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shouhai theory

I haven’t seen any theory out there for shouhai. For context, shouhai is a riichi game mode where you start out with one less tile, so you are playing with a 12-tile hand. In return, you get an invisible “joker” tile as your 13th tile that you can use to complete a regular 14-tile hand.

Because the goal can be considered as “getting to tenpai”, shouhai theory is essentially iishanten wait analysis. That is, your final waits in shouhai are those going from iishanten to tenpai. We will classify and analyze all the iishanten types, of which there are four:

• Five pairs
• Thirteen orphans
• Two completed groups (2-mentsu)
• Three completed groups (3-mentsu)

Five pairs

Chiitoitsu is really simple. You win as soon as you get 6 pairs (plus a floating tile, which your joker tile completes as the 7th pair). So tenpai is really getting five pairs, with two floating tiles serving as your tanki waits.

Five pair iishanten is 6 outs, 3 for each tanki pair. There is nothing else to say for now, but we will come back to five pair hands at the end.

Thirteen orphans

Thirteen orphans is similar, and much easier to achieve, thanks to the invisible joker completing a missing terminal/honor even if all four have been dealt.

To get thirteen orphans iishanten with your 12 tiles, you either need 12 unique terminal/honors, or 11 unique terminal/honors with one of them being a pair. It’s the same as regular riichi, you just need one less tile, so you probably want to go for it much more often than usual.

With the two irregular hands out of the way, we move on to the standard hand theory.

Two completed groups (2-mentsu)

When you have two completed groups (2-mentsu), you have six tiles remaining that make up your wait. There is essentially only one way to arrange the six tiles in order to achieve iishanten:

• One pair and two simple shapes, like

Here a simple shape is a two-tile shape, either ryanmen , penchan , kanchan , or a pair . If one of your two simple shapes is a pair, then both (or all 3) pairs contribute to the wait as a shanpon wait.

Unlike tenpai waits, with iishanten you get two shapes to wait on. Assume your pair is . So if you have and , you’re waiting on (12 outs). If you have and , you’re waiting on (12 outs). If you have and , you’re waiting on (6 outs). Yeah, try not to have 3 pairs.

Note that your completed groups can extend your waits if they overlap one of your waits. That is, if is one of your waits, then having extends that wait to , and having extends that wait to . For this type of iishanten, this is only relevant when extending ryanmen to sanmenchan , or extending shanpon to entotsu . So it’s enough to just notice that you have sanmenchan or entotsu when you do, and otherwise you can completely ignore the two existing groups.

In summary, to maximize the wait of your iishanten when you have two completed groups, maximize the wait of your two simple shapes.

Three completed groups (3-mentsu)

With three completed groups (3-mentsu), that leaves only three tiles to make up your wait. Even though it’s half as many tiles, the theory is much more complex. There are three ways to arrange the three tiles to achieve iishanten:

• A simple shape and a floating tile, like
• A ryankan, like
• One pair and a floating tile, like

I’m going to call these three arrangements headless, ryankan, and sticky.

Headless has a pretty simple wait: it waits on the simple shape, and the floating tile serves as a tanki wait. So waits on (11 outs). The fact that you have an extra flexible tanki wait is pretty good since you can easily wait on a wind tile, for instance.

Ryankan is when the floating tile adds onto one of the simple shape to make a 3-tile complex shape, further adding tiles to the wait. Actually, this can be in one of two forms:

• Ryankan: It extends a kanchan from e.g. to . This acts as a second kanchan, waiting on . In addition, the both serve as tanki waits, so this adds to the wait, for a total wait of (14 outs).
• Paired simple shape: It simply duplicates one of the tiles in a simple shape, like becoming . Now you’re waiting shanpon on and tanki on , so this adds to your wait, for a total wait of (10 outs). We’ll see why we ignore this case in a second.

Sticky is possibly the best one. If you have , then not only are you waiting on the pair and tanki on , you’re also waiting to turn into any simple shape, so add to your wait. (This is called a taatsu wait, and we consider a sticky tile.) Overall you are waiting on (21 outs). It’s really good.

Note that the paired simple shape case is completely subsumed by the sticky case. A paired simple shape waits on the same waits as the sticky tile, except it waits on two less tiles since your pair is always one of the waits. So you can simply consider the paired simple shape case as a worse sticky iishanten.

(Aside: In standard riichi iishanten theory there is a distinction between headless hands with a closed triplet (ankou) vs without a closed triplet, because of how it affects your tenpai wait. In shouhai we don’t care at all about the potential tenpai wait since we win with any tenpai, so we ignore this distinction entirely.)

