If you've been playing Mahjong for a while then you probably know of some environments where these yaku feature very prominently in the play style. Are you frustrated? This post will be intended to help people, not to criticise them, so we won't be complaining about this or that ruleset, environment, or whatever. Rather, we'll come up with ways to counterattack the people who take advantage of the opportunity afforded by the rules to cheapen the game.

Also, you might have heard some yaku counterattack strategy already, but only in cases where it is treated very briefly. Thanks to our extensive statistical research tools, I hope we will be able to go a bit more in-depth when looking at what our opponents are doing, and see how this compares with theories we have heard.

Them toitois

People who love to pon love to make Toitois. So you can generally tell that someone is making a toitoi after a few pon. But how can you tell someone is making a toitoi before they pon? Let's look at some discard reading theories that can be used to identify toitoi whether or not there are any pon.

First off, let's consider that one of the easiest ways to increase a toitoi's value is to pon Yakuhai. So, we can expect people who are considering going for toitoi to hold a few yakuhai in early game, and discard them later if they don't get paired. This is a fine theory, but what does it look like in practice? Let's take a look at some discard statistics! Let's also compare hands that scored toitoi against those which scored chiitoitsu, because the two often have similar patterns.

Here is the percentage of discards that were Yakuhai:

Well, it's easy to see that people who made toitoi discarded far fewer yakuhai overall. Both those aiming for toitoi and those aiming for chiitoitsu discarded fewer yakuhai in early game, but in the toitoi case, yakuhai came spilling out in late game when they couldn't be incorporated into the hand.

This trend might not be limited to yakuhai. Since toitois don't contain any shuntsu, players who are aiming for them don't need to be concerned about the efficiency of certain number tiles. Others, however, will be more cautious about discarding "inside" number tiles as these are more efficient in creating shuntsu. Let's take a look at the percentage split between tanyao and yaochuu tiles:

What is best for efficiency when making toitoi? Usually, people aiming for toitoi will need to draw a few extra pairs of tiles they already have. Thus, they'll keep tiles that they think have a good chance of pairing up. This can be seen in players discarding tiles immediately after someone else discarded the same tile, and discarding tiles when several are already visible on the table. Let's have a look at the percentage of the above tanyao and yaochuu discards that were shonpai:

It's not a huge difference -- you'll need to watch closely to guess when someone is trying to draw more pairs. However, I hope these stats give you a good idea of what kind of discards you can expect from someone who is aiming for toitoi.

The weakness of toitois is defense, and you can exploit this. Usually people will make toitois with several open melds -- doing this cripples their defense to the point where they can't discard safe tiles even if they want to. Be sure to riichi often, since riichi = free points on a table with no defense. Another advantage of riichi in this situation is that people with toitois are more likely to Kan, so you will have a high probability of scoring some uradora. Just be careful about bad waits on shonpai. You can't be sure that someone doesn't have at least a pair of your waiting tile hidden in their hand. Waiting on tiles that are already visible on the table means hidden pairs are less likely and you will have a better chance of ronning someone.

Yakuhai + rage

Ah, these are a scourge! Once someone pons yakuhai, they can do anything they want with their hand and still have yaku. Since there is no restriction on the rest of the tiles, this is the yaku that requires the least amount of skill to make. Also, since they can use any tile, it has plenty of opportunities to be inflated with Dora. Fortunately, there are a few strategies that can counterattack yakuhai rather well.

The most popular strategy is Shibori. A lot of people know this one; it basically entails holding on to tiles you think someone is likely to Pon or Chi. So when you want to stop someone from ponning yakuhai, don't deal any (obviously). The question is, when SHOULD you discard them? When it comes to yakuhai, you basically have 3 key opportunities. The first opportunity is on the very first turn. At this point, the chances of someone being able to pon is very low because they haven't had some time to draw pairs; the best they can have is a lucky starting hand. The second opportunity is immediately after someone else deals that tile. If nobody ponned it the first time, there is a good chance that they don't have a pair yet and you can discard it before they have a chance to draw one. The final opportunity is to discard it when you reach tenpai. This won't stop anyone from ponning it, but since their hand will have been held back the whole game, it's possible you will be ahead with a complete hand while theirs is incomplete.

Another thing to be careful about is the tendency of yakuhai hands to be inflated by Dora. Dora shibori will be another strategy to consider. Since it's easy to add dora by using Chi, you should start focusing on dora shibori if your shimocha pons yakuhai.

One good way to tell someone is going to try to pon yakuhai is to watch for a useless Chi. Since not a lot of yaku can be made with chis, it may be a sign that someone is planning to go for yakuhai and they want to complete their hand as quickly as possible. In fact, we can show this with statistics.

Here is the percentage of the time that various scoring patterns were made after a Chi was declared:

Pon palace

Here are some general tips which might help you in situations where both yakuhai and toitoi are rampant.

Unless you have a potential high-value hand, try not to be the first one to call any tiles. This puts a lot of pressure on opponents and may drive them to start calling more if they feel they need to "keep up".

If yakuhai + rage is giving you a headache, try playing some kuitan ari games, which will ensure a greater diversity of strategies used by the players.

Most of the time, chiitoitsu and toitoi evolve from very similar starting hands. Many of the tips used to predict toitois above can apply to chiitoitsu as well. Using the strategies and statistics above, you might be able to come up with some chiitoitsu counterattacks even if we didn't specifically target them in this post. =3=

Since it's not a standard yaku, there are many variations on how Open Riichi works. Here I'll try to explain the variants I know. Feel free to post any others you know about as well as how you've been playing it!

First up, what is Open Riichi? It is a variation on Riichi in which you reveal your hand to all players, so they know what your waits are. When you are in a situation in which you can declare Riichi, you can choose to make either a normal Riichi or an Open Riichi. Open Riichi is a yaku worth 2 han (but see below for some variants). Doing this on the first turn (Open Double Riichi) would be worth 3 han, not 4.

A popular variant is to make Open Riichi a Yakuman if someone intentionally deals in. When you make Open Riichi, anyone who's not already declared riichi has to pay for a Yakuman if they deal into your hand. However, anyone who declared riichi BEFORE you is exempt from this! Beware, as declaring riichi AFTER an opponent's open riichi means you still have to pay the yakuman.

