Tile Theory at One-Shanten (5)
Continuing from the previous page, this one also examines headless shapes.
By now it should be clear that turning the hand into taatsu + taatsu is usually the widest choice.
But what about a shape like Example 1, where only one taatsu remains on the outside?
Example 1
Tsumo 
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
    |
20 |
|
 |
21 |
|
|
21 |
As you can see, there is almost no difference here.
Even so, drawing produces Pinfu only if the manzu side is kept.
And the wait on is also better than - or -.
So discarding can be ruled out; it is clearly inferior.
Then which is better, discarding or discarding ?
When the acceptance count is the same, the basic rule is to compare good-shape improvements.
If you keep the inner , then improvements like Change A and Change B become available.
In other words, for a pseudo-ryanmen shape, keeping the inside tile is better.
Change A
(10 types, 33 tiles)
Change B
(9 types, 29 tiles)
Example 2
Tsumo
In headless shapes, good-shape improvements are a very important factor.
Many players would casually discard from a hand like Example 2.
But a one-tile difference in the current acceptance is not a big deal at all.
You need to think in terms of continuing to build taatsu + taatsu out of the connected manzu shape.
If you discard in Example 2, the current acceptance is only 5 types, 17 tiles.
It should be clear how painful it is to miss improvements like Change A and Change B below.
Change A
(10 types, 33 tiles)
Change B
(9 types, 29 tiles)
Example 3
Tsumo
So far the discussion has put tenpai chances first.
But the quality of the final wait also needs some consideration.
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
23 |
|
|
25 |
The width of the taatsu + taatsu shape in tenpai chances is so strong that it can almost be called absolute.
Even against a possible four-sided wait, it still comes out two tiles ahead.
But a penchan is a miserable wait.
So in this hand, dropping still gets you to a win faster overall.
Example 4
Tsumo
By Example 4, the choice becomes very close.
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
31 |
|
|
24 |
The strength of discarding is that it guarantees a tenpai with at least a ryanmen wait.
But I still think discarding , which often reaches tenpai faster, is more profitable.
Example 5
Tsumo
Finally, compare keeping a five-sided wait shape with keeping two ryanmen taatsu.
| Discard | Tenpai chances | Acceptance count |
|---|---|---|
|
|
28 |
|
|
28 |
The tenpai chances are exactly tied.
So now you compare the final waits after riichi.
Because it can leave a five-sided wait, Example 5 is better if you break either or .
It also has one extra type of acceptance that reaches a Pinfu tenpai.
Theory Summary
The basic comparison is still acceptance count, but when the difference is tiny, you also need to include the quality of the tenpai wait and the value of good-shape improvements.
Original Japanese page: http://beginners.biz/pairi/pairi17.html