
shousangen Little Three Dragons 2
honroutou All Terminals and Honors 2
chiitoitsu Seven Pairs 2 (NA)
junchan Ter minals in All Sets 3 (2)
honitsu Half Flush 3 (2)
ryanpeiko Twice Pure Double Chow 3 (NA)
chinitsu Full Flush 6 (5)
nagashi mangan mangan
dora Dora
aka dora Red five
ura dora Ura dora
Chapter 2
Advanced features of Tenhou
2.1 Rank and rating
Tenhou has two different player
Rank N Rank N
9
15 7780
130 5849
592 6481
1830 6383
3140 6971
5968 9964
9957 16606
14436 14509
18174 28283
15046 132411
Table 2.1: Player distribution
rating systems rank (kyu / dan)
and R (rate). The kyu / dan rank-
ing system is similar to the one com-
monly used in Japanese arts, games,
and martial arts. The kyu ( ) ranks
are shown in arabic numbers, go-
ing from 9 to 1 in descend-
ing order. After passing 1 , you
enter the dan ( ) ranks, shown in
kanji numbers, going from
( ; first dan) to (tenth dan)
in ascending order. Everyone starts
with (newbie; no rank), and if you pass the rank, you are
awarded the highest rank called (Tenhoui). Since t he incep-
tion of Tenhou in 2006, there have been only nine players who have
achieved at the time of writing this book. Table 2.1 shows the
distribution of active players holding each rank as of 20 December,
2015.
2.1.1 kyu / dan rank
To advance your kyu / dan rank, you need to earn points (called
“pt” or pt” on Tenhou). For example, to proceed from the
(newbie) status to the 9 (kyu) rank, you need to earn 30 points.
Required amount of points for promotion gets greater and greater as
2.1. RANK AND RATING 31
you move further up. For example, to proceed from (sixth dan)
to (seventh dan), you need to earn as many as 1200 points.
To find out how many more points you need to earn to advance
to the next rank from the current rank, see the top right part of the
main page.
Your current
rank (7 )
pt you have /
pt you need
Your R
In this example, the player currently holds the rank of 7 . The part
that reads “30 / 60 pt” means that he has earned 30 points since he
became 7 and t hat he needs 60 points in total to be promoted to
6 .
When you rise or fall in rank, your points will be reset to a default
value. For kyu rank players, the default value is 0 points. For dan
rank players, the default value is different depending on ranks. For
example, the default points for players are 1200 points. When
they get 1200 more points and reach 2400 points, they get promoted
to . When they lose all the initial 1200 points and reach 0 points,
they get demoted to .
The amount of points you earn or lose in each game depends on
your placement (but not scores with uma and oka), the type of game
(East-only or East–South), the room in which the game is played (
, , , or ), and your current rank.
1
You gain positive
points only if you come in first or second place. If you come in first
place, you will gain the following points regardless of your rank.
1
Points you earn or lose in East-only games are two-thirds of those in East–South
games.
32 CHAPTER 2. ADVANCED FEATURES OF TENHOU
45 points in the (ippan) room
60 points in the (joukyu) room
75 points in the (tokujou) room
90 points in the (houou) room
If you come in second place, you will gain the following points re-
gardless of your rank.
0 points in the room
15 points in the room
30 points in the room
45 points in the room
You don’t gain or lose points if you come in third place. The points
you lose when coming in fourth place depend on your rank but not
on the room. When your rank is 3 or below, you lose 0 point. How-
ever, each time your rank rises above 3 , the points you lose get big-
ger by 15 points. That is, 2 players lose 15 points if they come in
fourth place; 1 players lose 15 × 2 = 30 points; players lose
15 × 3 = 45 points, ... , and players lose as many as 180 points if
they come in fourth place.
Notice how severe the punishment is for coming in fourth, and
it gets severer and severer as your rank goes up. This is one of the
distinctive features of Tenhou. Avoiding t he fourth place tends to be
players top priority in Tenhou games. This is in contrast to standard
mahjong games, where the reward for coming in first usually out-
weighs the cost of coming in fourth, thanks to the oka system.
2
2
Recall that, although Tenhou does adopt the oka system, it is the placement,
not the scores, that determines the points you earn or lose. In this sense, EMA
games are actually more similar to Tenhou games than to standard games. Since
there is no oka in EMA games, the reward for coming in first is much smaller
than that in standard games.
2.1. RANK AND RATING 33
To easily find out how many
points you earn / lose for each place
in a given type of game for your rank,
mouseover the button in each
cell on the left-hand side of the main
page. Then, you will see something
like the picture above on the right-hand side of the main page. Un-
der the second bullet point, we see that, for this player’s rank ( ),
the point reward is: +75 for first place, +30 for second place, 0 points
for third place, and 105 for fourth place.
When you earn enough
points for promotion in a game,
a new rank is awarded after
the game. A certificate mes-
sage like the picture to the
right of this text will pop up af-
ter the game.
Since you never get negative points in games until you reach 2
and there is no demotion until you reach (first dan), it should
be relatively easy to reach . In fact, even without studying the
contents of this book, you can perhaps reach as high as (fourth
dan) if you play a few hundred games or so. However, moving fur-
ther up will probably require that you study basic strategies and tile
efficiency theories.
2.1.2 Rate (R)
In addition to the kyu / dan rank, Tenhou gives each player an-
other rating called R. The initial value of R is 1500, and higher-rank
players tend to have a higher R. For example, t he average R among
34 CHAPTER 2. ADVANCED FEATURES OF TENHOU
the players is 2248.
While kyu / dan rank remains relatively stable, R can change af-
ter each game. R is calculated based on your placement in a game,
but it also depends on the average R of the players you play with. A
change in R after a game, R , is calculated with the following for-
mula:
R = (P +
¯
R) × G
where
P is based on your placement in the game: + 30 for first, +10 for
second, 10 for third, and 30 for fourth;
¯
R is an adjustment that reflects how strong your opponents are,
calculated as (Average R in the game your R) / 40; and
G is an adjustment based on n, the number of games you have
played before. If n 400, G is equal to 1 0.002 × n. If n > 400,
G is set equal to 0.2.
R initially fluctuates a lot, as the scaling factor G is very close to
1 until you play many games. R may go up or down by 30 or so for
each of the first 100 games or so. As you play more games, however,
the fluctuation gets smaller and smaller as G approaches to 0.2.
Notice what the adjustment
¯
R does. This factor is positive when
you play against players who are “stronger” than you (i.e., have a
higher R than you) while it is negative when you play against play-
ers who are “weaker” than you. Therefore, when you win against
stronger players, your reward will be bigger than when winning against
weaker players. Likewise, when you lose against weaker players,
your punishment will be severer than when losing against stronger
2.2. FOUR ROOMS 35
players. Because of these features, one might say that your R better
reflects your skill levels than your kyu / dan rank.
2.2 Four rooms
As we have seen, there are four different rooms where ranking
matches are played. Qualifications to play in each room are based
on your rank and R.
1. (ippan; lower-level room)
This is the only room where you can play initially. Players with
an R higher than 1800 and a rank higher than are not allowed to
play here, however. Games in this room can sometimes be a bit ran-
dom, even chaotic at times. Some of the players in this room probably
do not understand the rules very well. You very rarely come across
strong players here.
2. (joukyu; upper-level room)
You can play here if (1) your rank is 1 or higher or (2) you buy
a two-month membership (¥ 1080 = e 8 = £ 6).
3
Players with an R
higher than 2000 and a rank higher than are not allowed to play
in this room, however.
Games in the joukyu room are more reasonable than those in the
lower-level room, but you still see many players who do not defend
at all, do meaningless dama / unreasonable riichi, and make serious
mistakes in maximizing tile efficiency. In my impression, games at
EMA tournaments most resemble games in the ippan and joukyu
rooms.
3
If you want to pay for the membership, click on the link that appears when you
click the sub-tab. Keep in mind that you need to buy 60 days worth of
membership. Choose “60 (1080 )” in the payment page.
36 CHAPTER 2. ADVANCED FEATURES OF TENHOU
3. (tokujou; advanced room)
Requirements to play in this room are pretty demanding. You
have to have a or higher rank and a 1800 or higher R. The latter
requirement is particularly difficult to satisfy for intermediate play-
ers. As I wrote above, achieving the rank of is not that difficult,
but satisfying the R 1800 condition requires t hat you take mahjong
rather seriously. Since weak players are shut out from the tokujou
room, games in tokujou are qualitatively different from those in the
joukyu and ippan rooms. Games in this room feel similar to those
youd experience at regular (furii ) mahjong parlors in Japan.
4. (houou; phoenix room)
This is the highest-level room in Tenhou. In order to play in this
room, you have to have all of the following: (1) a or higher rank,
(2) a 2000 or higher R, and (3) a paid membership (¥ 540 yen = e 4
= £ 3 per month). Satisfying the first two conditions can be really,
really challenging.
This is arguably one of the highest-level mahjong locales in the
whole world. It is not uncommon for you to come across a houou-
level player at a regular mahjong parlor in Japan. However, you usu-
ally play against at most one houou-level player at a table, and t he two
other players at t he table are either tokujou- or joukyu-level players.
What is remarkable about games in the houou room is that you will
be surrounded by three other houou-level players. It would be safe
to say that no other public mahjong locale in the world whether it
is online or offline could offer a comparable experience.
4
4
Perhaps the highest-level leagues in professional mahjong associations in Japan
have players who are of comparable quality, but you have to become a profes-
sional player to play at such leagues. Even after becoming a professional, you
will need at least a few years to reach the highest league.
2.3. READING THE STATISTICS 37
2.3 Reading the statistics
After you play 30 games or so, you may want to start paying atten-
tion to the statistics shown on t he right-hand side of the main page.
5
The upper half of the player statistics shows your statistics for the
entire period, whereas the bottom half shows your statistics in the
present month for a given type of game in a given room.
2.3.1 Overall statistics
The picture below show my old player statistics (upper half) back
from when I had a rank. Let me explain how to read these statis-
tics.
Entire period (4-player games)
first place
second place
third place
fourth place
bankruptcy
win rate
deal-in rate
call rate
riichi rate
Below a player name is the expiration date of my premium mem-
bership (17 November, 2015). When I started playing Tenhou on 17
September, 2015, I bought a 60-day membership so I can play in the
joukyu room. If you have just created a Tenhou account, the expira-
tion date will be shown as today’s or tomorrow’s date, since we are
given a 1-day premium membership when we open an account.
