Riichi Book I

A Mahjong Strategy Primer

for European Players

Daina Chiba

Riichi Book I

A Mahjong Strategy Primer for European Players

Version ﬀ

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.

The original form of this book is L

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of a manuscript. The L

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//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).

Founded in 2005, EMA has

been doing a fantastic job in maintaining common rule sets,

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

http://mahjong-europe.org/

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.

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.

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.

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.

If you want to learn how to play riichi, I’d recommend Barr (2009).

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. Katayama’s 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

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

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 don’t

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.

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

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 haven’t 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 you’d 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

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,

and games in the right column (under tonnansen)

are more standard East-South games that have both East and South

rounds.

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.

There is no red ﬁve in these games,

either. Open tanyao is allowed in all the other games. Games in t he

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.

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.

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 won’t 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 10−4 = 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 don’t 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.

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.

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.

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.

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).

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.

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

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.

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.

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.

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).

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.

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

you’d 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.

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.

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.

Af-

ter a day or two, it will turn into “—-/–/–” meaning t hat you do not

have a premium membership.

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.

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, you’d 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

= 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.

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

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 (

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)

, 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

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

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.

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.

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.

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.

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

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

Dragon tiles # $ %

White (haku) Green (hatsu) Red (chun)

Wind tiles ﬄ ! "

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.

win a standard hand, we need to complete four groups ( mentsu) and

one head (atama; ﬁnal pair).

Groups can be classiﬁed into two kinds

— run and set.

• 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.,

———, $$$.

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 ´ ¨.

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.

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.

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.

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˘.

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.

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

‚ˆ˜˚ will make this hand 1-away for chiitoitsu (Seven Pairs).

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.

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.

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 ﬀ

or ¨ makes the hand 1-away. You should thus discard ﬀ 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.

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 ﬁ, resulting in the

following hand.

Advancing a hand 2

ıﬀˆˆ¨˘˘¯˛‚”„« ﬁ

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 ﬂ, we can claim riichi, pinfu, and sanshoku (Mixed Triple

Chow), giving us 7700 points.

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.

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.

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

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).

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.

Alternatively, we can think of these combinations as a pair plus one ıı + ﬀ.

3.3. COMPLEX SHAPES 69

Protorun plus one

––ıﬀ›´ˆ˜¨ˇ˘¯¯ ı

Draw

What would you discard?

Discarding ı or ﬀ to break the protorun plus one ııﬀ is ineﬃ-

cient here. Discarding ı decreases tile acceptance by two, and dis-

carding ﬀ decreases tile acceptance by four. Moreover, discarding

ﬀ 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 ˛

”

, 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 — ﬀ ‰ ı – ﬁ  ȷ 8 kinds–28 tiles

‰ıȷﬀ  ﬁ ı ȷ — ﬂ ‰ ﬀ 8 kinds–28 tiles

ıȷﬀﬁ ‰ ȷ ﬀ ﬂ  ı ﬁ 7 kinds–24 tiles

ȷﬀﬁﬂ ı ﬀ ‰ ﬁ ȷ ﬂ 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 ﬁ  6 kinds–22 tiles

‰ȷﬀﬁ ı  — ȷ ﬂ ‰ 6 kinds–22 tiles

ıﬀﬁﬂ ‰ ȷ  ﬀ ı 5 kinds–18 tiles

–—ı ‰ ȷ  ﬀ ı 5 kinds–18 tiles

—‰ȷ ı ﬀ – ﬁ ȷ 6 kinds–22 tiles

‰ıﬀ ȷ ﬁ — ı ﬂ ﬀ 6 kinds–22 tiles

‰ıȷﬁ ﬀ  ȷ ﬂ ﬁ 5 kinds–18 tiles

ıȷﬀﬂ ﬁ ‰ ﬀ ﬂ 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).

‰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

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 –-‰-ﬀ 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 – ‰ ﬀ 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-ﬁ 3 kinds–7 tiles

“”„„««« ›-„ ” 3 kinds–9 tiles

ˆˆˆ˜¨¨˝ ˜-˚ ¨ 3 kinds–9 tiles

ıȷﬀﬁ ‰ ı ﬁ 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,

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.

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.

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.

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.”

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.

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

ﬀis 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 }

%%%

|{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 }

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 }

‹‹

|{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 }

¨˝˝˚˚

| {z }

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}

ﬀ ˛‚‹

|{z}

””„

|{z}

¨˝˚ˇ¯

| {z }

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 ﬀ.

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 won’t 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 ﬁ, we can expect to

have two groups in manzu (cracks) so we will discard ‚.

–ıȷﬀﬀﬁ

| {z }

‚ ”„

|{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 }

ˆˆ

|{z}

˚ˇ

|{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}

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 }

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 }

‚‚‹

|{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 }

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