Defense guide: Suji

(This is secon part of UmaiKeiki’s defense guide — Betaori and Suji posted in Osamuko’s Mahjong Blog)

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 .

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.