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 2m3m in your hand, then the Suji are 1m4m.

If you have 5m6m in your hand, then the Suji are 4m7m.

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: 1m 4m 7m

Group 2: 2m 5m 8m

Group 3: 3m 6m 9m

(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 4m. Since they are now Furiten for that tile, you can reasonably assume they are not using a 1m4m or 4m7mRyanmen wait. This means that the Omote-suji, 1m and 7m, 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:

3m through 7m = Safe. No Ryanmen waits are possible, but they can still complete Penchan, Kanchan, Shanpon, and Tanki waits.

2m or 8m = Safer. Only waits are Kanchan, Shanpon, and Tanki.

1m or 9m = 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 7m. This means that there is no 4m7m wait. Does this mean 4m is safe? No — they could still have a 1m4m wait.

When someone discards an “outside” tile, in this case a 7m, the remaining 1m4mwait is called To’oi-suji. These are pretty useless; you can’t discard the 4m because it’s still dangerous. However, if it’s a toss-up between discarding 4m or 4s, for example, then 4m is slightly safer because it completes fewer waits.

Now let’s suppose both 1m and 7m have been discarded. THEN it’s safe to deal the 4m, because both 1m4m and 4m7m 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 4m7m. 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 3m or 5m. Let’s look at the two situations this gives us:

Case 1: 4m5m7m. 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: 3m4m7m. 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 2m5m 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
1m 3m 6m
2m 4m 7m
3m 5m 8m
4m 6m 9m
6m 1m 4m
7m 2m 5m
8m 3m 6m
9m 4m 7m

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?

1m2m3m6m7m8m6p7p9p3s4s5s9s9s

In this case, it’s a matter of choosing between a 6p7p Ryanmen or a 7p9pKanchan wait. We know that a Ryanmen is better, so we’ll probably discard the 9p 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 5p8p 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
1m 2m 5m
2m 3m 6m
3m 4m 7m
4m 5m 8m
5m 1m 4m and 6m 9m
6m 2m 5m
7m 3m 6m
8m 4m 7m
9m 5m 8m

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?

1m1m5m6m7m1p2p3p6p7p8p4s4s5s

The most efficient move would be to discard a 4s. 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 4s are 2s5s and 3s6s. 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 4s4s5s. Someone playing by the most efficient strategy possible will be trying to form Mentsu and will worry about pairs later. This is where a 4s4s5s 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 2m discard, you can be almost certain that it didn’t come from a 2m2m3m shape. This means 1m 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
2m 1m4m
3m 1m4m and 2m5m
4m 2m5m and 3m6m
5m 3m6m and 4m7m
6m 4m7m and 5m8m
7m 5m8m and 6m9m
8m 6m9m

Think about this for a second: when an opponent discards a 4s, what’s dangerous? If we consider the various Suji theories presented here, we might guess the dangerous waits are the Senki-suji 6s9s, the Ura-suji 5s8s, and the Matagi-suji 3s6sand 2s5s. In fact, the only safe tiles left are the Omote-suji, 1s and 7s! 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 3m and 8m forms an Aida Yon Ken; the interval between the two discards is 4m5m6m7m.

What do 3m and 8m have in common? They’re both Ura-suji for the same wait, 4m7m! 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, 5m6m) are concealed in the hand, and the two outermost tiles (in this case, 4m7m) are the resulting wait.

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

DISCARDED TILES AIDA YON KEN
1m6m 2m 5m
2m7m 3m 6m
3m8m 4m 7m
4m9m 5m 8m

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?”

2m4m5m5m1p2p3p6p6p3s4s7s8s9s

With this hand, we are 1 Shan Ten, and the most efficient discard would be 2m. If we discarded it, we could reach Tenpai with any of 3m5m6m6p2s5s; in total 6 tiles, 20 instances. Now suppose we get lucky and draw 2s. What should we discard now?

4m5m5m1p2p3p6p6p2s3s4s7s8s9s

The most efficient discard is 5m, as it would leave us with a Ryanmen wait. Now when the opponents look at our discards, they’ll see a 2m5m pattern and will probably be able to recreate what was in our hand without much trouble. The 2m is an Ura-suji for a 3m6m wait, and the 5m 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 2m4m5m5m shape and the 3m6m 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
1m4m 6m — 5m — 2m3m
2m5m 7m — 1m6m — 3m4m
3m6m 1m8m — 2m7m — 4m5m
4m7m 9m2m — 8m3m — 6m5m
5m8m 3m — 9m4m — 7m6m
6m9m 4m — 5m — 8m7m

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:

1p9s2s2m7z5z
8m7s2z3z4s

Example 2:

1s7z3p1z3s2m
2s8m6p6z6p5m

In example 1, the patterns that should stand out are 2m8m and 2s7s4s. The 2m could be a Senki-suji, followed by a 8m Ura-suji, suggesting a dangerous 4m7mwait. Also, the 2s7s could both be Ura-suji, forming an Aida Yon Ken around 3s6s. The Matagi-suji 4s further suggests this wait is dangerous.

In example 2, the dangerous patterns are 3p6p and 2m8m5m. The 3p could be a Senki-suji combined with a 6p Matagi-suji for a 5p8p wait. Also, the 2m could be a Senki-suji combined with a 8m Ura-suji and 5m Matagi-suji for a 4m7m wait.

Answer 1:

4m4m0m6m7m5p6p7p7p8p9p4s0s

Answer 2:

5m6m7m8m9m7p8p9p7s8s9s9s9s

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.

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