The choices of allowing or not allowing the yakuman rule each can open up different strategic opportunities. For example, allowing the yakuman can make open riichi a counterattack against people who are using sashikomi (intentional deal-ins) as a strategy. There was a scene in Akagi where the gambler Urabe talked the yakuza bosses into dropping the yakuman rule so he could keep using sashikomi -- but don't let anyone tell you it's a "stupid rule" just because of Urabe's tricks.

There are also some variants regarding how to open the hand. The simplest way is to reveal the entire hand:

Some will instead require you to only reveal the tiles that generate waits:

Either way, your opponents will be able to know your waits, but the second rule would (usually) prevent them from knowing what yaku you have. Again the choice of which rule to use can open up different strategies. For example, under a no-yakuman partially-open ruleset, one might reveal only a single tile as a Tanki wait. Since there is no yakuman penalty, opponents can consider intentionally dealing in if they think the hand is cheap. However, since the hand is partially concealed, there's no knowing for sure if it's a junk 2600-point hand or a suuankou double yakuman!

When is a good time to use Open Riichi? Consider that a lot of advanced players would probably furiten riichi if they had a 3+ sided wait, because even if they can't Ron, they have a high chance of getting Tsumo. Thus, you might consider using Open Riichi when you have many waits, because you have a high chance of getting Tsumo even if the opponents can avoid dealing in. Another good opportunity might be if you are joining a Riichi roulette. If one or two opponents have already declared Riichi, it doesn't matter if they know what your waits are because they can't avoid dealing in. Finally, it may be possible to confuse beginners by using complex waits, but you shouldn't need such tricks if there is a big skill difference.

Now there's nothing terribly wrong with Occult Mahjong in that it can be a convenient way to explain away some minor issues -- such as that awful losing streak you just had, or some secret technique you don't want to share with everyone. However, it sure would be fun to test some of these claims against the mathematics of probability and statistics! Today we shall do exactly this, and see how well they stand up.

Are Tenhou's Tiles Random?

Was that ippatsu tsumo your opponent just got really due to chance, or did the game rearrange the tiles to give it to him on purpose? Does Tenhou intentionally give you extra character tiles in your starting hand? The answer is no, such things don't happen on Tenhou. According to the manual page, the walls are arranged randomly before the start of every game (random number generator / seed and wall generation). The walls are generated by Mersenne twister and can be recreated from the seed given in every game log, which looks something like this:

INIT seed="0,0,0,2,4,76" ... shuffle="mt19937ar,069A462D,7D366808,AE07C00E,CDB80045,F3637452,D39609BA,965B922D,DCDCC2BE"

In the past you could get the seed by observing your own games, and thus predict what everybody would draw. Fortunately Tenhou fixed that bug, but it proves tile order in the walls doesn't change during the game.

One specific complaint I heard was that starting hands can contain 4-6 character tiles, which can be a significant slowdown when going for Pinfu. How many character tiles SHOULD you get in the beginning? A basic, if flawed, calculation might look like this:

(7 / 34) * 13 = 2.676

Now to see what the statistics say. I tallied how often starting hands had each number of character tiles for a large number of games, and here are the results:

We can see that it is most common to start with 2-3 character tiles in the hand. The average turned out to be 2.569. The feeling that you start with 4-6 all the time can possibly be explained that such hands are more memorable because of the added frustration. By the way, the probability of starting with 4 or more character tiles seems to be 26.425%, so it will probably happen at least once per game.

If this talk of games fudging the draws sounds like a complete joke to you, be aware that major poker sites are notorious for doing this as it makes them a LOT more revenue. The idea is to give everyone a big hand at the same time so they are more likely to push all in. I wouldn't put it past any gambling site to do something like this, even Mahjong sites, so... (insert obligatory disclaimer to be wary of paysites)

Is A Hanchan Longer Than Two Tonpuusen?

Here's an interesting one. A Tonpuusen is a game consisting of East 1st through 4th rounds. A Hanchan has East 1st-4th and South 1st-4th. So, by default, a Hanchan has exactly twice the number of hands as a Tonpuusen. What, then, would cause someone to regard a hanchan as longer than that? The answer: Ren Chans. Since a hanchan has more rounds, there are more opportunities for a renchan to occur. Of course, if you look at many games over time, the average number of renchans in a hanchan would turn out to be twice the average in a tonpuusen. Or would it? Let's look at a large number of games and find out!

The average number of rounds per game were as follows:

Tonpuusen - 5.698
Hanchan - 10.766

From this data we can see that there isn't much difference between one hanchan and two tonpuusen. One interesting observation is that while hanchan are more likely to have renchan, they are also more likely to end early because someone busted out!

Of course, this says nothing of player mentality when sitting down for a game. Since a hanchan is a "normal" game, someone joining a tonpuusen would be more interested in getting the game over with as fast as possible. Thus, the players might play for speed instead of strategy in order to end a tonpuusen quickly.

Is The Suit Of The Riichi Tile Significant?

I heard a rumour that the tile discarded after a Riichi declaration can be used to guess which suit contains the waits. Well, sure, in combination with the other discards, you can probably figure it out. But here's a question: given only the tile discarded immediately after a Riichi declaration, can you ignore all other discards and identify a suit that's more safe or dangerous than another? Here's what the statistics say:

4475 Riichis examined,
1336 had a wait in the same suit as the discarded tile,
3139 had no waits in the same suit,
29.855% ratio.

So you should have a 1 in 3 chance of there being a wait in the same suit as the Riichi tile. And that's exactly how it should be, since there are 3 suits. But is there any difference in early or late game? Let's look at the turn number when the Riichis were made:

Both seem to follow the same curve. From this, I would conclude that turn number does not affect whether a riichi tile indicates nearby safe or dangerous tiles. This doesn't mean you should start ignoring the riichi tile completely, though. Late game discards from the hand can often tell you what tiles that player considered important enough to keep when close to tenpai.

Have fun, and I wish you... statistically favourable odds.