6
Af-
ter a day or two, it will turn into “—-/–/–” meaning t hat you do not
have a premium membership.
5
There is really no point in reading too much into the statistics when you have
played only a few games; the sample size is too small to be meaningful.
6
You need to have a premium membership to use Tenhou’s Windows client.
38 CHAPTER 2. ADVANCED FEATURES OF TENHOU
The box below the expiration date that reads / 4
indicates that the statistics below are for the entire period (not
just this month) and for 4-player games (not 3-player games). Below
that, we see that I had a rank, 565 points (the initial 400 points
plus 165 points earned after I became ) out of the 800 points I
need for promotion, and an R of 1987.
Three columns below these display my statistics. The first col-
umn shows my placement rates. I had come in first place 50% of the
games, second place 32.5%, third place 7.5%, fourth place 10 %, and
gone bankrupt 7.5% of the games. Ideally, youd want your first place
rate to be greater than your second place rate, your second place rate
greater than your third place rate, etc.
The middle column provides the following information. First,
shows t he number of games you have played. At this point, I had
played 40 games. Second, shows the average score (with
oka and uma) from all the games I have played. As I said before, this
does not influence your R nor rank. Third, shows the aver-
age placement. If you have obtained each of the four places equally,
the average placement would be 2.5
(
1n+2n+3n+4n
4n
= 2.5
)
. Therefore,
any values below 2.5 indicate that you are, on average, winning more
than losing. The two rows that follow (shown in light gray) are rel-
evant only if you play games in private rooms. Since I have only
played ranking matches, they are left blank.
The third column shows my statistics based on hand-level perfor-
mance. First, (houra rate; agari rate; win rate) is the number
of hands you have won divided by the total number of hands you
have played in all games.
7
7
The denominator includes hands where no one won.
2.3. READING THE STATISTICS 39
Second, (houju rate; deal-in rate) is the number of times
you have fed the winning tile to an opponent’s hand divided by the
total number of hands you have played. You would want this rate to
be lower, but keep in mind that (1) sometimes you would be better
off dealing into an opponent’s hand to secure your placement, and
(2) sometimes you need to discard dangerous tiles (which would in-
crease your deal-in rate, on average) in order to increase the chance
of winning your hand (which would increase your win rate, on aver-
age). The rule-of-thumb is that the difference between your win rate
and deal-in rate (win rate - deal-in rate) should be at least 10 percent-
age points. That is, if you have a high deal-in rate, you need your win
rate to be higher. Likewise, if you have a low deal-in rate, it is OK to
have a lower win rate as well.
Third, (fuuro rate; call rate) is the number of hands where
you have called chii / pon / kan divided by the total number of
hands you have played. Finally, (riichi rate) is the number
of riichi calls you made divided by the number of hands you have
played.
The ranking page on Tenhou
8
has a table that summarizes the av-
erage values of these statistics among players with different ranks
(under the heading that reads ). You may
want to compare your statistics with the average values among play-
ers who share your rank or those who have higher ranks than you do.
Figure 2.1 summarizes the average values of hand-level performance
statistics for players in different ranks.
We can see some interesting patterns here. The left-hand side
panel compares average win rates ( ) and deal-in rates (
8
http://goo.gl/suyQ5
40 CHAPTER 2. ADVANCED FEATURES OF TENHOU
Figure 2.1: Average hand-performance statistics
Note: These graphs show the hand-performance statistics reported in a table on the
ranking page (http://goo.gl/suyQ5) as of 20 December, 2015.
) for different ranks. Notice that the average win rate is relatively
constant across different ranks; once you pass the rank, it stays
around 20-22 %.
On the other hand, the average deal-in rate is steadily decreasing
after players move from the kyu ranks into the dan ranks. It is around
15% for almost all kyu rank players (except for and 1 ), but it
keeps going lower and lower as players rise in the dan rank. The
fact that high-dan players have lower deal-in rates on average is re-
markable, considering that they are facing stronger opponents than
low-dan players do. This pattern signifies the importance of defen-
sive skills.
Another interesting thing to notice on the left-hand side panel
is that the average scores deteriorate once you move from 2 to
1 (i.e., average win rate gets lower, and average deal-in rate gets
higher).
I can think of two reasons for why this happens. First, 1 is
where most players start playing in the joukyu (upper-level) room,
2.3. READING THE STATISTICS 41
where average player skills are much higher t han those in the ippan
(lower-level) room. If a player who belongs to the lower-level room
plays in the upper-level room, their performance will necessarily go
down, making it look that 1 players are worse than 2 players
even if they are not. Second, if you keep losing as a (first dan)
player, you get demoted to 1 but you will never be demoted to 2
. This means that 1 players might actually be worse than 2
players, on average.
The right-hand side panel shows the average call rates ( )
and riichi rates ( ) for different ranks. The former is increasing
as rank goes up, while the latter is decreasing, but the changes are
rather gradual for both rates.
42 CHAPTER 2. ADVANCED FEATURES OF TENHOU
2.3.2 Monthly statistics
The bottom-right part of the main page shows monthly statistics
from games you have played in a given room. The box is a pull-
down menu that lets you choose the room ( , , , )
and game type (East-only, East–South, with or without open tanyao ,
red fives, etc.). In the example below, the box reads /
, which means the following: means monthly, is short
for (joukyu)
9
, means with open tanyao and red fives.
Cumulative Average
Scores
Placement
first place
fourth place
Below the box, you see the raw placement scores. In this example,
17+11+3+4 = 35 means that I have played 35 games this month,
and I came in first place in 17 games, second place in 11 games, third
place in 3 games, and fourth place in 4 games. R shown here (1987)
should be the same as the R you see in the top part. 3382 means
that R=1987 puts me in 3382th place among all the active players on
Tenhou.
Two columns follow, where the left column shows the monthly
cumulative values and the right column shows the monthly average
values. In the first row that reads shows the monthly cumula-
tive or average scores from games (after adding oka
9
Likewise, is short for (ippan), is for (tokujou), is for
(houou).
2.4. VIEWING GAMES 43
and uma). In this example, my cumulative score is 727 from the 35
games I played, which puts me in 106th place among players who
have played 30 or more games this mont h. Similarly,
my average score is 20.7 (= 727/35), which puts me in 5th place.
Your placement for average scores will not be shown unless you have
played 30 or more games of a given type in a given room in a given
month.
In the second row that reads shows cumulative or average
placement from games. The cumulative placement is based on place-
ment values (+30, +10, 10, or 30), whereas the average placement
is based on raw placement (1, 2, 3, or 4). The (total) score is the
sum of four placements: cumulative , cumulative , average
, and average . In this example, I earn 106th, 80th, 5th, and
3th places for these scores, so my total score is 106+80+5+3 = 194 (the
lower, the better), which puts me in 12th place among all the players
who have played 30 or more games this month. At t he
bottom, you see (first place rate), (fourth place rate),
and (first or second place rate) for games this
month.
2.4 Viewing games
2.4.1 Game replay ( )
Tenhou keeps t he record of all the games played there, giving each
game a unique URL. You can easily take a look at any of the last 40
games you have played on the (haifu; game record) tab on the
main page. Click on any of the link shown in the tab to start
a replay of the game. You can choose to view the game from any of
the four players’ viewpoint, not to show t he hands of the other three
players, or to go back and forth between turns / hands, etc. When
44 CHAPTER 2. ADVANCED FEATURES OF TENHOU
we play mahjong, we often wonder what the opponents are doing
(e.g., what are their waits? are they doing honitsu?, etc.). You can
find out t he answers to these questions after the game by taking a
look at the game record.
If you would like to have someone take a look at a particular game
you played to ask for their opinions, you need to find the unique URL
assigned to the game you want to show. You can find out the URLs of
the last 40 games by going to the menu from the
pull-down on the main page. Clicking on will open a new
pop-up screen.
You can choose to open a game replay in t he current window (
), in a new pop-up window (
), or in a new window ( ) from the pull-
down menu above. Once you are happy with your choice, click on
one of the (replay) link next to the game you want replayed. You
will be taken to a page that looks like the one you saw after clicking
on the Play button on the top page of Tenhou. You can now find out
the URL assigned to the game in the URL field of your browser.
To start a replay, click on a link that reads » Flash
shown at the bottom of the page. Clicking on the HTML+JS
link will also work, but this one is the low-quality
picture version with limited options.
2.4. VIEWING GAMES 45
2.4.2 Spectating games ( )
You can watch games played in the (tokujou; advanced) and
the (houou; phoenix) rooms quasi-real time (with a five-minute
delay). Click on the (kansen; spectating) tab from the main page
and you will see the list of games you can watch. Click on one of
the player name links to start spectating the game from the chosen
player’s viewpoint.
Part II
Basic Tile Efficiency
46
Chapter 3
Riichi mahjong basics
3.1 Learning strategies
Mahjong is a game of skill and luck. There is a set of strategy
principles you can learn to improve your skills, but acquiring skills is
neither necessary nor sufficient to win a game. On the contrary, with
luck, an unskilled player can easily defeat strong players in mahjong.
At least in the short run, game outcomes are governed more by luck
than by skills.
1
However, learning strategy principles is crucial to
improve your performance in the long run. Moreover, you will be
able to enjoy the game in greater depth once you understand these
principles.
Because of the probabilistic nature of the game, making the best
choice does not always lead to the best outcome. The best choices
are those t hat lead to the best outcome, on average. An evaluation of
our choices thus requires a probabilistic (i.e., statistical) assessment of
different options. For example, consider the following hand.
‰‰““”´ˆ˜˚ˇ˘ $$L
What would you discard?
This hand becomes ready to win if you discard or . Let’s com-
pare the two choices.
1
An interesting question would be: how short is t he “short” run here. That is,
how many games do we need in order to discern a strong player from weak
players? Studies show that we would need at least 100 games or so to have a
reliable estimate of our skill levels. Given that EMA tournaments usually have
only 8 games, winning at these tournaments requires quite a bit of luck.
3.1. LEARNING STRATEGIES 49
Discard you wait for (2 kinds–8 tiles)
Discard you wait for (2 kinds–4 tiles)
Which discard choice is better? Although both of the two choices
yield a 2-way wait, waiting for is much better than waiting
for , probabilistically speaking. With the wait, there are
four tiles of and another four tiles of to win on, leaving at most
eight winning tiles.