Like in the previous 2-mentsu case, our three (!) completed groups can be used to extend our existing waits. It turns out that due to our waits no longer being just simple shapes, the extension theory is much more complex here, and it’s not enough to just look out for sanmenchan and entotsu . We’ll see why in a moment.

Choosing between 2- and 3-mentsu

Consider the following shouhai hand:

is not one of our outs, but it upgrades the 2-mentsu iishanten into a 3-mentsu. Let’s compare the waits. Our original is waiting on (16 outs). If we convert by dropping one of , say , we get waiting on (11 outs). Plus we lose our pinfu chances. Seems much worse, right?

This is generally true, but everything changes when extended shapes come into play.

Extending 3-mentsu

While 3-mentsu iishanten is not much more powerful than 2-mentsu iishanten (assuming ryanmen simple shapes), the strength of 3-mentsu comes from a richer extension theory.

With 2-mentsu, we only had simple waits to consider: ryanmen, kanchan, penchan, and shanpon. These can only be extended by sequences, and some of them are not very interesting:

• Penchan extended by : you get , which is a ryanmen ()
• Kanchan extended by : you get , which is a ryanmen ()
• Ryanmen extended by : you get , which is a sanmenchan
• Shanpon extended by : you get , which is entotsu

So you only have to look out for sanmenchan and entotsu.

With 3-mentsu, we introduce the following non-simple waits:

• Tanki waits: waiting on
• Taatsu waits: waiting on

Let’s start with tanki waits. Tanki waits can be extended by sequences two ways, and by triplets two ways. We have:

• Tanki extended by sequence : you get , which is aryanmen waiting on
• Tanki extended by sequence : you get , which is nobetan waiting on
• Tanki extended by triplet : you get , which is ryantan waiting on
• Tanki extended by triplet : you get , which is kantan waiting on

Since headless and ryankan both feature tanki waits, it is easy to extend them. In particular, if your tanki tile is not near a completed group, it takes only one draw/discard to swap it for one near a completed group.

Sticky, on the other hand, features a taatsu wait. Taatsu waits are extended by sequences:

• Sticky extended by sequence : you get , adding to the wait.
• Sticky extended by sequence : you get , nobetan. and are both sticky tiles now, adding to the wait.
• Sticky extended by sequence : you get , aryanmen, adding to the wait.

Like tanki waits, it’s just one draw/discard to swap out a sticky tile, and chances are that you’re getting something near a sequence. It’s not unusual for a sticky wait to wait on most of a suit. For example, waits on + + .

Because of the upgrade potential, it is seriously worth considering taking a 3-mentsu iishanten over 2-mentsu, even if it means breaking ryanmen.

Hybridizing with 5-pair iishanten

There is a little more to say about the 5-pair iishanten. In standard riichi, you usually consider going for chiitoitsu if you have 4 or more pairs. In shouhai, this number obviously decreases to 3 or more pairs, which is much easier to get, even though the 5-pair iishanten is one of the worst, with only 6 outs. However because of the potential for 5-pair iishanten, it is worth considering certain shapes that are often overlooked in standard riichi.

Let’s start off with iipeikou, which is the strongest shape in this category. If you’re in 2-mentsu iishanten, and your two complete groups are iipeikou , you can easily hybridize 2-mentsu iishanten and 5-pair iishanten. For example, waits on the standard , but since it is also a 5-pair hand, you are also waiting on . That gives a total wait on (18 outs). Pretty good!

Two more common shapes are tobi-toitsu and narabi-toitsu . If you have this plus another pair, it’s time to consider 5-pair iishanten. In addition, if you do get into 2-mentsu iishanten with this as your two simple shapes, it is not so bad since they serve as both a shanpon and as a kanchan or ryanmen wait. Tobi-toitsu waits on (12 outs) and narabi-toitsu on (14 outs). Obviously these are not as good as two ryanmen (16 outs) but you take what you can get, so look out for them.

There is also double aryanmen . In standard riichi, this shape is good in iishanten since it waits on and upgrades into ryanmen with . In shouhai, we can consider this as part of a sticky iishanten where the sticky tiles are and , so it wholesale waits on , just like the nobetan . So it is very good to have even if you don’t end up going for 5-pair iishanten.

Finally we have ryankan pair, . Standard riichi likes this shape since it’s waiting on to form a pair and a group. Shouhai likes this shape too for the same reasons, but also because of the two pairs it contributes – again, if you have this plus another pair, it’s time to consider 5-pair iishanten.

Yaku considerations

Obviously, every yaku is easier to get in shouhai than in standard riichi, so in your EV calculations expect scores to be higher than usual. (Though if you’re calculating EV while playing shouhai you might benefit from touching grass.)

