Choosing Riichi Waits (2)
Last time, we looked at relatively simple comparisons: number of winning tiles, point value, and how easy the tiles themselves are to ron on.
This time, we move on to the trickier question:
Which should you choose: fewer tiles with higher value, or more tiles with lower value?
When the Point Difference Is Small
Example 1
Dora
In a case like this, cutting and riichi is the clear answer.
A difference like 3900 versus 5200 (riichi iipeikou) is much less important than the difference in the number of winning tiles.
In other words, when the point gap is only this small, the wider wait is vastly superior.
2. A Difference of One Han
Example 2
Dora
Now the hand values differ by a full factor of two: 2600 versus 5200.
Even so, cutting is still better.
When the difference in tile count is more than double, the point value needs to be more than double as well before the trade starts to balance out.
Also, when you win after riichi, you get to draw ura-dora. And because of the mangan ceiling effect, the true average point values of the two options often do not end up differing by a full factor of two anyway.
For example, if you tsumo and flip one ura,
riichi tsumo dora 2 and riichi tsumo iipeikou dora 2
end up worth exactly the same number of points.
There is also a major negative expected-value issue in mahjong:
reducing your wait increases the chance that someone else will win first.
Especially when you are making a chasing riichi, you should prioritize tile count.
The more winning tiles you have, the more favorable the draw race becomes.
Example 3
Dora
In Example 3 as well, if someone else has already riichi'd first,
then cutting to take the narrower wait on
is a very costly choice.
It is wiser to choose one of the manzu sanmenchan options.
Example 4
Draw 
Dora
This hand gives you three choices:
- Ryanmen pinfu riichi
- Kanchan sanshoku riichi
- Sanshoku damaten
In this kind of position, none of the three is outright wrong.
Still, the basic answer is to cut and riichi.
It is enough to understand it this way:
the default is still cut riichi,
and only when is thin do you start considering the sanshoku route instead.
A Difference of Two Han
This is usually the trickiest case.
Example 5
Draw
Example 5 is a slight modification of Example 4, except now there is no pinfu.
In cases like this, the key is whether you have dora, and how many.
If there is no dora:
When the choice is between a good-shape 1300 and an ugly-shape 5200, the higher-value ugly wait is usually better after all.
So as a rule of thumb, remember: when there is no dora and the difference is two han, take the yaku.
If there is one dora (or another extra han, such as tanyao):
Ryanmen riichi, ugly-shape damaten, and ugly-shape riichi are all reasonable.
The expected values are very close, so this should be judged by the situation at the table.
If there are two dora:
Now the better recommendations are either the ryanmen riichi or the ugly-shape damaten.
This is the kind of position where you compare "a 5200 ryanmen" against "a guaranteed 8000 kanchan."
However, if the higher-value tile is something hard to discard, such as a 3 through 7, then I would lean toward the ryanmen riichi. For example:
Draw 
Dora
If there are three dora:
At that point the hand value is already more than enough, so you should absolutely take the good-shape riichi.
A Difference of Three Han or More
In most cases, you should aim for the higher-value hand.
Example 6
Dora
Here you should obviously take the junchan route and riichi.
Since the hand is already worth 5200, damaten is also an option, but taking the sanmenchan riichi instead would be too passive.
Example 7
Dora
However, if the wider option is already plenty valuable by itself, then the story changes.
In Example 7, cutting is simply too greedy.
You already have a chance hand, yet by chasing an even bigger score you turn the wait into something awful and let a perfectly good win slip away.
A tile like ,
right next to the dora indicator,
is about as bad a wait as you can ask for.
In practice, the real choices are:
- Cut and stay damaten, picking up the win as safely as possible
- Cut and riichi, aiming to tsumo
Even if itself is dangerous,
if there are still enough draws left in the wall,
I still think taking the fight is more favorable.
Original Japanese page: http://beginners.biz/reach/reach08.html