How to Think About Discard Choices
Choosing a discard that simply moves your hand toward winning should not be all that difficult.
Strong players can often spot the most efficient move at a glance.
Why can they judge it so quickly?
There are probably two main reasons.
(1) They recognize most hands as patterns, and already know which discard gives the widest acceptance
People often say that no starting hand ever comes twice.
But once you begin organizing a hand toward winning, its structure gradually falls into recognizable patterns.
Especially for shapes that appear often, you should remember the correct answer.
If you keep making inefficient choices, your results will obviously suffer.
(2) They have learned better ways to compare options
Actually counting things like “if I cut A, I get this many tile types and this many tiles, but if I cut B...” is not realistic during a game.
Even without literally counting every tile, you can still choose the discard with wider acceptance.
I think (1) and (2) together are the real essence of tile theory.
In mahjong strategy, people pay plenty of attention to (1), but for some reason (2) is rarely discussed in depth.
Example 1
Tsumo 
For example, in this hand, you cut .
That discard gives the largest number of tiles leading toward tenpai, and there is no difference in yaku value, so it is the absolute correct answer.
However, in real play, situations as clean-cut as Example 1 are actually rare.
Example 2
Tsumo
Example 1 appears often in strategy books, so many players may already recognize it as a memorized pattern.
But does a hand with three separated pairs always mean you should cut the middle pair?
Not at all.
In a hand like Example 2, where you have four pairs, the acceptance count is the same no matter whether you cut , , , or .
If that is the case, then cutting and throwing away the possibility of Iipeikou is obviously not a good choice.
I think skill (2) matters more than skill (1).
To me, pattern recognition in tile efficiency is there to:
prevent mistakes and speed up your discard decisions.
There is a limit to how much you can solve by memorization alone.
Ideally, no matter what hand you are dealt, you should be able to work out the correct answer yourself.
As an approach to tile theory, I think it works well to divide hands into these four categories:
- Three-shanten or worse
- Two-shanten
- One-shanten
- Tenpai
Why combine everything from three-shanten downward into one category?
There are two reasons. First, from appearance alone, those hands are often hard to judge by exact shanten count. Second, most of the time you are simply sorting out unnecessary tiles anyway, so there is not much need to subdivide them further by shanten number.
1. Basic Tile Theory for Three-Shanten or Worse
In the early stage of a hand, it is often best to compare options by asking:
“What do I lose if I cut this tile?”
At this stage, there is no need to be overly obsessed with reducing shanten immediately.
Of course, some choices are subtle, but when the gap between two options is small, there is no need to overthink it.
Tiny differences in efficiency still matter, but in many cases it is even more important to preserve yaku potential or think ahead about future defense.
2. Basic Tile Theory at Two-Shanten
Comparing the number of tiles that move you into one-shanten is certainly important, but if the difference is only one or two tiles, it can still be better to choose the line that gives you a thicker shape once you actually reach one-shanten.
Mahjong has an important property:
as you get closer to tenpai, your acceptance count tends to shrink.
The final real bottleneck is often:
one-shanten -> tenpai
If your acceptance is too narrow there, winning becomes much harder.
That is why it is often considered correct to sacrifice a little two-shanten acceptance in exchange for a thicker one-shanten shape.
That said, there is also a strong school of thought that says you should still prioritize the tiles that advance you to one-shanten as quickly as possible.
In practice, most two-shanten hands are either the pattern where isolated tiles remain, or the pattern where you have too many taatsu, so they are usually not that hard to sort out.
3. Basic Tile Theory at One-Shanten
At one-shanten, the number of tiles that lead to tenpai becomes the single most important evaluation point.
Even a difference of one or two tiles here should not be underestimated.
However, if the acceptance toward tenpai is unavoidably narrow, there are times when you deliberately reduce the current acceptance in order to preserve good-shape improvement.
When the acceptance count is equal, you can usually handle the choice by comparing the number of improvements into better waits.
4. Basic Tile Theory in Tenpai
Of course, the number of winning tiles is still the most important thing in tenpai.
But for ron wins, it is not true that a wait is automatically better just because the tile count is larger.
If the winning tiles are the kind of tiles that opponents are more likely to discard, that also makes for a strong wait.
Still, “how easy a tile is to come out” is hard to quantify precisely, so the basic rule should be to prioritize tile count first.
When the count is the same, it also matters to compare the number of shape changes.
Especially with tanki waits, shape changes are often plentiful.
That is the general overview.
From the next page onward, the discussion moves to concrete hand examples.
Original Japanese page: http://beginners.biz/pairi/pairi07.html