2
With the wait, on the other hand, you
have already used up two tiles of and two tiles of yourself,
leaving at most four winning tiles. It is clearly better to choose t he
wait over the wait, because that will give you a higher
probability of winning this hand.
It is possible that, after you decided on the wait, your op-
ponents end up not discarding or at all, while discarding lots
of . This is the kind of things that will happen often in mahjong
(or in any game of luck, for that matter). When things like this hap-
pen, do not t hink that you made a bad call; you didn’t. You made
the right choice, but you were just unlucky. When we experience
this kind of bad luck, we just need to keep calm and carry on.
Before discussing a practical method of maximizing tile efficiency
in the next chapter, I will discuss some basic principles of tile effi-
ciency in this chapter. In doing so, I introduce several key terms we
use in later chapters. I will also provide the original Japanese term
for each (shown in this font). I do so because you may find these
Japanese terms used in some online strategy discussions in English.
2
Of course, the number of winning tiles could be smaller than eight if some of
them have already been discarded.
50 CHAPTER 3. RIICHI MAHJONG BASICS
3.2 Basic building blocks
3.2.1 Tiles
Mahjong tiles can be classified into two categories number tiles
and honor tiles.
Number tiles
Number tiles
Cracks (characters) Manzu –—‰ıȷfffifl
Dots (circles) Pinzu ¸˛‚‹›“”„«
Bamboos Souzu ´ˆ˜¨˝˚ˇ˘¯
We further classify number tiles into simples (tanyao hai; tiles be-
tween 2 and 8) and terminals (1 and 9). They are differentiated be-
cause they serve different yaku and generate different minipoints
(fu).
It has become quite common to include some red five tiles. For
example, most games on Tenhou have one red five tile in each suit,
» ˙ `. These tiles are included in place of regular fives; we have
three regular fives and one red five in each suit. Red fives are treated
as dora regardless of the dora indicator. When a 4 in a given suit is
the dora indicator, the red five in that suit will be a double dora tile.
3.2. BASIC BUILDING BLOCKS 51
Honor tiles
Honor tiles
Dragon tiles # $ %
White (haku) Green (hatsu) Red (chun)
Wind tiles ! "
East (ton) South (nan) West (sha) North (pei)
Some honor tiles are value tiles (fanpai / yakuhai); we get one han
if we collect three identical value tiles. All dragon tiles are value tiles
regardless of the round and seating. On the other hand, the value
status of wind tiles depends on the round and the seating. East tiles
are value tiles for everyone during the East round, and South tiles are
value tiles for everyone during the South round. In addition, each
player gets their own seating wind as a value tile. For example, West
tiles are value tiles only for the West player, but they are valueless
wind tiles (otakaze) for other players.
52 CHAPTER 3. RIICHI MAHJONG BASICS
3.2.2 Group (mentsu)
One of the major goals in playing mahjong is to win a hand.
3
To
win a standard hand, we need to complete four groups ( mentsu) and
one head (atama; final pair).
4
Groups can be classified into two kinds
run and set.
5
Run (shuntsu; chow / sequence) is a set of three consecutive
number tiles: e.g., fffifl, ˜¨˝.
Set (kotsu; pung / triplet) is a set of three identical tiles: e.g.,
———, $$$.
6
3.2.3 Ready and n-away
We say a hand is ready (tenpai) when the hand can be complete
with one more tile. For example, the following hand is ready.
Ready hand
‚‹›„„ˆ˜˚ˇ˘%%%
This hand becomes complete wit h either ´ or ¨. We say that this
hand waits for ´ ¨.
3
Another important goal is not to deal into an opponent’s hand. See Chapter 8
for discussions of defense strategies. However, the most important goal of all
is to win a game. Winning a hand and playing defense are merely two means
to this end. See Chapter 10 for more discussions of t his.
4
There are three exceptions to this; chiitoitsu (Seven Pairs), kokushi musou
(Thirteen Orphans), and nagashi mangan (All Terminals and Honors Discard)
do not require four groups and one head.
5
EMA rules refer to run as “chow” and set as “pung. I realize that my use of
different terminology here might be confusing at first, but I hope you will get
used to it soon.
6
Technically speaking, there is a third type of groups, namely quad (kantsu;
kong), a set of four identical tiles. We treat quads as a variant of sets. See
Section 9.3 for discussions on this.
3.2. BASIC BUILDING BLOCKS 53
We say a hand is 1-away from ready (1-shanten) when the hand
can become ready with one more tile. For example, the following
hand is 1-away from ready.
1-away hand
‚››„„ˆ˜˚ˇ˘%%%
This hand becomes ready if you draw any of ‹›„´¨. We say
this hand accepts ‹›„´¨ (5 kinds–16 tiles) as any of them can
make this hand advance from 1-away to ready. Tile acceptance (ukeire)
refers to the kinds and the number of tiles a hand can accept. Other
things being equal, having a 1-away hand with greater tile accep-
tance is better than having one with smaller tile acceptance.
More generally, we say a hand is n-away from ready (n-shanten)
when the hand can be ready with n more steps. For example, the
following hand is 2-away from ready.
2-away hand
‚››„„ˆ˜˚ˇˇ%%%
This hand accepts all the tiles that the 1-away hand above accepts
(‹›„´¨), plus seven additional kinds of tiles ‚ˆ˜˝˚ˇ˘.
7
The hand will become 1-away if any of these tiles gets drawn.
A hand can also be 3-away, 4-away, 5-away, or 6-away from ready.
8
In practice, however, there is not much point in distinguishing 3-
away hands from 4-away (or worse) hands. You thus need to be able
7
‚ˆ˜˚ will make this hand 1-away for chiitoitsu (Seven Pairs).
8
6-away happens when a hand has no pair, in which case it takes 6 more tiles to
make it ready for chiitoitsu.
54 CHAPTER 3. RIICHI MAHJONG BASICS
to distinguish between four kinds of hands ready hands, 1-away
hands, 2-away hands, and 3-away or worse hands.
Tile acceptance shrinkage
As n gets smaller and the hand gets closer to completion, the
kinds and the number of tiles it can accept will necessarily get smaller.
Consider the three stages of a hand we have seen above.
When 2-away, it accepts: ‚‹›„´ˆ˜¨˝˚ˇ˘.
When 1-away, it accepts: ‹›„´¨.
When ready, it waits for: ´¨.
Tile acceptance is minimized when the hand is ready. Note also that
it is virtually minimized when it is 1-away. This is because with a
ready hand you can utilize not only the tiles you draw but also the
tiles discarded by others to complete the hand. With n-away hands,
however, you have to rely (almost) solely on the tiles you draw your-
self to advance your hand.
9
Therefore, in choosing a discard from a
2-away hand, we should try not to make for a 1-away hand with too
small tile acceptance.
Advancing your hand
To win a hand, we need to advance our hand by reducing the n of
an n-away hand until it is ready. When a hand is 2-away, we should
aim to make the hand 1-away. When a hand is 1-away, we should aim
to make the hand ready. For example, consider the following hand.
9
Melding (calling pon / chii) is not always possible. For example, the 2-away
hand above can accept ˜ if you draw one, but you can neither pon nor chii ˜.
3.2. BASIC BUILDING BLOCKS 55
2-away vs. 1-away
ıȷffff‚‹¨˝˝ˇ¯$$$
What would you discard?
Discarding ¯ makes the hand 2-away, whereas discarding either
or ¨ makes the hand 1-away. You should thus discard or ¨ to
make the hand 1-away. Reverting a 1-away hand to 2-away makes
sense only in some exceptional cases where tile acceptance at 1-away
becomes unbearably small (i.e., fewer than 2 kinds). With this hand,
the hand will be able to accept ˛›˘ (3 kinds–12 tiles) when it be-
comes 1-away.
3.2.4 Protoruns (taatsu)
Of the two kinds of groups, it is easier to complete a run than
to complete a set. There are only four identical tiles, and complet-
ing a set requires that you collect three out of the four identical tiles.
Therefore, we usually prioritize runs over sets in advancing a hand.
A pair of tiles that can become a run with one more tile is called a
protorun (taatsu). There are three types of protoruns, summarized
in Table 3.1.
Table 3.1: Types of protoruns
Name Japanese Example Wait Acceptance
side wait ryanmen ‰ -ı 2 kinds–8 tiles
closed wait kanchan ˛‹ 1 kind–4 tiles
edge wait penchan ˘¯ ˇ 1 kind–4 tiles
As we can see in the table, a side-wait (ryanmen) protorun can
56 CHAPTER 3. RIICHI MAHJONG BASICS
accept twice as many tiles as a closed-wait (kanchan) protorun or
an edge-wait (penchan) protorun can. Therefore, building side-wait
protoruns is the key to advancing a hand. Winning tiles of side-wait
protoruns are often denoted with a hyphen in the middle, such as
´-¨ or -.
Closed wait vs. edge wait
There is no difference in the kinds and the number of tiles ac-
cepted by closed-wait and edge-wait protoruns; they both accept 1
kind–4 tiles. However, closed-wait protoruns are superior to edge-
wait ones because they can more easily evolve into a side-wait pro-
torun.
A closed-wait protorun can evolve into a side-wait protorun in
just one step. For example, a protorun ¸‚ can become a side-wait
one if you draw and discard ¸.
¸‚ ‚‹
draw
On the other hand, it requires two steps for an edge-wait protorun to
evolve into a side-wait protorun. For example, a protorun „« can
become a side-wait one if you draw first and then .
„« “„ ›“
draw draw
Value ranking of protoruns
side wait > closed wait > edge wait
3.2. BASIC BUILDING BLOCKS 57
Tile versatility
Some tiles are more versatile than others. For example, number
tiles are more versatile t han honor tiles because honor tiles can never
form a run. Moreover, we can rank order the versatility of number
tiles based on the types of protoruns they can form.
Number tiles between 3 and 7 are the most versatile. This is be-
cause each of them can form a protorun with four kinds of number
tiles. For example, can form a protorun with ¸, ˛, , and .
Two out of the four resulting protoruns will be side wait.
2 and 8 are less versatile. They can form a protorun with only
three kinds of number tiles. For example, ˛ can form a protorun
with ¸, , and . Only one out of the three resulting protoruns is
side wait.
