I'll be separating the article into parts because it's really long. :(
We're basically at the end of the riichi theories, which is also the hardest part to understand.
Everyone should have had hands that can go into tenpai with different waits, and hands with a good shape that has a lower value than hands with a bad shape. For example:
This hand has three choices.
1. Good shape(Discard 7 sou) riichi
2. Bad shape(Discard 4 sou) damaten
3. Bad shape(Discard 4 sou) riichi
As mentioned before, you should declare riichi when you have a good shape, therefore there's no need to consider the first option.
The point of this article is to find out which is the correct method.
I'll first introduce an important theory.
The winning rate of riichi with a good shape is similar to that of damaten with a bad shape.
This theory is based on the huge amount of statistics by 凸本. If riichi and damaten has the same amount of points, it is more advantageous to declare riichi. This is due to ippatsu and ura-dora.
For this type of hand, discarding 1 wan and declaring riichi is better than discarding 4 wan and staying in damaten.
As for the example in the beginning, riichi with a good shape is 3900 points, while damaten with a bad shape is 5200 points. Similarly, riichi with a good shape is definitely better than damaten with a bad shape. A 3900 points ryanmen riichi has a winning average of 6000 points and above.
Then how does a good shape and a bad shape compare when declaring riichi?
For this kind of points, the good shape is more advantageous. The riichi with the bad shape is 4 han 30 fu, the effectiveness of ura-dora etc will be reduced. However, the winning rate will be a grade lower and the expected value is not comparable to that of the riichi with the good shape.
Hence, unless it's all last where you need tsumo haneman or other special situations, declaring riichi with a good shape is the correct answer. This sort of shape is worthwhile for everyone to take note.