This probably came about because Osamu and Fukuchi-sensei read each other's blogs and discovered how English and Japanese abbreviate three-player mahjong:

三人麻雀 = 三麻 (sanma)
3-player mahjong = 3p

I'll also try to include a list of common English terms that differ from the Japanese. Obviously I can only include the most common words or else this post would never end...

English list

Here's a list of commonly used English terms that differ from the Japanese equivalent to some extent. In most cases this is due to the influence of card games like rummy and poker.

Japanese list

Here's the list of basic game terms in Japanese, with kanji given whenever possible. You probably won't need many of the kanji, though, as mahjong terms seem to be frequently written in katakana. This list won't cover yaku names (which you can get here) and slang terms (in which case the list would never end). I'm not a Japanese expert so don't hesitate to make corrections or suggestions!

First off, here are a few resources you'll want to have at hand:

Guide to scoring

This post won't be a guide to scoring itself as there are already plenty of those. However, you will need one, and despite its age, Wei-hwa Huang's Japanese Mahjong Scoring is still the best English language guide on the internet.

http://www.ofb.net/~whuang/ugcs/gp/mahjong/mahjong.html

The best part about this guide is that it includes the Japanese terms plus several common English terms for everything, so you'll be better prepared to understand what other people are talking about in their own guides.

If you're a beginner, you might be interested in printing some kind of reference sheet that you can look at during games. The EMA have a sheet based on their custom rules, which are somewhat different than most common Japanese Mahjong rules. Since their sheet has caused so much confusion for beginners, I can't recommend it. You'll be better off playing against CPU opponents, so you can take your time while playing and study an in-depth rules guide like the one above. Here's a good CPU game:

http://gamedesign.jp/flash/mahjong/mahjong_e.html

Score chart

Once you have figured out how Fu and Han are multiplied to get the final score, you might wonder how people calculate their hand scores so quickly. The answer is that they don't calculate but rather memorize a score chart. You'll definitely want to obtain a good, concise score chart as soon as possible. Here's my favorite chart which I found on the website of Henachoko Mahjong Club.

If you're wondering how to memorize points higher than Mangan, try to think of them as multiples of Mangan. For example,

Haneman = Mangan x 1.5
Baiman = Mangan x 2
Sanbaiman = Mangan x 3
Yakuman = Mangan x 4

Sometimes people refer to double yakuman as "baiyakuman" and triple as "sanbaiyakuman", and so on, to maintain the pattern.

A challenger appears! Check out this coloured chart by CRiX!

Score quizzes

Yeah, shameless plug time!

The best way to memorize the yaku is to see them in use, and the best way to learn scoring is to score many hands. Playing live games is a good way to do this, but for those without this luxury, I made some applets that generate random hands for you to practice on. You can find them among the tools on Tenhou documentation site.

http://arcturus.su/tenhou/

The Yaku Quiz is for beginners who are trying to memorize the yaku. It gives you a big checklist and all you have to do is check off what yaku you can see. Don't be intimidated by the size of the list. There are just a lot of yakuman (and character tiles are expanded as well.)

The Score Quiz is mainly for people who play internet mahjong that want to figure out scoring before they go to a real game. This one covers Han, Fu, and payments. For those trying to practice counting Fu, you can enter the exact (unrounded) number if you want.

It uses basically the same rules as Tenhou, but with double Yakuman and two additional yaku: Dai Sha Rin and Open Riichi (because it's awesome.)

Also be warned that it counts Shanpon waits won by Ron as concealed (an kou), which is an oversight and not an actual scoring rule. (Suu an kou shanpon still has to be a tsumo though.)

Terminology

You'll probably notice that most english guides use their own English terms for everything. When everyone makes up their own terms to describe the same thing, it can get pretty creative, but not very helpful. The only constants are the Japanese terms, so you might want to learn as many of those as you can to avoid confusion.

Yaku vs. Han confusion

There are a lot of times when people confuse Yaku with Han. Sadly, the first two sites I linked make the same mistake. Here's clarification:

Yaku are scoring patterns in the hand. For example, Tanyao is a yaku, and Toitoi is a yaku.
Han are units that measure the value of the yaku. For example, Tanyao is worth 1 han, and Toitoi is worth 2 Han.

Pretty simple. Toitoi is 2 han, but it's not 2 yaku.

Kui-sagari

Kui-sagari is the property of some yaku that makes them worth 1 less Han when open. For example, Hon Itsu is normally worth 3 Han but is reduced to 2 Han if you have called any tiles. What I find funny, though, is that a lot of English guides present this the other way around: they'll tell you that Hon Itsu is normally worth 2 Han, but gets +1 when closed. It's as if they know that most games with westerners are going to be pon palace!

Jokes aside, the numbers are the same so it doesn't matter how it's presented. However it may help your play style if you think of there being a penalty for an occasional open hand rather than a bonus for an occasional closed hand.

Scoring Chii toi tsu

The "seven pairs" hand might be intimidating to beginners because it uses 25 fu instead of a round 10, some charts do not include a row for 25 fu, and some rulesets score it as 1 han, 50 fu.

Fear not! We can make it really simple. Just score your chii toi tsu as if it were worth 1 han, 50 fu and you'll get the exact same results (below mangan)!

As proof, here's a score chart comparing 25 vs. 50 fu payments.

The only difference between the two is that the 2-han 25-fu version will reach Haneman faster.

Associative property

The reason that 25 fu, 2 han is equal to 50 fu, 1 han is because:

25 * (2 * 2 * 2 * 2) = (25 * 2) * (2 * 2 * 2).

You might have noticed that this isn't limited to Chii toi tsu. In fact we can generalize this into two theories:

(1) Doubling the Fu is equivalent to increasing Han by 1.

(2) Halving the Fu is equivalent to decreasing Han by 1.

Here's how to put this into practice. Let's suppose you have memorized the hand values for 40 Fu at all Han. Without a chart, how can you give the value of 80 Fu at 2 Han?

Start at 40 Fu, 2 Han. Since you can't double the Fu, instead increase Han by 1. This gives 40 Fu, 3 Han which is equal to 80 Fu, 2 Han!

Now how can you get the value of 20 Fu, 2 Han? Again, start at 40 Fu, 2 Han. This time, subtract Han by 1. This gives 40 Fu, 1 Han which is equal to 20 Fu, 2 Han!