Terminals (1 and 9) are the least versatile. They can form a pro-
torun with only two kinds of tiles. For example, ¸ can form a pro-
torun only with ˛ and . Neither of the two resulting protoruns is
side wait.
Versatility ranking of tiles
3–7 tiles > 2, 8 tiles > 1, 9 tiles > honor tiles
Applying the same logic, we can also rank order the versatility of
closed-wait protoruns. For example, a closed-wait protorun ¸‚
can become a side-wait one only if we draw . Likewise, a closed-
wait protorun ˛‹ can become a side-wait one only if we draw .
However, a closed-wait protorun ‚› can become a side-wait one if
we draw ˛ or . Clearly, ‚› is more versatile than ¸‚ or ˛‹.
58 CHAPTER 3. RIICHI MAHJONG BASICS
Versatility ranking of closed-wait protoruns
35, 46, 57 > 13, 24, 68, 79
3.2.5 Pairs (toitsu)
A set of two identical tiles is called a pair (toitsu). Pairs can per-
form several different roles. A pair can be the head (final pair) of a
hand, a protoset (a candidate for a set), or a component of chiitoitsu
(Seven Pairs).
Building the head
Any hand including Thirteen Orphans and Seven Pairs re-
quires the head to be complete. Since building the head is much eas-
ier than building a group, we usually don’t worry too much about
the head. For example, consider the following hand.
Hand with no head
fffifl˛‚‹›“”˜¨˝ˇ
This hand currently lacks the head and the wait is not very good.
The hand is complete only with ˇ (1 kind–3 tiles). However, if we
draw any of ȷfl¸˛‹›”„ˆ˜˝˚ (12 kinds–41 tiles), the
wait will be significantly improved. For example, if we draw and
discard ˇ, the hand becomes:
fffifl˛‚‹››“”˜¨˝
This hand is now waiting for ˛ - (3 kinds–9 tiles). When a
3.2. BASIC BUILDING BLOCKS 59
hand is missing the head, it is often the case that the wait gets signif-
icantly improved quite easily.
3.2.6 Pairs and sets
Another important role a pair can play is to work as a candidate
for a set. Especially when a hand has two pairs, we can count on
one of the two pairs to become the head while the other becomes a
set. In other words, the value of pairs is maximized when there are
two (and only two) pairs in a hand. Let’s see why this is the case by
comparing hands with one, two, and three pairs.
1. Hand with one pair
–ı›“”„«ˆˆ˚ˇ"
This 2-away hand has one pair: ˆˆ. This pair is not very useful as
a candidate for a set for two reasons. First, if we draw another ˆ,
we will complete a set but then we will lose the head at the same
time. The hand will still be 2-away from ready after all. Second, the
probability of drawing another ˆ is not very high because there are
only two tiles left.
What if a hand has two pairs? Suppose we drew and discarded
", as follows.
2. Hand with two pairs
––ı›“”„«ˆˆ˚ˇ
This hand is also 2-away, but it has two pairs: –– and ˆˆ. Each
of these pairs is now functioning as an effective candidate for a set.
Whenever one pair becomes a set, the other pair becomes the head.
Drawing or ˆ will advance this hand from 2-away to 1-away.
60 CHAPTER 3. RIICHI MAHJONG BASICS
Moreover, whereas the hand with one pair was able to accept two
tiles of ˆ, the hand with two pairs can accept four tiles (two of ˆand
two of ). The probability of drawing any one of four tiles is obvi-
ously higher than the probability of drawing any one of two tiles. In
general, for each additional pair in a hand, tile acceptance increases
by two.
What if a hand has three pairs? Suppose we draw ˚, as follows.
3. Hand with three pairs
––ı›“”„«ˆˆ˚ˇ ˚
Draw
If we keep the second ˚ and discard the ˇ or the ı, the hand has
three pairs. However, keeping three pairs in a hand is inefficient. Re-
call that each additional pair increases tile acceptance by two tiles. In
this case, keeping a pair of ˚ means that the hand can accept two
additional tiles of ˚. However, doing so comes with a cost. Keep-
ing three pairs by discarding the ˇ means the hand can no longer
accept ˝ ˘ (2 kinds–8 tiles). The net tile acceptance gain will be
negative (2 8 = 6). Similarly, keeping three pairs by discarding
the ı means the hand can no longer accept (4 tiles). Therefore,
discarding a ˚ to maintain two pairs is the most efficient.
What we have seen so far is generalizable beyond the current ex-
amples. As long as we intend to keep the hand closed (i.e., not calling
pon or chii), we should avoid having three pairs in a hand. Having
three pairs makes for the weakest form, whereas having two pairs
makes for t he strongest form.
10
10
What if there are four or more pairs? Whenever a hand has four pairs, it is
2-away from ready for chiitoitsu (Seven Pairs). It may be faster to pursue
chiitoitsu than pursuing a standard hand in such cases.
3.2. BASIC BUILDING BLOCKS 61
Value of pairs: closed hand
2 pairs > 1 pair, 4 pairs > 3 pairs
Open hand
There is an important caveat to the above rule. When we intend
to call pon, having three pairs is actually better than having two pairs.
This is because the hand will become a two-pair hand after we call
pon once. For example, consider the following hand.
Two pairs vs. three pairs
––ı‹›ˆ¨¨ˇ˘¯%% %
Dora
What would you discard?
We would definitely intend to call pon on %. Anticipating that, we
should discard ı to keep t hree pairs in this case rather than dis-
carding to have two pairs. After calling pon on %, we will have a
choice between discarding or ˆ.
––‹›ˆ¨¨ˇ˘¯ %M%
––‹›¨¨ˇ˘¯ %M%
In either case, the hand will have two pairs after calling pon.
Value of pairs: open hand
3 pairs > 2 pairs
62 CHAPTER 3. RIICHI MAHJONG BASICS
3.2.7 Perfect n-away
Perfect 1-away
When a 1-away hand has two side-wait protoruns and two pairs,
it is called perfect 1-away.
Perfect 1-away
—¸˛‚““˚ˇ###
The hand above is an example of perfect 1-away. It is called “perfect”
because this hand can become ready either by calling chii, calling
pon, or drawing a tile to complete a run or a set, and no matter how a
hand becomes ready, you will always have the option to choose side
wait as the final wait.
Perfect 2-away
One step prior to achieving perfect 1-away, we may get a perfect
2-away hand. Perfect 2-away is made up with three side-wait pro-
toruns and three pairs, as follows.
Perfect 2-away
—˛‚““˚ˇˇ###
When a perfect 2-away hand becomes 1-away, it can always be perfect
1-away (unless you choose not to, for some reason). However, not all
perfect 1-away hands evolve from a perfect 2-away hand.
3.2. BASIC BUILDING BLOCKS 63
3.2.8 Putting things all together: an example
Let’s see some hand examples that illustrate how we can apply
the tile efficiency logics we have learned so far. Consider the follow-
ing 2-away hand.
Advancing a hand 1
ııffˆ¨˘˘¯˛‚”„« ˆ
Draw
What would you discard?
The hand now has three pairs, and we should avoid it. In order to re-
duce the number of pairs in this hand from three to two, our discard
candidates should be ı, ˆ, or ˘. Which one should we choose?
Recall t hat a closed-wait protorun of 57 is stronger than a closed-
wait protorun of 24 or an edge-wait protorun of 89. Therefore, it is
OK to cut down the ııff shape to ıff by discarding ı. This is
because ıff can become a side-wait protorun relatively easily. On
the other hand, the ˆˆ¨ shape and the ˘˘¯ shape are both
weak; the first can become a side-wait protorun only if we draw ˝,
and the second one will never become a side-wait protorun in one
step. Therefore, both ˆˆ¨ and ˘˘¯ should be kept as a can-
didate for the head or a group rather than making them into weak
closed-wait protoruns.
Let’s say we discard ı, and then we draw , resulting in the
following hand.
Advancing a hand 2
ıffˆˆ¨˘˘¯˛‚”„«
Draw
What would you discard?
64 CHAPTER 3. RIICHI MAHJONG BASICS
Now that we have a side-wait protorun fffi, we should discard ı.
Let’s say we draw ˇ, resulting in the following hand.
Advancing a hand 3
fffiˆˆ¨˘˘¯˛‚”„« ˇ
Draw
What would you discard?
This hand is now 1-away from ready, and our discard choice is be-
tween ¨ and ˘. Both tiles are equally useless from our perspective,
and so we will eventually discard them both. The question is which
one we should discard first. Recall that a 4 is more versatile than an
8. This means that ¨ in this hand may later become dangerous for
the opponents; we should thus discard ¨ now rather than later.
Let’s say we draw after that, resulting in the following hand.
Advancing a hand 4
fffiˆˆˇ˘˘¯˛‚”„«
Draw
What would you discard?
The hand is now ready. We should discard ˘ and call riichi. If we
win on , we can claim riichi, pinfu, and sanshoku (Mixed Triple
Chow), giving us 7700 points.
11
11
We will discuss scoring and yaku more extensively in later chapters.
3.3. COMPLEX SHAPES 65
3.3 Complex shapes
The three basic types of tile blocks we have covered so far
groups (runs and sets), protoruns (side wait, closed wait, and edge
wait), and pairs form the basis of any standard mahjong hands.
12
When a hand has some tiles that do not constitute any of these three
shapes, we treat them as floating tiles. For example, ı and ˚ in
the following hand are both floating tiles.
Hand with floating tiles
ıfifl˛‚‹›“”´ˆ˜˚
In addition to these basic blocks, we often come across complex
shapes that are made up of two or more groups, protoruns, pairs,
and floating tiles combined. It is useful to comprehend such com-
plex shapes as they are rather than breaking them up into smaller
parts. We will discuss three-tile complex shapes and four-tile com-
plex shapes in turn.
3.3.1 Three-tile complex shapes
There are two kinds of three-tile complex shapes double closed
shape and protorun plus one shape.
12
Standard hands are those with four groups and one head. Non-standard hands
are chiitoitsu (Seven Pairs) and kokushi musou (Thirteen Orphans).
66 CHAPTER 3. RIICHI MAHJONG BASICS
Double closed (ryankan) shape
When two closed-wait protoruns are combined, we have a dou-
ble closed (ryankan) shape. There are five different patterns in each
suit, as follows.
