Taatsu Theory (1)
1. Basic Tile Theory
There are five points to look at when evaluating taatsu.
(1) Acceptance count (how many tiles complete the set)
(2) Improvement into better shapes (three-sided waits, ryanmen, ryan-kan, and so on)
(3) Hand value (yaku and dora involvement)
(4) How likely the wait is to come out once you are in tenpai
(5) How many copies seem likely to remain in the wall
This page evaluates taatsu using only the two most basic criteria, (1) and (2).
Also, the ranking of taatsu introduced in Chapter 1 should already be treated as basic common knowledge.
Ryanmen ＞ Ryan-kan ＞ Kanchan ＞ Penchan
2. Direct Comparison
Now let us compare real one-shanten hands with taatsu overload shapes.
Strictly speaking, "taatsu overload" is the more accurate term, but in practice these are often just called "mentsu-over" shapes.
Example 1
By the basic taatsu ranking, you discard the penchan .
Example 2
Here again, since ryanmen is better than kanchan, you should remove the pinzu kanchan.
However, it is best technique to start by cutting from , so that 
remains an effective tile.
When dropping a kanchan taatsu, there are many cases where you should cut from the outside inward to preserve shape improvement. Of course, if safety matters more, there are also times when the correct order is inside outward.
Trying to chase Sanshoku or Tanyao by cutting is a way of breaking your own hand and can only be called completely wrong.
What matters is to look at the hand structure itself: "This hand already has two complete sets and one pair, and still needs two more sets, so one of the three taatsu must be unnecessary."
Example 3
The two kanchan taatsu have the same acceptance count,
so we compare the pinzu and souzu blocks by how easily they improve into better shapes.
| Ryan-kan improvement | Ryanmen-or-better improvement | Shanpon + kanchan improvement | |
|---|---|---|---|
| Pinzu | |
|
|
| Souzu |  |
  |
|
Once you compare them, it is clear that the pinzu kanchan improves into good shapes more easily, so the correct answer is to drop the souzu side.
As for the order of discarding , either order is fine.
In practice, you will often cut the more dangerous first.
Example 4
This is a comparison of three kanchan shapes.
The best one is the manzu kanchan, because drawing 
or turns it into a three-sided wait.
Between the pinzu and souzu shapes, the souzu one is less likely to improve into a ryanmen,
so from the standpoint of tile theory, the correct answer in Example 4 is to cut .
Example 5
Example 5 compares three ryanmen taatsu.
The conclusion is that you should drop .
The two manzu ryanmen shapes overlap on ,
so if you reject the souzu ryanmen instead, you lose four tiles of acceptance.
If you dislike the souzu side and then conveniently draw , it does become a three-sided wait.
But even taking that into account, cutting the manzu side wins in pure speed to agari.
This kind of overlap in taatsu acceptance is called nido-uke, or "double acceptance," and is generally inefficient.
There is not much difference between the two manzu sides, but if you drop , then drawing also leaves a Sanshoku possibility, so we take that as the model answer.
Of course, cutting is the worst possible discard.
Even if you first secure one-shanten, Tanyao can still be pursued.
Example 6
Very few people would make the wrong cut in Example 6,
but this is the same principle: the manzu creates nido-uke and narrows the acceptance.
So the correct discard is .
Theory
Original Japanese page: http://beginners.biz/pairi/pairi04.html