If you're confused, take a look at this table.

Knowing how to use the associative property will save you a LOT of time, as it means you only really need to memorize the charts for 30, 40, and 50 Fu to cover most situations.

The smallest possible score

Many charts won't have a value for 20 Fu, 1 Han. That's because you just can't make a hand that cheap.

What happens if you make an open Tanyao using Shuntsu only, a Ryanmen wait, and win by Ron? Should be worth 20 Fu, 1 Han right?

Actually, such a hand is called "kui-pinfu" or open pinfu, and will be scored as 30 Fu, 1 Han. Since a kui-pinfu is the only way to get 20 Fu, 1 Han, we can thus say the lowest possible score for a hand is 1000 points.

Unrelated to kui-pinfu is the 30 Fu, 1 Han hand won by Tsumo. Such a hand is called "gomi", because of the payments (500, 300 = 5, 3 = go, mi), and because "gomi" means "trash".

The highest possible score

What's the highest possible score you can get? While this probably won't have any real life application, ever, here's a cool example that I once found on Japanese Wikipedia. When I went back to find it again, I discovered that it had been deleted due to being "original research". Pfft! It was amusing enough to me, so here I have reproduced it:

Round wind: East
Seat Wind: East

Ron:

Dora indicators:

Uradora indicators:

Not shown: All 8 flower tiles extracted from the hand.

Here's how it works. This is using a rule known as "aotenjuu" (one reading of 青天井). It means "no limits" and eliminates Mangan, Yakuman, etc. So for example if you have a 30 Fu, 5 Han hand, it's worth 15400 points instead of being capped at 8000. Yakuman are worth 13 Han and can be combined with normal yaku. In addition, Wareme is also in effect, meaning that the payment for this hand is doubled.

So here's what the above hand gets:

Dai san gen: +13
Tsuu ii sou: +13
Suu an kou tanki wait: +26
Suu kan tsu: +13
Renhou: +13
"Flower Yakuman": +13
Open riichi, win by Ron: +13
8 Ren Chan: +13
Riichi + Double + Open: +3
Ippatsu: +1
Toitoi: +2
Yakuhai: +5
Dora: +24
Flowers: +8

Total: 160 fu, 160 han.

(160 x 6 x 2^162) x 2 = 11,224,332,574,701,334,411,804,299,515,261,053,590,957,561,930,055,800 points.

Fun, eh? If you ever get hit by this, you'll have a debt that can only be paid off by playing restricted Rock Paper Scissors on a cruise ship...

Yo, this is UmaiKeiki again. If you are reading this, it means I actually made more of my defense guide (a surprise, I know). This is a continuation of my previous post which you should probably read first. I apologize if this turns into another novel/tl;dr/wall of text/whatever.

Kabe

While Suji represent information broadcast to everyone through discards, Kabe can often be privileged information gained from tiles in your own hand. "Kabe" translates as "wall", and that's exactly what they do: Kabe act as barriers that prevent shuntsu from being formed.

A Kabe is formed when all four instances of a number tile are visible. They can be in discards, in open melds, as Dora indicators, or in your hand. The more instances of the tile you have in your hand, the more of an advantage you have over opponents. For all they know, those tiles could still be available in the walls and they may try (unsuccessfully) to build shuntsu around them.

Kabe are great for identifying safe tiles during Betaori. Let's suppose all four are visible to you. That means nobody can have a shuntsu containing it (although, it could still be a waiting tile). Since there are no shuntsu containing it, then you know that and can not possibly complete any Ryanmen waits! The only waits on those two tiles can be Shanpon and Tanki.

Now let's say you have a Kabe on . This blocks three shuntsu: , , and . Now it would still be possible for someone to have a , , or Ryanmen wait, but it would be impossible for them to have a or wait. That makes and safe against Ryanmen.

Now consider a Kabe on . This makes and Ryanmen waits impossible, but someone could still have or waits. Thus, the safe tiles are and .

By symmetry, we can show the following tiles are safe when we have a Kabe:

Kabe	Safe tiles
	,
	,
	,
	,
	,

As you can see, Kabe only really indicate safe "outside" tiles (123, 789). To get safe 456, you need to have TWO Kabe that form a "sandwich".

If there are one or two tiles sandwiched between the Kabe, both are safe. For example, if you have and Kabe, then and are not usable for shuntsu -- and can thus only be Shanpon or Tanki waits.

And if you have a and Kabe, then the inner tile, , is safe, but the and are still dangerous.

Naturally, Kabe are only reliable when you can see all 4 instances of a tile. When all 4 are visible, it's known as "No Chance"; if there are only three visible, it's called "One Chance". As you can imagine, One Chance Kabe aren't nearly as safe. If you can see three , for example, it's still not safe to throw a because the opponent you are defending against could have waiting on . However, if it's a toss-up between discarding and , for example, it's somewhat safer to discard the .

Of course, the existence of two One Chance Kabe is much better: if you can see three and three then the is mostly safe. However, it's not nearly as safe as it would be if there were a No Chance.

Even if you don't have the opportunity to use Kabe every time you defend, make sure you watch the discards so that your own shuntsu don't get blocked by Kabe.

Saki-giri

When talking about defense in Mahjong, it's only natural for discard reading to come up. You'll definitely learn a lot about discard reading by studying Urasuji and Matagisuji. Suddenly, all the internet tough guys come out of the woodwork and yell "STOP READING SUJI, IT DOESN'T WORK." What's wrong? Surely it's because nobody wants their own discards to be read?

Well, as it turns out, Suji really isn't all that useful against tougher opponents. The problem is that the theories only work if (1) the opponent uses Ryanmen waits and (2) they make only the most efficient discards. Break either of these two conditions and Suji yields a bunch of misinformation, if anything.

Naturally, there are plenty of tricks designed to thwart Suji readers. Here's the most basic one:

Let's say you start the round with in your hand. This is a great versatile setup which can become Shuntsu, Koutsu, Toitsu, or whatever you need later. Most people wouldn't discard any of these tiles in early game simply because of the efficiency they contribute to the hand. However, it's entirely possible that you'll discard the later in order to get a Ryanmen wait. Watch out! People will be looking for Matagi-suji in late game, so it's possible they'll see right through your plan. What would happen if you discarded the in early game instead?