´˜˝ ˆ¨˚ ˜˝ˇ
¨˚˘ ˝ˇ¯
Each shape accepts as many as 2 kinds–8 tiles. For example, ´˜˝
accepts ˆ (4 tiles) and ¨ (4 tiles). This is twice as many as the num-
ber of tiles an isolated closed-wait protorun can accept.
Sometimes a double closed shape is embedded within a tile block,
making it difficult to detect it. For example, consider the following
1-away hand.
Hand with a double closed shape
Red
»ıfffifl‹›““”ˇˇ ˛
Draw
What would you discard?
Before drawing ˛, the hand was already in a very good shape. It was
perfect 1-away, accepting any of ıȷ›„ˇ (6 kinds–19 tiles).
The question is whether we should keep ˛ and discard ı instead.
Notice that, if we keep ˛, we have a double closed shape ˛‹“.
This is because the block ˛‹›““” can be split into ˛‹“
and ›“”. If we keep ˛ and discard ı, the hand is still 1-away
from ready, accepting ȷ‚›„ (5 kinds–19 tiles). The benefit of
discarding ı to keep the double closed shape is that t he hand can
3.3. COMPLEX SHAPES 67
always be pinfu when it is ready. On the other hand, discarding ˛
means that the hand may become a yaku-less hand when drawing ı
or
ˇ
.
Double closed shapes are particularly useful when a hand is rel-
atively far from ready (2-away or worse). As a hand advances, how-
ever, its usefulness diminishes because this block requires three (not
two) tiles even though it is not a complete group. Moreover, it will
ultimately become a single closed-wait protorun when t his block re-
mains incomplete when the hand is ready. Therefore, we should not
rely too much on a double closed shape. For example, consider the
following two hands.
––‰ı“”„ˆ¨˚%%
Draw
‰fffifl‚‹›„„ˆ¨˚
Draw
Both hands are 1-away from ready and both contain a double
closed shape in souzu (bamboos) tiles. Maintaining the double closed
shape in these cases will not be ideal. It is true that, if the hand be-
comes ready by drawing ˜ or ˝ first, each of the hands makes for
a good-wait ready hand. However, if the first hand becomes ready
by calling pon on % or the second hand becomes ready by drawing
or ı first, they only make for a closed-wait ready hand.
Therefore, when we draw a tile next to the head, creating a side-
wait protorun, we should keep it and break the double closed shape
instead. In the first example above, as we draw t hat creates a side-
wait protorun ‰ı, we should keep it and discard t he ˆ instead.
68 CHAPTER 3. RIICHI MAHJONG BASICS
In the second example above, as we draw that creates a side-wait
protorun ”„, we should keep it and discard ˆ instead.
Protorun plus one shape
As we saw with the first example in Section 3.2.8, we often come
across a tile combination such as ııff that is made up with one
protorun plus one floating tile (ıff + ı).
13
Depending on the type
of protoruns, we can classify protorun plus one shapes into three
types, as summarized in Table 3.2.
Table 3.2: Types of protorun plus one shapes
Name Example Wait Acceptance
side wait +1 ‰ -ı 3 kinds–10 tiles
closed wait +1 ˛˛‹ ˛ 2 kinds–6 tiles
edge wait +1 ˘˘¯ ˇ ˘ 2 kinds–6 tiles
A protorun plus one can accept two additional tiles that an iso-
lated protorun cannot. This is because these blocks can now be a
candidate for a set as well as for a run.
Breaking a protorun plus one can be inefficient. For example, if
we break a closed wait plus one shape into an isolated pair (i.e., dis-
card from ˛˛‹), the tile acceptance decreases from 6 to 2; it
can accept only ˛ (1 kind–2 tiles). Similarly, if we break it into an
isolated protorun (i.e., discard ˛ from ˛˛‹), the tile acceptance
decreases from 6 to 4; it can accept only (1 kind–4 tiles). With this
in mind, consider the following hand.
13
Alternatively, we can think of these combinations as a pair plus one ıı + .
3.3. COMPLEX SHAPES 69
Protorun plus one
––ıff›´ˆ˜¨ˇ˘¯¯ ı
Draw
What would you discard?
Discarding ı or to break the protorun plus one ııff is ineffi-
cient here. Discarding ı decreases tile acceptance by two, and dis-
carding decreases tile acceptance by four. Moreover, discarding
leaves three pairs in this hand, which should be avoided. Discard-
ing ¯ is much more efficient.
Sometimes we have to make a choice between multiple protorun
plus one shapes, just like we did in examples in Section 3.2.8. Con-
sider the following hand. What would you discard?
Multiple protoruns plus one
‰‰ȷ‚‚‹´ˆ˜¨˚˘""
What would you discard?
There are two protorun plus one shapes in this hand: ‰‰ȷ and
‚‚‹. We have to break one of the two into either an isolated Pair
or an isolated protorun, because the other parts of t his hand are more
or less self-sufficient. Which one should we choose?
When choosing between which protoruns plus one to break, pri-
ority should be given to the weaker one. Since the side-wait pro-
torun ‚‹ is much stronger than the closed-wait protorun ‰ȷ, we
should prioritize the latter and maintain ‰‰ȷ. In other words, the
side-wait protorun ‚‹ is so strong that we do not need to provide
a cover by maintaining the “plus one” tile, . On the other hand,
the closed-wait protorun ‰ȷ is weaker so we should cover it by
keeping another as a back-up. You should thus discard .
70 CHAPTER 3. RIICHI MAHJONG BASICS
3.3.2 Four-tile complex shapes
Among several different kinds of four-tile complex shapes, we
will focus on those that are made up of one group and one floating
tile. There are three variants of this kind stretched single, bulging
float, and skipping.
Stretched single (nobetan) shape
A set of four consecutive tiles such as ˛‚‹› is called a stretched
single (nobetan) shape. Stretched single shapes are very useful both
when a hand is ready and when a hand is 1-away or worse.
When a stretched single shape is in a ready hand, that part forms
the wait of the hand. For example, the following hand is ready, wait-
ing for .
Ready hand with a stretched single shape
–—‰˛‚‹ˆ˜¨%%%
In a ready hand, the stretched single shape can be thought of as a
candidate for the head ( or ) and a candidate for a run (—‰
or –—). For example, if we win this hand on , then becomes
the head, and —‰ becomes a run. On the other hand, if we win
this hand on , then becomes the head, and –— becomes a
run.
Another important role that a stretched single shape can play is
to work as a candidate for two runs. When a hand is 1-away or worse,
we can count on a stretched single shape to produce two runs. For
example, consider a stretched single shape ‚‹›“. If we draw ,
we will have a side-wait protorun ‚‹ in addition to a complete run
3.3. COMPLEX SHAPES 71
‹›“. Similarly, if we draw , we will have a side-wait protorun
›“ in addition to a complete run ‚‹›. Moreover, if we draw ˛
or
, we will have a 3-way side-wait shape
˛‚‹›“
(waiting for
¸--) or ‚‹›“” (waiting for ˛--).
There are six patterns of stretched single shapes, from 1234 through
6789. Table 3.3 summarizes the tiles each shape can accept to produce
various waits.
Table 3.3: Types of stretched single shapes
Shape 3-way 2-way 1-way Pair Acceptance
–—‰ ı ȷ – 6 kinds–20 tiles
—‰ı ȷ ‰ ff ı 7 kinds–24 tiles
‰ıȷ ı fi  ȷ 8 kinds–28 tiles
‰ıȷff ı ȷ fl ‰ 8 kinds–28 tiles
ıȷfffi ȷ fl  ı 7 kinds–24 tiles
ȷfffifl ı fi ȷ 6 kinds–20 tiles
As we can see, the middle two ones 3456 and 4567 are the
most versatile. They can accept two different tiles to produce a 3-way
wait (27 or 38), two different tiles to produce a 2-way side wait (45 or
56), and two different tiles to produce a 1-way wait (18 or 29 to pro-
duce a closed wait). The 3456 and 4567 shapes are the most valuable
of all four-tile shapes, and we should not lightly break such shapes
when a hand is far away from ready. With this in mind, consider the
following 2-away hand.
72 CHAPTER 3. RIICHI MAHJONG BASICS
2-away hand with a stretched single shape
‰ıȷ¸¸‚›´ˆ˚˚ˇ¯
What would you discard?
It is true that discarding or ȷ would lead to the greatest tile ac-
ceptance (7 kinds–24 tiles) temporarily. However, doing so is too my-
opic. If we do that, all the remaining protoruns will be closed-wait or
edge-wait ones. We should rather discard ¯ to keep the 3456 shape,
which we can expect to produce two side-wait protoruns later. The
resulting tile acceptance (6 kinds–20 tiles) is not much smaller, either.
Four-tile complex shapes 1: nobetan
Try to keep a stretched single shape if a hand has one. In partic-
ular, 3456 and 4567 should be kept until the hand becomes ready
or 1-away from ready.
Bulging float (nakabukure) shape
When we have a floating tile in the middle of a run (e.g., ‰‰ı),
we have a bulging float (nakabukure) shape. Bulging float shapes
are quite good at producing side-wait protoruns. Any bulging float
shapes from 2334 t hrough 6778 can accept four kinds of tiles to pro-
duce a side-wait protorun and a complete run. Take ‰‰ı, for
example. It can produce a side-wait protorun and a complete run if
we draw any of —ıȷ. With this in mind, consider the following
2-away hand.
3.3. COMPLEX SHAPES 73
Hand with a bulging float shape
‰‰ı‹“„„´˜˝˝˚˘
What would you discard?
Discarding to break the bulging float shape is not ideal. Although
doing so increases tile acceptance temporarily, the hand will be filled
with closed-wait protoruns. Alternatively, you should discard ˘ to
maintain the bulging float shape.
That being said, when this shape remains as is when a hand is
ready, it does not make for a good wait. For example, consider the
following ready hand.
Ready hand with a bulging float shape
‰‰ı˛‚ˆ˜¨"%%%
Draw
What would you discard?
Discarding " to keep the bulging float shape ‰‰ı makes the
wait of this hand pretty bad. It is waiting for , but we are already
using two of it in t he hand, leaving only two winning tiles. We should
rather discard to wait for ".
Four-tile complex shapes 2: nakabukure
Try to keep a bulging float shape until a hand becomes 1-away.
