Standard 1-Shanten With Yonrenkei

Yonrenkei, the crown jewel of four tile shapes. Early in our studies of tile efficiency, we learned its utility. It serves as two floating tiles, easily creating ryanmen blocks; or (equivalently) seen as two ryanmens conjoined at the hip; it can grow to form a sanmenchan; or a nobetan wait finding our pair. We quickly learn to love the shape and keep it around, and in return, the yonrenkei returns the favour and give us improvements in our hand.

However, as we approach tenpai, it becomes increasingly harder to justify using 4 tiles for one block. Players, seduced by its beauty, often opt to keep it longer than reasonable, hence stifling the growth of other blocks, leading to an overall loss of tile efficiency. Today, let us study how to handle the yonrenkei as we get to 1-shanten.

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Types

Recall the three types of 1-shanten:

• Standard (2 mentsu with a pair)
• Headless (3 mentsu without a pair)
• Kuttsuki (3 mentsu with a pair)

The standard shape occurs the most frequently in our games. Thus, to keep this article short and to maximise the efficiency of our study, we shall restrict the scope to standard 1-shanten hands with a yonrenkei. Our yonrenkei would be one of the two completed blocks, leaving 5 tiles to divvy up between the two incomplete blocks. Our classification will be based on what our two incomplete blocks are:

Floating Tile

The utility of a floating tile is primarily safety or improvements. We shall first consider the safety aspects.

In Hand A1, we have two ryanmen. There are two benefits to keeping the yonrenkei around: we can upgrade a ryanmen to sanmenchan, and on a 47m draw, we can discard 11m to aim for a tanyao hand. The main takeaway is that the first factor is fairly insignificant. With a strong ryanmen-ryanmen 1-shanten, our primary focus should be for safety and not further upgrades. Thus, we will cut 7m (or 4m).

If we are behind on points, we can consider aiming for tanyao. In those situations, cutting 4z is acceptable. In a flat situation, we generally would not greed for an upgrade from a 3900 hand.

In contrast, for Hand A2, we still have weak kanchan block. This is not strong enough to retain a safe tile, and we should focus on shape upgrades. We will cut 4z here and maintain our yonrenkei.

The floating tile might also be beneficial efficiently. Here, under our classification, this would be a ryanmen (78s) & weak group (99s pair) & floating tile (3m). But, we can treat the 7899s aryanmen as a single block, thus this is a kuttsuki 1-shanten. Between 9s and 3m, we should cut 9s to maximise acceptance.

Finally, we should be careful that our floating tile is indeed a floating tile.

On the surface, one may accidentally regard the 1p as a floating tile. However, we have an extended ryankan shape (134568p) and thus the actual floating tile is 9p. Every other tile is used, and our best option is to cut 9p.

There is a potential ittsu in the pinzu, but the tile acceptance between a two weak shape 1-shanten and a ryanmen ryankan 1-shanten are worlds apart. Moreover, we can get a pinfu 50% of the time. Thus, we will not cut our 56s ryanmen (cf. Nemata et al., Modern Mahjong, Ch6 Ex21).

2 Ryanmen

The strength of yonrenkei lies in its potential. As such, with strong ryanmens as our incomplete blocks, keeping the yonrenkei around for upgrades becomes less appealing.

With a perfect 1-shanten, we shouldn’t consider upgrades. Hence, we straightforwardly cut from the yonrenkei. Here, cutting 2m allows us to keep the 345 sanshoku possibility.

In general, with any yaku (on top of pinfu) or dora, we will prioritise the perfect 1-shanten. However, with only pinfu and dora 0, taking the perfect 1-shanten might lead us to a sinful riichi nomi (with a good wait). Consider the following example,

We should instead cut 6m to take a ryanmen-ryanmen 1-shanten instead as we can preserve the high value aka dora floating tile. The author would like to note that they personally will also cut 6m if 222m was replaced with 123m, with a pinfu nomi hand. In this variation, 0m is acceptable as well.

This question tests how we partition the hand. If we naïvely treat this as a standard shape, 4567m + 340p + 667p + 34s + 55s, we will cut from the yonrenkei as per our above discussion, to take the perfect 1-shanten. This is wrong. Remember that general principles are never a substitute for concrete calculation.

This hand should instead be viewed as a kuttsuki 1-shanten: 4567m + 340p + 66p + 345s (with 7p5s floaters). If we compare the aryanmen 3455s to the yonrenkei 4567m, cutting from the aryanmen will lead to better acceptance, and also better chance of a good wait tenpai. Thus, we should cut 5s from this hand. This is a general theme, don’t downgrade a complicated headless or kuttsuki 1-shanten to a standard 1-shanten.