Matagi-suji are very unlikely to come out in early game (and note this well if you are playing some average or weak opponents) because most people won't break apart a pair when there are useless inefficient tiles still in the hand -- and even if they did, efficient shapes like ryanmen are likely to be filled by late game, right? So an early discarded usually means is safe -- little do they know, you could have a wait ready to trap them!

Here's another example. Let's say this time you have . The most efficient move here is to discard first, then . Unfortunately, this announces to everyone that is a dangerous wait. Instead, let's pull a reverse-order discard here and get rid of first, then . We still wind up with a Ryanmen wait so nothing of value was lost, but now our discards suggest that is safe.

Dama-ten

Here's a simple technique which has a lot of versatility. Basically, Dama-ten means "silent tenpai", and all you have to do is not declare Riichi when you hit Tenpai. In fact, there are plenty of situations where you should be doing this purely for attacking strategy -- for example, if you can upgrade to a better wait or more Han, it's a bad idea to lock in your hand with Riichi right away. What I want to point out, however, are its uses for defensive strategy, or perhaps "counter-defensive" strategy.

Riichi is an announcement to the whole table that you are Tenpai. It tells everyone that you are a threat and they should take immediate action to defend. If they do, you'll be winning a whole lot less because everyone is throwing safe tiles at you. However, if there are people who attack recklessly right up to the point where you Riichi, you can use Dama-ten to prevent them from going into defensive mode. This way they'll keep discarding dangerous tiles and you'll have a much better chance of getting your winning tile from one of them.

Another reason to use Dama-ten is to keep your defensive options open. If someone else has declared Riichi, or if you think they are about to do so, you might want to avoid declaring Riichi yourself. Once you declare Riichi, you HAVE to discard everything you draw, including dangerous tiles. Using Dama-ten is a good way to be prepared in case you do draw a dangerous tile.

If you have a really high-value hand, Dama-ten can be important. (Depending on how competitive the game is, "high-value" could be as low as 8000 points.) You absolutely do NOT want to give away that you are shooting for a monster hand, or opponents will do anything they can to stop you!

Now for some counter-counter-defense. (It never ends.) If you decide to Dama-ten but tsumokiri everything after that, opponents might get an idea of what you are up to. (A reminder that tsumokiri means discarding the tile you just drew.) Make sure you don't tsumokiri every turn or your cover will be blown! If you ever watch any pro games, you might see them going to great lengths to avoid tsumokiri when they have a good hand. It's all about bluffing. Look weak when you are strong; look strong when you are weak.

Speaking of looking strong when you are weak, don't forget the old No Ten Riichi trick. Just declare Riichi when you aren't actually Tenpai, and watch everyone turn their hands into crap out of fear of your potential monster hand. Just be careful, though; since No Ten Riichi is a Chombo, you'll have to make the payment if the round ends and you have to show your hand. Also of note is that many computer games won't let you do anything that counts as a Chombo, so this won't work as well in a game of internet mahjong. What you might try instead is declaring Riichi with a 1000 point hand instead of taking time to turn it into something bigger.

Naturally, all this is only useful against opponents that are defensive. If they aren't defensive, then Riichi = free points.

What's up. This is UmaiKeiki, a Mahjong fan with a shorter attention span than that of a dog with ADD.

Some time ago I set out to write one of my Mahjong-addict buddies a guide to defense strategy. Once it was about half finished, something shiny caught my attention and the guide was long forgotten... One day Osamuko mentioned that she wanted to put something about Suji reading on here; I remembered that old guide and offered to revive it into blog form. This whole fetus is what I recovered off my old computer -- I make no guarantees that it doesn't suck horribly.

Brace for tl;dr!

Introduction to defense

Defense in Mahjong is focused primarily on how to avoid dealing into opponents' hands. In other words, playing defensively means making fewer payments. You know that saying "a penny saved is a penny earned"? This is VERY true in Japanese Mahjong! Your points are valuable; don't let someone take them without a fight!

As with many gambling games, the good hands will come to you eventually; you must be patient and wait. Until then, it is only natural for some of the other players to reach Tenpai faster than you, and to win before you do. Don't sweat it! However, why should YOU be the one to deal into their hands? This can hurt your standing to the point where recovery is almost impossible, and it gives the other players a lead over you as well. Essentially, Japanese Mahjong seems to have become a game which is not about "winning more" but about "losing less". It is considered a wiser move to preserve the points you have rather than to risk them on the chance of getting some more. Therefore, the key to defense is to identify "safe tiles", which are tiles with a low probability of being an opponent's winning tile.

Fortunately there are a number of strategies that you can use to find safe tiles and identify which are more or less safe than others. The basics are Betaori, Suji, and Kabe. Against advanced players you may be interested in Damaten and Saki-giri. (I originally intended to include them all in this guide. Maybe there will be a "Part 2" in the future.)

Finally, a caution about discard reading. While it's most certainly possible to guess an opponent's waits and hand tiles, it's not an exact science. Because of this, it seems to be regarded as some kind of "black magic". Most people are afraid of it to some extent, so don't expect every discussion you have about discard reading to be entirely supportive of your ambitions.

Betaori

Betaori is the number one defensive strategy. Most people will use it as soon as someone declares Riichi, as it means that person is most likely to win this round. Don't worry about other people winning -- it happens. What you should be worried about is dealing into that person's hand and thus being the only one to lose points. To avoid this, you must often discard otherwise useful tiles from your hand and take apart mentsu.

Ouch! Taking apart your hand? Some people hear this much and decide not to bother. I maintain that this is an important strategy and urge you to give it a try. Just watch what happens when someone declares Riichi. Chances are the others are going to start discarding tiles that very clearly indicate that they are in Betaori. So if anyone is going to deal into that Riichi, you're the most likely! And consider this: that opponent is Tenpai and could win at any second, but if you are still something like 2 Shan Ten, why would you keep attacking? It would take you much longer to catch up, and you would most likely have to discard some dangerous tiles to do so.