74 CHAPTER 3. RIICHI MAHJONG BASICS
Skipping shape
When we have a floating tile two tiles away from a run, we have
a skipping shape. For example, in a shape ıȷff, is floating
next next to a run ıȷff. in a skipping shape is more valuable
than isolated , because it increases t he kinds of tiles the hand can
accept to produce a protorun or a 3-way side-wait shape. Table 3.4
summarizes all the skipping shapes and the tiles each shape can ac-
cept.
Table 3.4: Types of skipping shapes
Shape 3-way 2-way 1-way Pair Acceptance
–‰ı ȷ 4 kinds–14 tiles
—‰ıȷ ff — 5 kinds–18 tiles
ıȷff ı 6 kinds–22 tiles
‰ȷfffi ı ȷ 6 kinds–22 tiles
ıfffifl ȷ ı 5 kinds–18 tiles
–—ı ȷ ı 5 kinds–18 tiles
—‰ȷ ı ȷ 6 kinds–22 tiles
‰ıff ȷ ı 6 kinds–22 tiles
‰ıȷfi ȷ fl fi 5 kinds–18 tiles
ıȷfffl 4 kinds–14 tiles
Bearing in mind that of ıȷff is more valuable than iso-
lated , consider the following hand.
3.3. COMPLEX SHAPES 75
Hand with a skipping shape
fffi›“”ˆ¨˚ˇ%%%
Draw
What would you discard?
We should keep and discard instead. This is because is a
part of a skipping shape ‚›“”, but is an isolated floating tile.
As we can see in Table 3.4, skipping shapes with a terminal tile
(1345 and 5679) are also valuable. The 1 of 1345 and the 9 of 5679 can
accept more tiles than an isolated 2 or 8 (let alone than an isolated 1
or 9).
76 CHAPTER 3. RIICHI MAHJONG BASICS
3.4 Waits
There are five basic wait patterns, as summarized in Table 3.5.
More complicated wait patter ns can emerge when some of these five
basic patterns are combined.
Table 3.5: Five basic waits
Name Japanese Example Wait Acceptance
side wait ryanmen ‰ -ı 2 kinds–8 tiles
dual pon wait shanpon ˜˜›› ˜ 2 kinds–4 tiles
closed wait kanchan ˚˘ ˇ 1 kind–4 tiles
edge wait penchan ¸˛ 1 kind–4 tiles
single wait tanki 1 kind–3 tiles
As we can see in the table, side wait is the strongest of all the basic
waits in terms of the kinds and the number of tiles to win on. Single
wait appears to be much worse than others, but single-wait hands
tend to have many possibilities of improving the wait and/or scores
further. Moreover, single wait of an honor tile has a relatively high
chance of winning it by ron.
Stretched single wait and semi side wait
Table 3.6 summarizes two wait patterns, each of which can be
thought of as a combination of some basic wait patterns. As I men-
tioned before, a stretched single shape in a ready hand forms a 2-way
single wait. It is a decent wait pattern, as the number of tiles to win
on (2 kinds–6 tiles) is twice as big compared with a regular single
wait.
3.4. WAITS 77
Table 3.6: Stretched single wait and semi side wait
Name Example Waits Acceptance
stretched single wait —‰ı — ı 2 kinds–6 tiles
semi side wait ˜˜¨˝ ˜-˚ 2 kinds–6 tiles
However, stretched single wait should not be confused with side
wait for a few reasons. First, the number of tiles a 2-way stretched-
single-wait hand can win on is at most 6, whereas it is 8 for a 2-way
side-wait hand. The difference between 6 and 8 is non-trivial. Sec-
ond, stretched single wait is still a variant of single wait, which means
two t hings. On the one hand, we cannot claim pinfu when the wait is
stretched-single wait. For example, the following hand has no yaku
and hence we cannot win it by ron without calling riichi.
‰ıȷ¸˛‚‹´ˆ˜¨˝˚
On the other hand, we get 2 minipoints (fu) with a stretched single
wait. For example, if we win t he following hand by drawing ¸, we
get 40 minipoints (20 base minipoints + 8 for a concealed set of honor
tiles + 2 for self-draw + 2 for single wait = 32, rounded up to 40).
14
‰ıȷ¸˛‚‹´ˆ˜%%%
When we have a side-wait protorun right next to a pair (e.g., 1123,
2234, 7899, etc.), we call it semi side wait. We distinguish this from
regular side wait for two reasons. First, the number of tiles to win
on is smaller (6 rather than 8) because we are already using 2 of the
14
We will discuss methods of scoring and minipoints calculations extensively in
Chapter 6.
78 CHAPTER 3. RIICHI MAHJONG BASICS
8 winning tiles in our hand. Second, we can treat this wait pattern
either as single wait or as side wait, depending on which interpre-
tation gives us a greater score. For example, consider the following
hand.
‰ıȷ¸¸˛‚´ˆ˜¨˝˚
We will treat the wait in this hand as side wait because that will give
us pinfu. However, consider the following hand that has the exact
same wait pattern: ¸¸˛‚.
‰ıȷ¸¸˛‚´ˆ˜%%%
If we win this hand by drawing ¸, we will treat the wait as single
wait: ¸ + ¸˛‚, which will give us 40 minipoints. If we treated
the wait as side wait: ¸¸ + ˛‚, we would get only 30 minipoints.
Of course, if we win this hand on , we cannot think of the wait as
side wait (because it is not). Similarly, if we win it by ron, it does not
make a difference if it is side wait or single wait (either way we get
40 minipoints).
3.4. WAITS 79
3-way side wait
When a side-wait protorun is combined with an adjacent run, we
get a regular 3-way side-wait pattern. There are only three of this
kind, summarized in Table 3.7.
Table 3.7: Regular 3-way side wait
Example Wait Acceptance
—‰ıȷ -- 3 kinds–11 tiles
‚‹›“” ˛-- 3 kinds–11 tiles
¨˝˚ˇ˘ ˜-˚-¯ 3 kinds–11 tiles
When we have a stretched single shape or semi side-wait shape
combined with an adjacent run, we also get a 3-way wait pattern.
Table 3.8 summarizes some examples.
Table 3.8: Some irregular 3-way waits
Example Wait Acceptance
–—‰ıȷff 3 kinds–9 tiles
˛‚‹››“” ˛ - 3 kinds–9 tiles
¨˝˚ˇ˘¯¯ ˜-˚-¯ 3 kinds–9 tiles
Notice that the number of tiles to win on in each pattern is smaller
than those for the regular 3-way side waits, although the kinds of
tiles to win on are t he same (either 1-4-7, 2-5-8, or 3-6-9). This is
because we are already using some of the winning tiles within the
hand.
80 CHAPTER 3. RIICHI MAHJONG BASICS
Notice also that not all the wait patterns qualify as side wait, so
claiming pinfu is not always possible (similarly, claiming single wait
is not always possible). For example, the first pattern in Table 3.8 is
essentially a 3-way stretched single shape; none of the waits embed-
ded in this shape qualifies as side wait. In the second pattern, if we
win on ˛, the wait must be interpreted as single wait; if we win on
, the wait must be interpreted as side wait; and if we win on ,
we adopt whichever interpretation that generates the higher score.
In the third pattern, winning on ¯ allows us to claim single wait if
doing so gives us a higher score.
Complex waits
When a set is combined with a floating tile nearby, we get some
complex wait patterns with multiple waits. Table 3.9 summarizes a
few examples of irregular waits that involve a set and a floating tile.
Table 3.9: Some irregular waits (set and a floating tile)
Example Combination Wait Acceptance
–——— single and edge 2 kinds–7 tiles
¸‚‚‚ single and closed ¸ ˛ 2 kinds–7 tiles
ˆ˜˜˜ single and side ˆ ´-¨ 3 kinds–11 tiles
When a set is combined with a protorun, pair, or a four-tile shape,
we get even more complicated waits. Table 3.10 summarizes only a
few representative examples.
3.4. WAITS 81
Table 3.10: Some irregular waits (set and a protorun, pair, or a four-tile shape)
Example Wait Acceptance
––——— 3 kinds–5 tiles
¸¸˛˛‚‚‚ ¸ ˛ 3 kinds–5 tiles
´´ˆˆ˜˜¨¨"" ´ ¨ " 3 kinds–6 tiles
ıııȷff ı- 3 kinds–7 tiles
“”„„««« - 3 kinds–9 tiles
ˆˆˆ˜¨¨˝ ˜-˚ ¨ 3 kinds–9 tiles
ıȷfffi ı 3 kinds–10 tiles
¸¸¸‚››› ˛ 3 kinds–11 tiles
82 CHAPTER 3. RIICHI MAHJONG BASICS
3.5 Glossary
Simple tiles (tanyao hai) are tiles between 2 and 8.
Terminal tiles are 1 and 9.
Honor tiles (jihai) are non-number tiles (dragon tiles and wind tiles).
Value tiles (fanpai / yakuhai) include dragon tiles, seat wind tiles,
and prevailing wind tiles. We get one han for a set of value tiles.
Valueless wind tiles (otakaze hai) are wind tiles that are neither a
prevailing wind tile nor a seat wind tile.
Run (chow / sequence; shuntsu) is a set of three consecutive num-
ber tiles.
Set (pung / triplet; kotsu) is a set of three identical tiles.
Quad (kong; kantsu) is a set of four identical tiles.
Protorun (taatsu) is a set of two tiles in the same suit that can be-
come a run when one more tile is added.
Pair (toitsu) is a set of two identical tiles.
Ready (tenpai) is when a hand is ready to win.
1-away (1-shanten) is when a hand can be ready with one more tile.
Perfect 1-away is when a 1-away hand has two side-wait protoruns
and two pairs.
Tile acceptance (ukeire) refers to the kinds and the number of tiles
a hand can accept.
Stretched single (nobetan) shape is a set of four consecutive num-
ber tiles.
3.5. GLOSSARY 83
Bulging float (nakabukure) shape is a four-tile shape that is made
up with a run and one floating tile in the middle of the run.
Skipping shape is a four-tile shape made up with a run and one
floating tile located at two tiles away from the run.
Chapter 4
The five-block method
In introducing basic building blocks of riichi mahjong in the pre-
vious chapter, I have also touched upon a number of important tile
efficiency principles e.g., superiority of side-wait protoruns, the
value of having two pairs in a hand rather than three, and the value
of stretched single or bulging float shapes, to name a few.
