Early-Hand Tile Theory (1)
One of the hardest parts of tile theory in hands that are three-shanten or worse is deciding how much weight to give to yaku value.
Even if your current acceptance becomes a little narrower, the speed to tenpai can reverse once calling is taken into account.
To keep the conclusions as clear as possible, this page discusses the problem from the standpoint of menzen efficiency.
As an introduction to early-hand tile theory, let us start with hands that still contain several floating tiles.
Example 1
Tsumo 
=> Cut
When a hand still has isolated tiles, you can simply compare the functions of the remaining isolated tiles.
Here,
are the isolated tiles that do not currently belong to a set, taatsu, or pair.
The weakest one is obviously .
can only improve by drawing another to make a pair or triplet.
The suited tiles are clearly more valuable because they can become sequences.
So the only correct discard here is .
Cutting would not create some huge loss immediately, but if you draw
without drawing 
, you would fail to make one set.
There is simply no reason to cut here.
Example 2
Tsumo => Cut
Cutting would also be completely acceptable.
However, in this hand, whether you later draw or , the eventual discard will still be .
In other words, just like an honor tile, it has almost no use except pairing up.
If that is the case, then may actually be slightly more valuable.
If someone riichis on the next turn, you can immediately discard it. Even if it pairs up first, it can still become two safe tiles later.
Theory Summary
Example 3
Tsumo => Cut
There are four isolated tile types here, so you cut the least valuable one.
For suited tiles, the general relationship is:
1 and 9 < 2 and 8 < 3 to 7
So and are the leading candidates.
Which of those two you cut first is not extremely important.
But because there is already a suji tile in , even drawing both and will not create a real loss.
By contrast, if you cut , then drawing both and would cost you one full set.
So the standard discard is to cut first.
Example 4
Tsumo 
=> Cut
The isolated tiles here are
.
If you look only at menzen riichi efficiency, even the yakuhai could be discarded.
But in a hand this weak, the speed boost from pairing a yakuhai and calling on it is too important to ignore.
So as long as there are other useless tiles left, you should not discard the yakuhai first.
You keep because there is no tile like
that can properly support it. That leaves the pinzu tiles for comparison.
There are suji tiles on both sides in
,
but is already tied up inside the complete set
.
If you cut , you lose out in the case where you draw
without drawing
.
That makes the least valuable tile.
Example 5
Tsumo => Cut
When comparing suited tiles against each other, you should preserve the more connected shape.
Even if both are terminal tiles, a one-gap connected shape is still stronger than a completely isolated terminal tile in both acceptance and good-shape improvement.
That point was already covered in Chapter 1: Four-Tile Composite Shapes.
Also, in an ordinary sequence-based hand, an isolated terminal tile is always worse than any pair or taatsu.
Of course, this does not apply when yaku such as Honitsu are involved.
Trying to build your hand around tiles like
is generally a very disadvantageous choice.
Theory Summary
Example 6
Tsumo => Cut
In Example 6, the comparison is between
and
.
The key is the tile you just drew: .
If you cut , then drawing afterward still creates a kanchan taatsu.
But if you cut , then drawing afterward becomes a complete loss.
That is another example of why holding isolated floating tiles along a suji line is disadvantageous.
This was already discussed in Chapter 2: The Theory of Floating Tiles.
The difference between cutting and is not huge, but cutting is simply a bad move.
It is basic mahjong knowledge that a 7 tile is more useful than an 8 tile.
And here there is also Iipeikou value involved, so the yaku loss is significant.
For some reason, some people still feel uncomfortable keeping the shape this way...
Example 7
Tsumo => Cut
What you need to watch out for in a shape that combines an ankou with a four-tile connected shape is the case where the hand already has two or more pairs.
In that case, you no longer need another head, so you cannot evaluate the connected shape as “one set plus one pair.”
You must evaluate it as a block that still has to produce two complete sets.
Once you see it that way, it becomes clear that this block is actually quite hard to use.
is thin enough already, and even if you draw
,
the resulting shape is still awkward.
By contrast, the isolated is better, because at least it still has the possibility of improving on a draw of .
Original Japanese page: http://beginners.biz/pairi/pairi08.html