By the way, the No Ten payments are no excuse to avoid Betaori. If the round ends, you'll only be paying 1000, 1500, or 3000 points, and this is usually a lot better than dealing into someone's hand. (Anything with Riichi, specifically, will usually be worth more than 3000 points. USUALLY.) Besides, you should be able to make back those points in due time. Also, if you are playing "inflated" Mahjong, No Ten payments are really insignificant compared to the average winnings, so don't worry about it.

OK, so we know that we'll be breaking down the hand and trying to avoid a loss. How exactly do we do this? Well, the strategy goes like this:

1. Discard Furiten tiles

2. Discard into impossible waits

3. Discard into improbable waits

4. Discard into improbable yaku

5. Break apart An Kous etc.... and cross your fingers.

Step 1: Furiten tiles

At any given point in time, there is one 100% safe tile. This is the tile just discarded by your Kami Cha, aka the player to your left. At that moment, all 3 opponents are Furiten for that tile at the same time. So if you have the same tile in your hand, go ahead and discard it now because nobody can Ron it.

On a similar note, if all 3 opponents have discarded the same tile at some point in the game, they are all Furiten for that tile. So if you have the fourth one, it also is a 100% safe tile. The difference here is that this one stays safe; the Kami Cha's discard is only safe for the current turn. Since some opponents will no longer be Furiten for the Kami Cha discard next turn, discard that one first!

Since you'll be using Betaori mainly against an opponent who has declared Riichi, you can focus on discarding that person's Furiten tiles. Just take a look at their discard history: they are Furiten for everything they've discarded so far. Also, you can use tiles that others have discarded since the Riichi was declared. Depending on the strictness of your house's Furiten rule, the others' discards may be safe for only one turn. However, if the person who declared Riichi didn't call them the first time, you can reasonably expect them to still be safe. (The only reason they would become dangerous again is that it wasn't considered advantageous to Ron off that specific opponent, so the person who could have won decided instead to become temporarily Furiten and wait for that tile to come from someone else.)

Now don't get ahead of yourself! Furiten tiles are the safest tiles you can deal. So if you are facing someone who has declared Riichi, discard their Furiten tiles before anything else. The key here is STALLING. Discarding a Furiten tile buys you one more round; for each round you stall, they could get their winning tile from someone else, meaning that you successfully dodged making the payment! Also, since more Furiten tiles can appear during each round, defending will become easier for each round you stall.

Step 2: Impossible waits

Impossible waits are somewhat rare, but keep an eye on the discards and you might find some. Jihai are common candidates for impossible waits: since they can't be used in shuntsu, the only possible waits are Shanpon and Tanki. (Kokushi Musou is an exception, but it should be easy to tell whether it is a threat.)

Suppose you have a Chun in your hand, and you can see the other three Chun have been discarded already. That means nobody can have a shanpon or tanki wait on Chun, so it is an impossible wait. This also works if you have 2 Chun and the other 2 are discarded, or if you have 3 and one is the Dora indicator, or really any situation in which all 4 are visible.

Now finding impossible waits on number tiles is a bit harder, since you need to block any possible Shuntsu. Let's suppose all four of the and are visible. That means none of your opponents can have a shuntsu containing either or , so the only waits possible on and are Tanki and Shanpon. So if you have the last or the last , they are 100% safe.

Step 3: Improbable waits

OK, we know that Furiten and impossible waits give us safe tiles, but what happens when we run out of safe tiles? We have to start discarding "mostly safe" tiles, which means that it is POSSIBLE for an opponent to be waiting on them, but it is not PROBABLE.

Let's assume your opponents are fairly intelligent. They probably know a lot of attacking strategy. What kind of wait do you think they'll use? Ryanmen? You bet! Since Ryanmen is considered the "best" wait, you'll naturally see opponents using it most of the time. The less efficient the wait, the less likely someone is to Riichi on it. So if you are trying to avoid dealing into a Riichi, look for tiles that could only be used in "bad" wait types like Tanki, and work your way up. The goal is to just avoid dealing any tiles that could be used in Ryanmen waits.

The strategy for Tanki and Shanpon waits is pretty much the same as for impossible waits as described above. Let's go back to the Chun example. Suppose you have one Chun in your hand, and none are visible in discards. Then it's a "live" tile, and thus very dangerous. Now what if there were one Chun visible in discards? Then the efficiency of a Shanpon wait on Chun is reduced, but someone might still go for it just because they want to get that extra Han. What if 2 were visible? Then Shanpon is impossible; the only wait is Tanki. That makes it a lot safer; the only time you should worry about dealing it is when it's the Dora.

After we run out of Tanki and Shanpon waits, let's look for number tiles that could deal into Kanchan and Penchan waits, but still avoid Ryanmen. To do this, we'll need to "block off" any Ryanmen waits.

Let's suppose that all four of the are visible. That means there can be no Ryanmen waits on and . (Note however that someone might be waiting on , as it would still count as Ryanmen.) The only possible waits on are Tanki, Shanpon, and Kanchan; the waits on are Tanki, Shanpon, and Penchan. If you have one of those tiles in your hand and at least two are visible on the table, Shanpon is no longer possible. And if 3 were visible and you had the last one, Tanki is impossible and the only possible wait would be Kanchan/Penchan.

We can also use Suji to identify which Ryanmen waits are more dangerous than others. To cite the classic example, suppose your opponent is Furiten for . That means and Ryanmen waits are less probable, since your opponent is already Furiten for one side. In this case, the is safer because the only waits left are Shanpon and Tanki. The could be used in Shanpon, Tanki, Kanchan, and Penchan.

While Ryanmen is the main threat, do be aware that Kanchan and Penchan are somewhat dangerous. Sometimes people will use Kanchan waits as a really sneaky way of getting someone to throw them the Dora. And Penchan might be used in the interest of speed. To see how that works, put yourself in their shoes: suppose you are the first one to reach Tenpai, but you have an "inefficient" wait. You probably won't declare Riichi just yet, because you are more likely to draw a tile that will upgrade it to a better wait than you are to draw the winning tile. So you'll hold off until a better wait forms and then you'll Riichi. The exception would be if your wait were Penchan. Penchan waits are really hard to upgrade; you are more likely to draw the winning tile than you are to upgrade the wait. That means if you decide to upgrade, you'll be giving the opponents plenty of time to advance their hands and catch up. You'll probably try to Riichi now while they are weak, because it will force more of them to defend. Because of this, expect Penchan Riichis to be more frequent in early game than in late game.