These principles are all important, but trying to take all of the
important principles into consideration at once could be a daunting
task. We have to make our discard choice in a limited amount of
time,
1
and tile efficiency is not the only factor we need to consider in
making a discard choice. Moreover, some of the tile efficiency prin-
ciples can at times clash with one another, requiring us to make a
judgement call about which principle to follow. For example, we may
at times wonder whether to retain a bulging float shape or to retain
two pairs in a hand, when we have to discard one of the two.
The five-block method I introduce in this chapter will help us
prioritize between competing principles and find the most efficient
discard choice quickly.
2
The core idea of t he five-block method is
deceptively simple; we first identify five tile blocks in a hand four
groups + one head, or their candidates and try to complete each
block.
1
Recall that, on regular (slower) tables on Tenhou, each discard choice must be
made within 5 seconds. In offline games, we should make choices even faster
so as not to irritate your fellow players.
2
As I mentioned in the Preface, the exposition of this chapter is based on Makoto
Fukuchi’s books. In particular, I am indebted to Makoto Fukuchi 2015 Haik-
ouritsu Nyumon Doriru 76, Yousensha. ISBN978-4-8003-0634-0.
4.1. FINDING A REDUNDANT TILE 85
4.1 Finding a redundant tile
We all understand that a standard hand must have five blocks of
tiles four groups and one head to win. The five-block method
encourages us to be always conscious about five tile blocks in a hand.
Consider the following hand. What would you discard and why?
ııfffi˛‹››´˜˜%%%
To figure out which tile is the least useful in this hand, let’s divide
the hand into tile blocks, as follows.
ıı
|{z}
fffi
|{z}
˛‹››
| {z }
´˜˜
|{z}
%%%
|{z}
(4.1)
Notice that, although we do not know which block is going to be the
head and which blocks are going to be four groups at the moment,
the hand already has five tile blocks. This means that there is no need
to increase or decrease the number of blocks from here.
Looking at each of the five blocks, the pair of ı, the protorun
fffi, and the set of % are all self-sufficient; we keep them as they
are. Our discard choice should thus be from the third or the fourth
blocks, ˛‹›› or ´˜˜. Let’s now compare these two closed-
wait blocks. While ´ is being useful within the block it belongs to,
enabling the hand to accept ˆ, ˛is completely redundant; the hand
can accept without having ˛. Therefore, the ideal discard here
is ˛.
There are two key points to remember in applying t he five-block
method. First, we should not make any one of the five blocks “too
86 CHAPTER 4. THE FIVE-BLOCK METHOD
weak.”
3
In the current example, if we discard ˜, the ´˜˜ block
becomes an isolated closed-wait protorun, which is too weak com-
pared with the other blocks. Likewise, if we discard
´
, this block
becomes a pair of ˜. Since this hand already has two other pairs,
having a third pair makes all the pairs in the hand too weak.
Second, each of the five tile blocks should ideally have three tiles.
In t he current example, the ´˜˜ block has exactly three tiles and
so we should not choose a discard from this block. On the other
hand, the ˛‹›› block currently has four tiles so we should dis-
card one from this block to make this a three-tile block.
Five-block method
Identify five tile blocks in a hand. Try to make sure:
(1) there is no block that is too weak; and
(2) each block has at most three tiles.
3
Basically, any block that is weaker than a side-wait protorun is a weak block.
4.1. FINDING A REDUNDANT TILE 87
Let’s see another example.
ıff‹›““”¨˚˚˘## #
Dora
We can easily see that there is one block in manzu (cracks), two blocks
in pinzu (dots), and a pair of white dragons, giving us four blocks.
This means that we need to have only one more block in souzu (bam-
boos). Therefore, we divide the hand as follows.
ıff
|{z}
‹›“
|{z}
“”
|{z}
¨˚˚˘
| {z }
##
|{z}
(4.2)
Since we should not create a block that is too weak, discarding or
is not an option. Notice that the block in souzu (bamboos) has four
tiles. We should thus discard one from this block. In case the pair
of white dragon later becomes a set, we should keep the pair of ˚,
leaving ¨ or ˘ as a discard candidate. Given that ¨ has a higher
chance of creating a side-wait protorun, we should discard ˘. Then,
none of the five blocks is too weak, and each block has at most three
tiles.
In the two examples we saw above, you might have been able
to identify the redundant tiles without really thinking too hard. If
so, that was probably because you have implicitly and unconsciously
applied t he five-block method in your mind. The goal of this chapter
is to train our mind further, so that it becomes our second nature to
identify five tile blocks in a hand.
88 CHAPTER 4. THE FIVE-BLOCK METHOD
4.2 Alternative configurations
Consider the following hand. What would you discard and why?
‰ȷ˛˛‹›““”%%%
Let’s first divide the hand into five tile blocks.
‰ȷ
| {z }
˛˛
|{z}
‹›“
|{z}
“”
|{z}
%%%
|{z}
(4.3)
This makes it clearer that, just like the previous example, ȷ is
creating a redundant closed-wait protorun, so we should discard it.
Also, discarding ȷ makes this a three-tile block.
However, there is an alternative way to divide this hand into five
blocks, and situational changes may call for such an alternative con-
figuration. Suppose that your opponents have already discarded all
four tiles of . Suppose also that seems live in the wall. Or, sup-
pose -ȷ tiles seem too dangerous to discard against an opponent.
Then, we might want to divide the hand in the following way instead.

|{z}
‰ȷ
|{z}
˛˛‹›““”
| {z }
2
%%%
|{z}
(4.4)
That is, we aim to make the pair of the head of this hand, and
we seek to have two runs in pinzu (dots). If we discard ˛, this block
becomes ˛‹›““”. Recall that a block like this can be split into
4.2. ALTERNATIVE CONFIGURATIONS 89
˛‹“ + ›“” (recall the discussion of double closed shape in
Section 3.3.1). Therefore, this block can accept as well as - to
make two runs in
pinzu
(dots). The block in
pinzu
(dots) will have
six tiles, but this is OK because this block is worth two.
To master the five-block method, we need to be able to instanta-
neously envision the first block configuration (4.3) the moment we
see this hand. However, that is not enough. We should also be able
to imagine an alternative configuration (4.4) at the same time. In the
game of mahjong, situations change very quickly each time a new
tile gets drawn or a new tile gets discarded. Therefore, the ideal
five-block configuration would also change accordingly as situations
evolve. We thus need to develop our skills to picture many possi-
ble five-block configurations and to prepare for possible situational
changes t hat would call for a change in the configuration.
I provide several exercises in the following pages. The answer
key to each exercise is provided on the next page. Try not to look at
the answers before you actually derive your own answer.
Exercises: finding a redundant tile
Exercise 1
What would you discard?
How do you divide the hand into five tile blocks?
––‰‚‹›˜˜˝˚ˇˇ ¨
Draw
90 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 1
––
|{z}
‰
|{z}
‚‹›
|{z}
˜˜¨˝˚ˇˇ
| {z }
2
With the draw of ¨, we now have a 3-way side-wait block in
souzu (bamboos). ˜ or ˇ could be our back-up candidate for
the head, in case we draw another . Since there is sanshoku
(Mixed Triple Chow) of 345, we discard ˜.
Exercise 2
What would you discard?
How do you divide the hand into five tile blocks?
ıff¸¸˛‚‹‹›”˜˝˝
Draw
4.2. ALTERNATIVE CONFIGURATIONS 91
Answer 2
ıff
|{z}
¸ ¸˛‚
|{z}
‹‹‹
|{z}
›”
|{z}
˜˝˝
|{z}
Before we drew the third , the pinzu (dots) tiles were ¸¸ +
˛‚‹ + ‹›, so the was simply a floating tile. Now that
we have another , the five-block configuration changes accord-
ingly. The ideal discard is ¸, as this has become redundant.
Exercise 3
What would you discard?
How do you divide the hand into five tile blocks?
‰‰ȷȷfffi˛‚˜¨˚˚ˇ
Draw
92 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 3
‰‰
|{z}
ȷ ȷfffi
|{z}
˛‚
|{z}
˜¨
|{z}
˚˚ˇ
|{z}
There are two “side wait plus one” shapes, ‰‰ and ˚˚ˇ,
that might later become the head or a run. At this point, how-
ever, we cannot determine which one will be which, so we should
keep them as they are. One of the two ȷ has become an obvious
redundancy so we should discard one.
Exercise 4
What would you discard?
How do you divide the hand into five tile blocks?
—ıȷ‹‹“„«˜¨˝"
Draw
4.2. ALTERNATIVE CONFIGURATIONS 93
Answer 4
—‰ıȷ
| {z }
2
‹‹
|{z}
“„
|{z}
« ˜¨˝
|{z}
"
The " is obviously redundant, but « is also useless. Without
«, the hand can accept . Since honor tiles can be used as a
safety tile (see Chapter 8), we discard « first.
Exercise 5
What would you discard?
How do you divide the hand into five tile blocks?
—ıffff˛‹“„¨˝ˇ˘ ˘
Draw Dora
94 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 5
—
|{z}
ıffff
|{z}
˛‹“„
| {z }
¨˝
|{z}
ˇ˘˘
|{z}
This is a bit difficult, as there are so many closed-wait protoruns.
Recall that each tile block should have at most three tiles and that
pairs are most valuable when there are two of them in a hand.
The block in pinzu (dots) has four tiles, so we discard one from
this block. Since is dora, we discard , leaving the double
closed shape around dora: ˛‹“.
Exercise 6
What would you discard?
How do you divide the hand into five tile blocks?
—‰‰‚‹›“¨˝˝˚˚
Draw
4.2. ALTERNATIVE CONFIGURATIONS 95
Answer 6
—‰
|{z}
‚‹‹›“
| {z }
2
¨˝˝˚˚
| {z }
2
Finding the best discard by actually comparing tile acceptance
counts for each possible discard candidate is super tedious. The
five-block met hod simplifies the process quite a bit. Since we
have two blocks in pinzu (dots) and two blocks in souzu (bam-
boos), we only need one block in manzu (cracks), hence one is
redundant. If we discard , the hand can be made ready with
11 kinds–34 tiles. If we discard or ˝, the hand can be
ready only with 6 kinds–19 tiles.
Exercise 7
What would you discard?