Ryanmen+1 & Weak

I used to frequently mistreat this class of hands. For beginners, this should be the main lesson from this article. On the surface, we have three options:

1. Cut from the yonrenkei. In our example hand, this would be 36m.
2. Cut the +1 tile from the ryanmen+1. In our example hand, this would be 8s.
3. Cut the weak group and revert to 2-shanten. Here, we will be cutting 13p.

When pigeonholing our hand into 5 blocks, the first option seems rather attractive. However, this should only be done if our yonrenkei is bad, like an edge 1234 yonrenkei, or with an exceptional hand, like hand C7 later. First, let us see some examples where the second option is preferable.

The five block theory says that cutting 2p (or 5p) gives us the maximum acceptance. This is true, but we shouldn’t give up strong improvements like our yonrenkei and end up with a weak shape tenpai. Here, we also have an additional incentive with the 8m being dora. Do note that the reasoning of “securing the dora” is also short-sighted, as we could draw another dora 8m.

All in all, we should cut 7m here with the reasoning “the yonrenkei allows us to upgrade the weak shape to a good shape”. We are willing to give up immediate acceptance, for better acceptance at tenpai. As we already have a dora, we are also willing to give up additional dora acceptance. This is the ideal thought process behind our 7m cut, learning this will allow us to apply to similar situations.

After the above discussion, this is now straightforward. For Hand C2, Give up the four tiles of immediate acceptance to avoid having to tenpai on 7p penchan. We should cut 3s from this hand. Similarly, for Hand C3, cut 6s from the ryanmen+1 shape. Now, let us see a situation where we disagree with Uzaku et al. .

From this hand, Uzaku and Fukuchi recommends we cut 6m, cutting the yonrenkei while eyeing the 345 sanshoku. We can think of a ryanmen-kanchan shape in the pinzu as an extended ryanmen+1 shape. It uses 6 tiles, giving a mentsu, a ryanmen, and a follow-up tile that gives an additional 4 tiles of acceptance. Thus, by our above discussion, we should cut 8p from this hand. Our hand now has even higher value, so the value of a good wait increases even more.

However, we also need to consider two additional factors when comparing 6m and 8p. The first is whether we intend to riichi the hand while waiting on 35s kanchan with sanshoku. This is a 3 han 40 fu hand waiting on a kanchan middle wait with 3 copies remaining (note the dora indicator). Thus, we will not riichi this. This makes keeping the 8p less appealing, as the additional 7p draw leads to this.

The other main consideration is if we do intend to open this hand, we do lose the 7p chii for tanyao sanshoku dora 1. But once again, this is waiting on the kanchan middle tile, so it is an acceptable loss. Note that we can still chii-ten 4s as we have tanyao (albeit without a choice for a ryanmen or sanshoku).

NAGA also unaninimously supports our approach of cutting 8p. Indeed, if we make the 5s into 0s (double dora), NAGA still prefers to cut 8p. Only Omega shows a slight preference for 6p with the double dora change.

Next, we consider the possibility of reverting to 2-shanten by dropping the weak group. For Hand C5, we should cut 1m as we have the potential of +2 han. Moreover, the eventual wait is likely a good shape. Hence, it is acceptable to lose the direct draw of 3m even with a dora and aim for +2 han.

However, for Hand C6, cutting the 12m penchan is only looking for pinfu upgrades. Without the tanyao upgrade, even without any dora, we can’t afford to revert shanten. As such, we will take the direct option of cutting 6m. (Note that Hand C2 is similar, even though it is much closer to tanyao, tanyao is far from guaranteed.)

This is where our classification fails us. On the surface, this can be partitioned into a ryanmen+1 & weak shape: 2345m + 234p + 66s + 667s + 57p. However, as we shall see from the table below, this hand is far stronger. Let us compare the three main candidates, cutting from the yonrenkei (2m), ryanmen+1 (6s) and weak group (7p).

Cut	Bad Wait	Good Wait	Very Good Wait
2m	7s (3 Tiles)	7p58s (11 Tiles)	256p (10 Tiles)
6s	25m (6 Tiles)	578s (11 Tiles)	6p (4 Tiles)
7p		25m25p58s (20 Tiles)

In this problem, the strength of the resulting groups make the behaviour more characteristic of two strong groups, and thus, we should instead look towards cutting from the yonrenkei. The choice between 2m and 5m is due to 3m being the dora. If we do end up drawing a manzu dora, incorporating it is easier with an aryanmen rather than a nakabukure.

Interestingly, NAGA disagrees with Uzaku et al. here and opts to cut 7p, perhaps not intending to take tenpai on 7s draw and wish to avoid furiten, or to better incorporate a dora 3m draw. Only Kagashi considers 2m slightly favourable to 7p. Even snakes get charmed by the seduction of the yonrenkei! The author disagrees with this assessment, and will personally cut 2m.

The failure of our classification is as the groups can be partitioned as 666s + 67s, so this is an ankou headless 1-shanten, reinforcing the maxim that we shouldn’t downgrade our 1-shanten for ease of classification.