Step 4: Improbable yaku

When you reach the point where anything you can discard would deal into a dangerous wait, it's time to choose tiles that ruin the opponent's chances of getting extra Han. You can still get hit by Ron, but at least the payments will be smaller.

For example, if you think the opponent might be aiming for Tanyao, deal 1's and 9's. There is always a chance that the opponent has waiting for or , but if they really did have Tanyao, the payment you make for dealing is less than what you would pay for dealing .

And if you think they might be aiming for Chanta, start by dealing 5's, then 4's and 6's. Again, there is always a chance that the opponent has waiting for or , but if they really did have Chanta, the payment you make for dealing is less than what you would pay for dealing .

If you suspect they might be aiming for Hon Itsu, just discard some tiles from a suit they probably don't have. Sometimes it won't be a Hon Itsu, but the majority of tiles will be in one suit. In that case, you can sometimes use their early number tile discards to find out what suits are safe.

Maybe your opponent built a wait around the Dora? Don't deal any tiles that are close to the Dora! Also, don't deal any red 5's until you see the nonred 5 pass.

Step 5: Break apart An Kous, etc.

This is something of a "last resort" strategy. If you have two, three, or maybe even all four instances of a tile in your hand, try discarding one. It's still dangerous, BUT if it passes, you know the rest are safe! Then you can just discard one each turn until you run out. The more instances of a tile you have, the longer you can stall, meaning some more Furiten tiles or other safe tiles are likely to come out.

Another good move might be to discard tiles such that there are already several instances of that tile visible on the table. Your opponents might not Riichi if they know most of their waiting tiles are accounted for.

Suji

Suji is one of the more complex theories in Mahjong. There are many variations and types of Suji, but it all boils down to one basic goal: to identify which Ryanmen waits are safe and which are dangerous.

Ordinary Suji are the tiles that complete Ryanmen waits. So for example...

If you have in your hand, then the Suji are .

If you have in your hand, then the Suji are .

In total, there are six Suji: 14, 25, 36, 47, 58, and 69. Multiply this by three suits, and there are 18 Ryanmen waits in all. Now we already know that most people who Riichi are going to use a Ryanmen wait. If there are only 18 possible waits they could have, wouldn't it be great if we could determine which are safe and which are dangerous? This is where Suji theories come in!

A common practice is to arrange the Suji into three groups, as follows:

Group 1:

Group 2:

Group 3:

(Note -- I originally started rambling about "equivalence classes modulo 3" here, but I have decided to remove all the mathematical stuff from this post for sanity reasons.)

Every Shuntsu must contain one element from each group. Similarly, every Ryanmen wait is completed by two tiles from the same group. Now let's start with the most common Suji reading technique:

Omote-suji

(Or: "That 147 trick everyone already knows")

Omote-suji is a rather basic discard reading technique; since it's somewhat intuitive, I expect a lot of players will have independently derived the underlying strategy before they even find out it has a name. Don't underestimate its power, though. It's great for identifying safe tiles during Betaori!

Suppose someone who has declared Riichi discards a . Since they are now Furiten for that tile, you can reasonably assume they are not using a or Ryanmen wait. This means that the Omote-suji, and , are safe!

Remember, this scales across 147, 258, and 369. So if they discard a 5, then the Omote-suji (safe tiles) are 2 and 8. And if they discard a 6, then the Omote-suji are 3 and 9.

Depending on the strictness of your house's Furiten rule, this might be a little less reliable for tiles discarded early in the game. For example, if you discard a 6 early in the game but wind up with a 36 wait later, you can still Ron the 3 (but not the 6) under some rulesets. However, I don't expect this to happen very often, so we can assume Omote-suji applies to the opponent's entire discard history.

Don't forget that this applies to other players' discards as well! So if there is one person who declares Riichi, and someone ELSE discards a 5, then you can now safely discard the Omote-suji (2 and 8). And if you ever run out of safe tiles and throw a 4, 5, or 6 at random, then you just bought yourself two Omote-suji (assuming it passed).

Let's return to the 147 example for a minute. The opponent discards a 4; 1 and 7 are now safe. However, they are not EQUALLY safe! Remember, we can't guarantee the opponent is using a Ryanmen wait. Thus, if we are going to take into consideration the risk of other wait types, we should discard the 1 first because there are fewer wait types that it could complete.

When there are multiple Omote-suji, this list shows what waits are less dangerous:

through = Safe. No Ryanmen waits are possible, but they can still complete Penchan, Kanchan, Shanpon, and Tanki waits.

or = Safer. Only waits are Kanchan, Shanpon, and Tanki.

or = Safest. Only waits are Shanpon and Tanki.

You might have noticed that Omote-suji are really only useful when people discard 4, 5, or 6. Let's suppose someone discards a . This means that there is no wait. Does this mean is safe? No -- they could still have a wait.

When someone discards an "outside" tile, in this case a , the remaining wait is called To'oi-suji. These are pretty useless; you can't discard the because it's still dangerous. However, if it's a toss-up between discarding or , for example, then is slightly safer because it completes fewer waits.

Now let's suppose both and have been discarded. THEN it's safe to deal the , because both and waits are impossible.

OK, now that's out of the way, so let's turn our attention to types of Suji that indicate DANGEROUS waits. These are a lot more fun, simply because every once in a while they'll predict the exact wait an opponent is using, and it's awesome when they reveal their tiles and your prediction was correct!

Senki-suji

Senki-suji usually show up in early game discards of number tiles. They indicate a potentially dangerous wait two counts higher (or lower). Here is how it works:

Let's say that at the start of the round, your only Man tiles are . Recall that two tiles from the same Suji group can't form a Shuntsu, so this is a somewhat useless combination. Now let's assume the next tile you draw is either or . Let's look at the two situations this gives us:

Case 1: . Now we have something useful. With this pattern early in the game, we could wind up with a really nice wait later, so we are probably not going to discard any of these tiles right away. That 7 probably won't come out until we are somewhat closer to Tenpai.

