Basic Waits (1)
The tiles that complete your hand are called your wait. Mahjong has many different kinds of waits, but the fundamental ones are only the following five. Every multi-sided wait is built on top of these basics.
Basic Wait Types
| Example shape | Name | Winning tiles | Number of winning tiles |
|---|---|---|---|
 |
Tanki wait | |
3 |
  |
Penchan wait |  |
4 |
  |
Kanchan wait |  |
4 |
  |
Shanpon wait | |
4 |
  |
Ryanmen wait |   |
8 |
The table above makes the strength of ryanmen stand out immediately.
Tanki may look weak at first glance, but it often has many ways to improve. And if you are waiting on an honor tile of which one copy is already visible in the pond, it can actually be a very practical wait beyond what the raw tile count suggests.
Shanpon is also sometimes called shabo.
Besides these, the following waits also appear often in actual play.
Nobetan and Pseudo-Ryanmen
| Example shape | Name | Winning tiles | Number of winning tiles |
|---|---|---|---|
    |
Nobetan | |
6 |
|
Pseudo-ryanmen |  |
6 |
Nobetan is really a combination of two tanki waits. As a shape for building sets it is first-rate, but unfortunately, as a final wait it is only an ordinary six-tile wait.
Pseudo-ryanmen is a shape where one side of a ryanmen is fused together with the pair, so it has two fewer winning tiles than a pure ryanmen wait.
Example 1, unlike nobetan, can win as Pinfu.
(Example 1) 
In Example 2, a nobetan wait cannot win by ron unless you declare riichi.
(Example 2) 
Pseudo-ryanmen also has another feature: it can be interpreted as a tanki wait.
(Example 3) 
Riichi Tsumo
In Example 3, if you pull out the set ,
what remains is a tanki wait on .
2 fu for tanki + 2 fu for closed tsumo + 8 fu for a concealed terminal/honor triplet = 12 fu
That rounds up to 40 fu, making the hand 1300-2600.
If you draw , the hand can only be taken as an ordinary ryanmen.
And if you ron on , it falls short by 2 fu.
So this is a high-value branch that exists only on tsumo.
Mahjong follows the principle of taking the highest-scoring interpretation, meaning you must score the hand in the way that yields the most points. So in Example 3, calling the win "1000-2000" would actually be an incorrect score call. There is no penalty for saying it, but you should be careful.
Ankou Composite Waits
| Example shape | Name | Winning tiles | Number of winning tiles |
|---|---|---|---|
|
Penchan tanki | |
7 |
|
Kanchan tanki | |
7 |
|
Ryanmen tanki | |
11 |
These are the shapes that were also introduced in Pairs (1). They are all irregular waits built around a concealed triplet, and all of them appear frequently in actual play.
Basic Three-Sided Waits
Any wait with three kinds of winning tiles counts as a three-sided wait, but the first thing to learn is the basic pattern where two ryanmen waits are joined together.
| Example shape | Winning tiles | Number of winning tiles |
|---|---|---|
|
|
11 |
|
  |
11 |
|
|
11 |
These three are the complete set of basic three-sided waits. There are also variations that include tanki while still remaining three-sided waits.
| Example shape | Winning tiles | Number of winning tiles |
|---|---|---|
|
|
9 |
|
|
9 |
|
|
9 |
In all of these cases, the number of winning tiles goes down because you are already using two copies of one of the wait tiles yourself.
But pay attention to the fact that the actual waits are still the same 147, 258, and 369.
Even a basic three-sided wait becomes easy to misread once the sets start overlapping.
(Example 4) Tsumo
In Example 4, the correct good-shape riichi is to discard and take the three-sided wait.
Be careful not to absent-mindedly discard or instead.
Three-sided waits with a high-side iipeikou come up often enough that it may be worth memorizing them directly as patterns.
Original Japanese page: http://beginners.biz/kihon/kihon11.html