Taatsu Theory (2)
This page is about ryan-kan shapes.
A ryan-kan is a composite shape made from two kanchan blocks, such as 
.
Its acceptance count is 8 tiles, but because:
(1) it uses three tiles
(2) if it remains as the final wait, it becomes a kanchan wait
for those two reasons, in functional terms it is still nowhere near as good as a ryanmen shape.
1. Ryan-kan and Shanpon
Example 1
Tsumo 
The real question with a ryan-kan shape is often whether to take it as a ryan-kan or as a shanpon-style acceptance.
If we only look at the chance of reaching Pinfu, Example 1 seems to suggest cutting .
Drawing gives you a Pinfu tenpai.
By contrast, after cutting or , only one tile type leads to a Pinfu tenpai.
So at first glance, taking the ryan-kan seems better.
But if you judge by tenpai efficiency, the correct play here is to cut .
That is because drawing 
turns the hand into a complete one-shanten shape for Pinfu.
Tsumo
When the pair is a middle tile that can still turn into a ryanmen,
it is generally more favorable to take the shape as kanchan + shanpon rather than as a ryan-kan, because that gives you more chances to improve into a good shape.
Example 2
Tsumo
In Example 2, Sanshoku is visible, so it is tempting to cut .
However, cutting is the better discard,
because it still allows for the manzu three-sided-wait improvement.
Tsumo 
Example 3
Pon 
Tsumo
In an open hand, shanpon-style acceptance becomes even more favorable.
In Example 3, you cut and aim for a pon-ten on and .
Even if you cut and take the ryan-kan, the acceptance count stays the same,
but the speed to tenpai does not.
That is because chi can only be taken from the player on your left, while pon can be called from any of the three opponents.
Example 4
Tsumo
That does not mean shanpon is always correct.
The matter is not quite that simple.
In Example 4, it is better to cut and take the one-shanten.
That leaves more room for good-shape improvement.
Not only is effective,
even the apparently backward draw of is also effective.
Tsumo
At that point, by cutting either or , the acceptance count rises sharply.
By contrast, if you take the shanpon by cutting , then after drawing , that is not an effective tile at all.
It is a complete backward draw.
Theory Summary
2. Easy-to-Miss Ryan-kan Shapes
When a ryan-kan combines with complete sets, it becomes easy to overlook, so you need to be careful.
Example 5
Tsumo 
In a shape like Example 5, some people casually tsumogiri the .
Their attention gets drawn to Iipeikou.
But if you remove the completed set ,
the pinzu part is really a ryan-kan shape: .
If you discard here,
you erase the acceptance on .
Example 6
Example 6 is an Ittsuu one-shanten hand, but the manzu part is a ryan-kan shape.
So even if you later draw a safe tile, do not carelessly cut ,
or you may miss the tenpai chance from drawing .
3. Irregular Ryan-kan Shapes
Very occasionally you encounter what might be called a split ryan-kan shape.
For example:
This is a six-tile shape with eight tiles of acceptance.
Example 7
Tsumo
You often encounter this shape when giving up on Ittsuu.
In Example 7, you naturally switch your target to Menzen Tanyao Pinfu Iipeikou.
But cutting and cutting are worlds apart.
If you choose the latter, you lose the kanchan acceptance.
Tsumo
Tsumo
Original Japanese page: http://beginners.biz/pairi/pairi05.html