Ryanmen & Ryankan

Having a ryankan is often awkward. An 1-shanten with 16 tile of acceptance can be good enough, and when our hand is pinfu-compatible, half the time we can fill out the ryankan and get a pinfu. Another key aspect is the difficulty of improving the shape to a ryanmen-ryanmen 1-shanten, thus requiring us to decisively choose between acceptance and improvement.

Let us begin by learning the factors that make us choose to cut the yonrenkei.

A 1234 yonrenkei barely offers any improvement at all. At best, it is a way to hold a floating middle tile, with a lot less risk. Another factor is if our ryankan can lead to improvements, like the shape here (this is strictly speaking a ankou headless 1-shanten). The last factor to note is the presence (or absence) of another han, such as a dora. We shall explain the last factor in greater detail in Hand D4.

The turn counter is an important aspect to decide whether to pine for improvements or to focus on tile acceptance to tenpai. Let us look at some more “typical” hands.

The tipping point is turn 6. Earlier than that, we tend to prioritise the yonrenkei for improvements and afterwards, we tend to cut the yonrenkei for tile acceptance. However, if we have a pinfu when we end up with a good-shape tenpai, we would instead keep strong floating tiles around until turn 9.

For example, hand D2 has no dora and has pinfu chances, so turn 9 and earlier, we will cut 8s but afterwards, we will cut 7p from the yonrenkei. The reason we cut 8s instead of 4s from the ryankan is to maintain aka 0s acceptance and 3s upgrade. For hand D3, there isn’t any pinfu chance. Thus, until turn 6, we will cut 5s. Afterwards, cutting 7p from the yonrenkei is preferred.

For Nemata et al., hand D4 values the strong floating tiles even more, due to dora acceptance and pinfu chances. Thus, Nemata and Fukuchi recommends us to keep the yonrenkei until turn 12.

The author insteads follows the approach of NAGA. This hand already has one dora, as such it is more valuable to quickly form a tenpai hand. When we already have a dora, the potential of the pinfu is less. Thus, turn 6 and earlier, we should cut 8s from the ryankan. Afterwards, we should cut 7p, trying to get a riichi pinfu dora 1 hand as quickly as we can. The difference with D3 is not the dora acceptance, but rather that it already has value.

Here is an more extreme example,

This hand has a dora, tanyao, 567 sanshoku and pinfu chances. Moreover, the yonrenkei is slightly hampered by its proximity to our ryanmen. As such even on turn 2, we should cut 2s directly.

Ryanmen & Weak+1

We are out of the woods, with the most complicated cases over. For this shape, we would cut from the yonrenkei to maximise acceptance, unless both of the following conditions are met:

• The turn count is early enough.
• The other pair in our hand is a terminal pair.

The reason is found by studying the difference between a weak+1 shape and a ryankan. We shouldn’t cut from the weak+1 shape if we would hold onto the ryankan. Note that we often will cut to form two pairs rather than a kanchan. Thus, a good heuristic for the turn count being early enough is if we change the weak+1 shape into a ryankan, we will cut from the ryankan.

Another difference is that a ryankan tends to only have one draw to upgrade to a ryanmen, however, with two pairs, drawing tiles adjacent to either pair will form a ryanmen. This advantage is negated if the other pair in our hand is a terminal pair. This is the justification with the “two pairs is best” idiom, the flexibility of two pairs allow upgrades in the hand.

With one dora, this hand is similar to Hand D4. Thus, turn 7 is already too late to cut from the weak+1 group. As such, we should cut 8m and prioritise acceptance.

The author also believes that without the aka dora, it is also correct to cut 8m. Here, the hand would be similar to Hand D2 instead, so turn 7 is early enough. However, as our other pair isn’t a terminal pair (22p), and with the potential ittsu, this hand leans towards 8m being cut.

Removing both factors of ittsu and aka dora, this would be a controversial hand. The author’s personal approach is to cut 8s on turn 7 and earlier and 8m after. After all, we want to do our best to avoid a riichi nomi. Note that 6s is also a possible consideration when creating your own style.

2 Weak Groups

With two weak groups, we would think about returning to 2-shanten by cutting one of our weak groups. Here, it is convenient to think of a yonrenkei as two ryanmen groups.

On Turn 4, we will cut 8p here to revert to 2-shanten and attempt to extend the manzu yonrenkei or draw a improve to a ryanmen. We shouldn’t lock in bad shapes so early on. However, how early is too early?

For this hand, Nemata and Fukuchi recommends we can revert to 2-shanten as late as turn 9. Turn 10 and onwards, they recommend cutting 7m as there isn’t enough time left to get to tenpai. The author agrees with this assessment, but in practice, with a weak hand, the board state influences this decision greatly.