Some yaku get more benefit than others:

• Chiitoitsu: As discussed above there are many more routes to a 5-pair hand, and a 6-out tanki wait in shouhai is better than a 3-out tanki wait in standard riichi.
• Pinfu: In fact a taatsu wait in sticky iishanten is a ryanmen wait no matter what. If your sticky tile is , then all complete a ryanmen; just place the joker in the correct spot. This also applies to extended taatsu waits. (Here is still a tanki wait, so it won’t count as a ryanmen wait, unless you have aryanmen or something.)
• Sanshoku doujun: You’re looking to complete only 7 of the required 8 tiles for sanshoku, which is much easier to force, especially when one of them is your sticky tile in sticky iishanten.
• Ittsu: Likewise you only need 7 of the 8 required tiles for ittsu, and it’s not the end of the world if all 4 of them have been thrown. This makes ittsu much easier to get.
• Chanta/Junchan: The hardest part here is often getting keeping a pair of terminal/honors. In shouhai a single terminal/honor becomes a pair, so feel free to pon away your real terminal/honor pair since you can get one with ease.
• Sanankou: If you have a triple shanpon wait like , plus another triplet, that’s actually all you need for sanankou, if you tsumo.
• Yakuhai/Shousangen: Although you can’t pon with your invisible joker tile, you only need a yakuhai pair to make a triplet.
• Iipekou: No more waiting for the “correct” tile to complete this thing, your joker is always the correct tile.

Also all yakuman are much easier so definitely consider going for them more often.

Defense

Furiten is still a thing in shouhai. If you got the above iishanten theory down, then you should have no trouble navigating furiten while playing, but how does this translate to analyzing others’ plays for defense reasons?

Here I list the standard riichi strategies for defense and how they differ in shouhai.

• Genbutsu: Discarding a tile someone else has discarded is 100% safe against them. Always works, let’s move on.
• Suji: Suji still works, but it’s somewhat less effective. For starters, 5-pair iishanten is easier to achieve, and suji is useless against it. For 2-mentsu hands, suji is 100% effective against a ryanmen-ryanmen 2-mentsu, but since the opponent has to build 2 shapes, it’s not as likely that both of them are ryanmen (compared to standard riichi, where you only have one shape so it better be good). For 3-mentsu hands it depends on the arrangement. Headless iishanten includes a simple shape that could be ryanmen, but you also have a tanki, so suji isn’t very effective. Suji is useless against a ryankan iishanten. But for sticky iishanten, suji is incredible, because every wait of a sticky iishanten is technically a ryanmen wait, save the tanki wait on the sticky tile itself.
• Early sotogawa: The idea behind sotogawa is that if a player ends up waiting with or or it’s unlikely they would have dealt away early, since those tiles all upgrade those shapes. Therefore if you do see early, then are much safer. This doesn’t change in shouhai, I think, because shapes like are indeed still strong early-game. Honestly early sotogawa might be one of the stronger defense strats in shouhai.
• Kabe: The main thing that changes in shouhai is that the joker tile can act as a 5th tile (provided the other 4 tiles are not in hand). So just because all four have been cut doesn’t make much safer, as it can still be part of a nefarious taatsu wait with the joker acting as . Also tanki waits are more common, which kabe is useless against. So kabe is weaker in shouhai.
• One-chance: Absolutely weaker in shouhai. This is because in 2-mentsu you have two shapes that make up your wait instead of one. So it’s basically twice the possibility that the one-chance tile will actually deal in. In addition, tanki and taatsu waits are more prevalent, which one-chance is helpless against.
• Watching for tedashi: This is important against open 3-mentsu hands. Since it’s so easy to swap out the tanki or sticky tile it’s easy to completely change your wait in 3-mentsu, so watching for tedashi is invaluable.
• Terminal/honors: These are actually more dangerous in shouhai due to headless iishanten, which features a tanki that can be easily changed to a terminal/honor tile. On top of this, 5-pair iishanten is easier to achieve, and have two tanki waits that can also be easily changed to terminal/honors. Honestly I feel like 2/8 is a bit safer than terminal/honors due to this.
• Reading calls: Given that certain yaku are much easier to achieve in shouhai, you will probably see some more obvious calls for things like chanta. I don’t think there’s much to see beyond that, though.
• Mind games: Given the increased mental processing power required for shouhai I don’t really know if psyching your opponent out with weird discards works better (due to adding even more pressure) or worse (due to others not having the capacity to focus beyond their own hand).

Closing

I have barely played shouhai and I pulled most of this theory out of my ass based on what I know about iishanten theory in standard riichi mahjong, so take everything I have said here with a large pinch of salt.

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