‰ff˛‚‹””„¨˝ˇ¯ ˚
Draw
96 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 7
‰
|{z}
˛‚‹
|{z}
””„
|{z}
¨˝˚ˇ¯
| {z }
2
Do not discard the ¯ just because it forms a closed wait or be-
cause discarding it gets us tanyao (All Simples). Avoiding closed
wait too much and being hung up on tanyao are two pathologies
common among intermediate players.
The block in souzu (bamboos) is actually not too bad; this is a
stretched single plus one, which can become either two runs im-
mediately (if we draw ˘), one run plus one side-wait protorun
(if we draw any of ˜˝˚), or one run plus the head (if we draw
¨ or ˇ). Note also that we need both and , because t his
part may become the head if we get two runs in souzu (bamboos);
when we get t he head in souzu (bamboos), we will treat this part
as a side-wait protorun. We thus discard .
4.3. SELECTING TILE BLOCKS 97
4.3 Selecting tile blocks
All the hands we have seen so far in this chapter already have
five tile blocks. In practice, however, this is not always the case. A
hand can sometimes have fewer or more tile blocks. Since we need
to have exactly five blocks to win a hand, we will need to bump up
tile block s by using a floating tile when we have fewer of them or to
discard some blocks entirely when we have a plethora of them.
In selecting which tile blocks to keep and which ones to discard,
we focus on a combination of the following three criteria:
1. tile efficiency;
2. hand value;
3. the safety of tiles to be discarded.
As we will see below, we can sometimes find a block to discard based
on all the three criteria. Consider the following hand. How do we
divide the hand into tile blocks, and what would you discard?
Red
–—‚‹››”„¨`ˇ˘ ˛
Draw
We can see that the hand currently has six tile blocks, as follows.
–—
|{z}
˛‚‹
|{z}
››
|{z}
”„
|{z}
¨`
|{z}
ˇ˘
|{z}
Since the first two tile blocks are already complete and the third block
is the head, our discard choice should be from the last three tile
blocks, ”„, ¨`, or ˇ˘.
98 CHAPTER 4. THE FIVE-BLOCK METHOD
From a perspective of tile efficiency, discarding the ”„ block
means that we lose the ability to accept both and «. On the other
hand, if we discard the
ˇ˘
block, we only lose the ability to accept
¯; because of the ¨` block, we can still accept ˚. We should
thus choose between the two blocks in souzu (bamboos). Keeping
the ` is desirable from a perspective of hand value (it is a red five) as
well as safety (discarding ˇ˘ is much safer than discarding ¨`,
generally speaking). Therefore, the three criteria collectively suggest
that we should discard ˇ˘.
In practice, however, satisfying all three criteria may not be fea-
sible. A common tradeoff we face is between speed and hand value.
That is, maximizing tile efficiency to gain speed often entails giving
up possibilities of pursuing an expensive hand. Consider t he follow-
ing hand.
–ıffff‚”„˜¨˘˘¯¯
Let’s divide the hand into tile blocks. There are several ways to do
this. One way to do this is to split it into the following blocks.
–ı
|{z}
ffff
|{z}
”„
|{z}
˜¨
|{z}
˘˘
|{z}
¯¯
|{z}
If we simply maximize tile efficiency, we discard , as we already
have six tile blocks and we wont need any more floating tile.
However, as it stands, the hand has no yaku and it is likely to be
a very cheap riichi-only hand. Moreover, the hand has three pairs,
which is not ideal as we saw in the previous chapter. Therefore, we
4.3. SELECTING TILE BLOCKS 99
might want to split the hand into the following five blocks.
–ıffff
| {z }
|{z}
”„
|{z}
˜¨
|{z}
˘˘
|{z}
¯¯
We count the floating as an independent block, hoping it to grow
into a run. We also treat the tiles in manzu (cracks) as a single block,
hoping to get at least one group or the head out of it. We thus discard
one ¯ now, then another ¯ in the next turn. Depending on what
tile gets drawn, our five-block configuration will be different.
For example, suppose we draw and then ˝. We will then have
the following.
–ıffff
| {z }
‚‹
|{z}
”„
|{z}
˜¨˝
|{z}
˘˘
|{z}
We will discard the as a first step toward reducing the number of
tiles in the manzu (cracks) block to three. We can now see that this
hand has a potential of getting sanshoku of 345 as well as pinfu and
tanyao.
On the other hand, if we draw ȷ and then , we can expect to
have two groups in manzu (cracks) so we will discard .
–ıȷfffffi
| {z }
2
”„
|{z}
˜¨
|{z}
˘˘
|{z}
In selecting tile blocks, we should try to achieve the best balance
between speed and hand value. Don’t fantasize too much about get-
ting an expensive hand. At the same time, don’t fixate too much
100 CHAPTER 4. THE FIVE-BLOCK METHOD
about tile efficiency at the cost of hand value. This is of course easier
said than done; it is quite difficult even for advanced players.
Exercises: selecting tile blocks
Exercise 8
What would you discard?
How do you divide the hand into five tile blocks?
—fffi›“´´ˆ¨¯¯ ¯
Draw
4.3. SELECTING TILE BLOCKS 101
Answer 8
—
|{z}
fffi
|{z}
›“
|{z}
´´
|{z}
ˆ¨
|{z}
¯¯¯
|{z}
The hand currently has six blocks so we need to get rid of one.
The ˆ¨ block is the weakest it is the only closed-wait pro-
torun so we should get rid of this one. We should discard ¨
first; if we draw ˜ we will discard ´ to leave the possibility of
pinfu. If not, we discard ˆ next, and then .
Exercise 9
What would you discard?
How do you divide the hand into five tile blocks?
—‰”„«««ˆˆ˚ˇ##
Draw
102 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 9
—‰‰
|{z}
”„«««
| {z }
2
ˆˆ
|{z}
˚ˇ
|{z}
##
|{z}
We were planning to discard the —‰ block because this was the
weakest block among the six blocks in this hand. However, now
that we drew another , the ˆˆ block is now the weakest. We
thus discard ˆ.
Exercise 10
What would you discard?
How do you divide the hand into five tile blocks?
–ıȷff¸‚˜¨ˇ˘"" ˝
Draw
4.3. SELECTING TILE BLOCKS 103
Answer 10
–
|{z}
ıȷff
|{z}
¸‚
|{z}
˜¨˝
|{z}
ˇ˘
|{z}
""
|{z}
The hand currently has six blocks so we need to get rid of one.
Comparing the two closed-wait blocks – and ¸‚, the –
block is more valuable because it is adjacent to a run. If we draw
, we will get a 3-way side-wait block. On the other hand, the
¸‚ block will only become a 2-way side-wait block when we
draw . We should discard ¸ first, not , because if we draw
next, we will discard the – block.
Exercise 11
What would you discard?
How do you divide the hand into five tile blocks?
ıff¸¸‚””´´¨˝˚ˇ ˜
Draw
104 CHAPTER 4. THE FIVE-BLOCK METHOD
Answer 11
ıff
|{z}
¸¸‚
|{z}
””
|{z}
´´
|{z}
˜¨˝˚ˇ
| {z }
2
Now that we have a 3-way side-wait block in souzu (bamboos),
we should get rid of one block. Comparing a closed-wait block
ıff and two pairs ”” and ´´, we should value the closed-
wait block. This is because the hand has three pairs already so we
should get rid of one of them. Since we see a (remote) possibility
of sanshoku of 567, we should discard ´.
4.4 Building a block
When a hand has fewer than five blocks, we need to build a new
block, possibly from a floating tile we already have in the hand. In
doing so, we should envision the kind of yaku that the hand is going
to have eventually. Consider the following hand. Suppose you are
the dealer and t his is East-1. What would you discard?
ȷfffffi‚‚‹«¨ˇ˘¯%"
As usual, we will split the hand into blocks. Notice that the hand
has at most four blocks only.
ȷfffffi
| {z }
2
‚‚‹
|{z}
« ¨ ˇ˘¯
|{z}
% "
We should thus compare the four floating tiles « ¨ % " in terms
4.4. BUILDING A BLOCK 105
of their relative capabilities to grow into an independent block. Of
these four tiles, ¨ is the strongest candidate, because it can form a
side-wait protorun with two kinds of tiles, ˜ and ˝. Any simple tiles
between 3 and 7 are a strong floating tile because of their ability to
form a side-wait protorun. Terminals (1 and 9) will never become
a side-wait protorun, and 2 and 8 can become a side-wait protorun
when paired with only one kind of tiles (3 or 7). However, number
tiles are still stronger than honor tiles because honor tiles can never
form a run.
We should thus choose between the two honor tiles, % and ".
Which one should we discard? Notice that this hand is clearly a
pinfu hand and that it is currently lacking the head. Since value tiles
can never be the head of a pinfu hand, we should discard % rather
than ".
We may want to choose a discard from an existing block rather
than discarding a floating tile in order to enhance the hand value.
Consider the following hand.
ıȷȷfi¸˛˛“´´¨˝˚ˇ
From a pure perspective of tile efficiency, the discard choice should
be either ¨ ˇ or , for discarding either of the three will maximize
tile acceptance. The block configuration behind such a decision is as
follows.
ıȷ
|{z}
ȷfi
|{z}
¸˛˛
|{z}
´´
|{z}
¨˝˚ˇ
| {z }
However, doing so makes it almost inevitable that the hand ends up
having a low score and/or a bad wait. Alternatively, we can expect
106 CHAPTER 4. THE FIVE-BLOCK METHOD
the stretched single shape ¨˝˚ˇ to produce two runs, to form
a run, and the tiles in manzu (cracks) to produce one run, as follows.
ıȷȷfi
| {z }
¸˛˛
|{z}
|{z}
´´ ¨˝˚ˇ
| {z }
2
We should thus discard the ¸ for now, anticipating to discard the
pair of ´ eventually. That way, we can expect to have tanyao, pinfu,
and possibly sanshoku.
Exercises: building a block
Exercise 12
What would you discard?
How do you divide the hand into five tile blocks?
Red
–»fifl‚‹‹ˆˆ˜˝˚ˇ
4.4. BUILDING A BLOCK 107
Answer 12
–»
|{z}
fifl
|{z}
‚‹‹
|{z}
ˆˆ˜
|{z}
˝˚ˇ
|{z}
If we were to simply maximize tile acceptance, the discard choice
should be either or ». However, that would make the block
in manzu (cracks) too week. Breaking the ‚‹‹ or ˆˆ˜ is
not ideal, as these blocks are very strong. We should therefore