Case 2: . In this situation, we do have a Ryanmen wait shape, but that 7 still isn't helping. In all likelihood, that 7 will come out within the first few turns.

What does this tell opponents? An early discarded 7 is likely to be a Senki-suji, indicating a possible dangerous wait 2 counts away. In this case, 7 - 2 = 5, so it would be understood that is a dangerous wait.

Here is a list of all the Senki-suji. Note that there is no Senki-suji for 5. An early discarded 5 is more likely to be an Ura-suji, or possibly an indication of Hon Itsu.

Discarded tile	Senki-suji

Ura-suji

Ura-suji can show up at any time, but they are most frequent in midgame. They represent a Kanchan wait upgrading to Ryanmen. This means the discarded tile lies just outside of a dangerous wait, one count higher (or lower). To illustrate, let's use an example Tenpai hand. We can Riichi here, but what tile should we discard?

In this case, it's a matter of choosing between a Ryanmen or a Kanchan wait. We know that a Ryanmen is better, so we'll probably discard the and Riichi.

What does this tell opponents? That 9 is likely to be an Ura-suji, lying outside a dangerous wait one count away. In this case, 9 - 1 = 8, so it would be understood that is a dangerous wait.

Here is a list of the dangerous waits indicated by Ura-suji. Watch out for TWO Ryanmen waits that can be used when a 5 is discarded.

Discarded tile	Ura-suji
	and

Matagi-suji

Matagi-suji are almost exclusive to late game discards. They indicate a Toitsu being broken down to take a Ryanmen shape. This means that the discarded tile lies between the two ends of a dangerous wait (and there are often two possible waits that enclose it). Again, here's an example to illustrate how it works. We can Riichi with this hand, but which tile should we discard?

The most efficient move would be to discard a . What would this tell opponents? Since it was kept until late game, it may be a Matagi-suji, which lies between the two ends of a Ryanmen wait. The two Ryanmen waits that enclose are and . Therefore, it would be understood that one of those two waits is dangerous.

This concept of Matagi-suji is based on the versatility of a shape like . Someone playing by the most efficient strategy possible will be trying to form Mentsu and will worry about pairs later. This is where a shape is so useful: it can be broken down at any time to get either a Toitsu OR a Ryanmen shape. So it will most likely be saved until late game when another Toitsu has appeared and the Ryanmen shape is now needed.

Because of this, you'll rarely see Matagi-suji in early game. Take advantage of this! If you see an early discard, you can be almost certain that it didn't come from a shape. This means is likely to be a safe tile later!

Here is a list of dangerous waits indicated by Matagi-suji. Note that the 1 and 9 won't form Matagi-suji, so watch out for Ura-suji instead.

Discarded tile	Matagi-suji
	and
	and
	and
	and
	and

Think about this for a second: when an opponent discards a , what's dangerous? If we consider the various Suji theories presented here, we might guess the dangerous waits are the Senki-suji , the Ura-suji , and the Matagi-suji and . In fact, the only safe tiles left are the Omote-suji, and ! Just knowing what all the Suji are is only the first step. We must be able to identify which Suji types are most likely to be indicated by each discarded tile. From here on, let's focus on strategies that narrow down the options for dangerous waits.

Aida yon ken

Aida Yon Ken is a discard pattern in which a four-count interval is enclosed between two number tile discards. For example, discarding and forms an Aida Yon Ken; the interval between the two discards is .

What do and have in common? They're both Ura-suji for the same wait, ! So whenever you see an Aida Yon Ken, watch out for a dangerous wait sandwiched between the two discarded tiles. Aida Yon Ken generally suggest that the two innermost tiles (in this case, ) are concealed in the hand, and the two outermost tiles (in this case, ) are the resulting wait.

Here is the list of Aida Yon Ken and the dangerous waits they box in:

Discarded tiles	Aida yon ken

Multiple Suji

A good way to identify which waits are more dangerous is to watch for multiple types of Suji for that wait. To get an idea of just how much information you are telegraphing through your discards, let's return to the age-old question, "What would you discard?"

With this hand, we are 1 Shan Ten, and the most efficient discard would be . If we discarded it, we could reach Tenpai with any of ; in total 6 tiles, 20 instances. Now suppose we get lucky and draw . What should we discard now?

The most efficient discard is , as it would leave us with a Ryanmen wait. Now when the opponents look at our discards, they'll see a pattern and will probably be able to recreate what was in our hand without much trouble. The is an Ura-suji for a wait, and the is a Matagi-suji for the same wait! Someone who is playing by the most efficient strategy possible will discard Ura-suji first, then Matagi-suji later. Therefore, it won't be too hard for opponents to guess that we were discarding out of a shape and the wait is dangerous!

So when you see multiple types of Suji for the same wait, you can be extra sure that wait is dangerous. Watch for Senki-suji to come out first, then Ura, then Matagi. Here are the six Ryanmen waits and the Suji that make them dangerous:

Ryanmen wait	Suji discard order
	-- --
	-- --
	-- --
	-- --
	-- --
	-- --

Examples

Have a look at these discards taken from Tenhou logs and test yourself on how well you can read Suji. Can you identify what kinds of Suji have come out? What waits look dangerous?

Example 1:

Example 2:

In example 1, the patterns that should stand out are and . The could be a Senki-suji, followed by a Ura-suji, suggesting a dangerous wait. Also, the could both be Ura-suji, forming an Aida Yon Ken around . The Matagi-suji further suggests this wait is dangerous.

In example 2, the dangerous patterns are and . The could be a Senki-suji combined with a Matagi-suji for a wait. Also, the could be a Senki-suji combined with a Ura-suji and Matagi-suji for a wait.

Answer 1:

Answer 2:

As you can see, Suji theories aren't an exact science. They will often indicate several dangerous waits rather than just one. Also, there are plenty of cases where opponents won't use Ryanmen waits or where they will make inefficient moves on purpose just to throw you off. Ultimately you must be prepared to adapt to different situations and different opponents -- but it never hurts to have some theory by your side.