Tile Theory at One-Shanten (4)
This page looks at headless one-shanten shapes.
To state the conclusion first:
with this kind of hand, the widest choice is usually to keep the head unfixed and preserve it as “taatsu + taatsu.”
This is especially true when you already have a concealed triplet, or when one of the taatsu can become a composite shape.
Example 1
Tsumo
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
    |
28 |
|
|
16 |
|
|
16 |
|
 |
17 |
Here all the discards that leave the hand at one-shanten are listed, together with their tenpai chances.
It should be clear that discarding is overwhelmingly superior.
And when it reaches tenpai, it is guaranteed to be a ryanmen wait, so there is hardly any room for debate.
Example 2
Tsumo
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
24 |
|
|
12 |
|
|
12 |
|
|
17 |
If one of the two taatsu is a bad shape, then breaking that bad taatsu also becomes a serious option.
Keeping two taatsu still gives more ways to reach tenpai, but if the souzu side fills in, every one of those tenpai outcomes becomes a kan wait.
By contrast, if you discard , tenpai will probably arrive a little later, but it is guaranteed to be a good-shaped tenpai.
Breaking the bad taatsu can also make later improvements more likely to turn into a hand that is easier to win with.
Tsumo 
If the hand changes into this shape, it becomes a 7-type, 25-tile one-shanten, and even the tenpai chances themselves beat the “taatsu + taatsu” route.
Of course, the hand will not always improve that neatly.
If you need to hurry to tenpai, remember how strong discarding is for speed.
In actual play, there are not many situations where you can afford to deliberately slow your tenpai down.
Example 3
Tsumo
Finally, here is a headless one-shanten with two bad taatsu left.
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
20 |
|
|
8 |
|
|
8 |
|
|
13 |
In this case, you should simply give up on insisting on a good-shaped tenpai.
Of course a riichi hand is better with a good wait, but this shape just does not support that expectation.
So the best choice is to discard , which gives the largest tenpai chance.
First aim for tenpai. After tenpai, you can decide whether to riichi and attack, or stay dama and fold later if you draw a dangerous tile.
Everything above has been the pattern with a concealed triplet.
From that, one clear conclusion follows:
in headless hands with a concealed triplet and two taatsu left, fixing the pair is absolutely the wrong choice.
For example, consider this hand:
Even cutting here to fix the pair is a mistake.
Compared with discarding , the difference in acceptance is enormous.
Theory Summary
Leaving the pair unfixed gives more ways to reach tenpai than fixing the pair in advance.
If there is no concealed triplet in the hand, another concern appears: leaving two taatsu may end in a tanki wait.
Example 4
Tsumo 
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
28 |
|
|
16 |
|
|
17 |
In pure tenpai chances, discarding is still overwhelmingly better.
But if you draw , the hand becomes a tanki wait.
Out of those 28 tiles, only the 12 vertical draws of produce a ryanmen tenpai.
By contrast, if you fix the pair:
- a ryanmen tenpai is guaranteed
- Pinfu is also guaranteed, so there is a scoring advantage as well
As for the route that discards , if it eventually becomes the wait , that wait has two fewer tiles than .
So some players would say discarding is better even though its acceptance is one tile lower.
There is room for disagreement between discarding and discarding .
Personally I still think is better, because even if it becomes tanki temporarily, you can still wait for improvements.
Whether to fix the pair in this Pinfu-type hand is still not fully settled, so choosing by preference is acceptable.
However, if the taatsu is a composite ryanmen shape, the stronger current view is still that leaving the pair unfixed is better.
Example 5
Tsumo
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
  |
33 |
|
|
15 |
|
|
20 |
The gap in tenpai chances is even wider now.
On top of that, even if you draw , you can still take a Pinfu tenpai by discarding .
Out of the 33 accepting tiles, 26 become good-shaped tenpai.
So in Example 5, discarding is clearly correct.
Example 6
Tsumo
If one of the taatsu is bad, then breaking that bad taatsu is again a strong option.
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
24 |
|
|
12 |
|
|
17 |
In tenpai chances, keeping two taatsu by discarding is still stronger.
But discarding has three merits:
- the final wait becomes better
- the chance of Pinfu increases
- the hand is more likely to improve into a better shape
Example 6 is especially a case where the souzu are connected, so you should pay attention to good-shape improvements.
☆ Change
Tsumo
What matters is being able to judge whether you have enough room to delay tenpai.
In the late game, collecting the tenpai payment can matter more than actually winning, so the route with more tenpai chances may then be preferable.
The best play is to understand the strengths and weaknesses of each discard and choose the one that fits the situation.
Example 7
Tsumo
Finally, if both remaining taatsu are bad shapes, then you should still choose simple speed and discard .
Original Japanese page: http://beginners.biz/pairi/pairi16.html