Choosing Between Dora and Yaku
There are many situations where you have to give up either the dora or the yaku.
So how should you decide what to discard in those moments?
The Choice at Tenpai
As a rule, choose the option with the larger number of winning tiles.
Example 1
Dora
With this hand, the correct play is to discard and riichi.
One 
is already used up as the dora indicator, so a kanchan on leaves only three tiles.
That is less than half of the seven-tile wait on 
through .
Even with Sanshoku, the hand value does not become more than double, so the sanmenchan is overwhelmingly better.
Example 2
Dora
This time, the Pinfu hand that cuts the dora is better.
It is an eight-tile wait for 3900 versus a four-tile wait worth 5200 to 8000,
but even a Pinfu riichi can still become mangan with ippatsu or ura-dora,
and when everyone is racing to tenpai, the side with more winning tiles is stronger.
Example 3
Pon 
Pon 
Dora
In a case like Example 3, where the point difference is already more than double
(2000 versus 5200), yaku is clearly more favorable.
Unless this is a spot where you want to settle cheaply,
you should discard and accept Toitoi.
The Choice at One-Shanten
Example 4
Dora
This is a taatsu choice in an overmeld shape.
Even if you aim for 234 Sanshoku, you would need to keep drawing the high-value route all the way, otherwise it still ends up as riichi only.
Breaking the taatsu that contains the dora is a very costly choice.
Discards like or , which only slow the hand down, are completely out of the question.
Theory Summary
An uncertain two-han gain is generally worse than a guaranteed one-han gain.
Example 5
Dora
This is a huge chance hand: Dora 2, and 456 Sanshoku is clearly visible too.
But if you want to convert the hand reliably, the best discard is still .
It is hard to break into that wide souzu connected shape,
but I do not think there is any need to cut the dora just to chase Sanshoku.
Example 6
Dora
This one, by contrast, is a clear dora-cut.
The hand can already aim for Tanyao, Pinfu, and 345 Sanshoku, so the dora is not needed.
You cannot make a blanket rule that dora is always better, or yaku is always better.
Sometimes you should prioritize yaku, and sometimes you should prioritize dora.
The choice should be made by comparing hand width and winning ease.
Theory Summary
When choosing between dora and yaku, you will make fewer mistakes if you choose the side with the wider acceptance.
The Choice in the Early Hand
In the early hand, overwhelmingly often, it is better to keep both the dora route and the yaku route alive.
Example 7
Dora
★ East 1, turn 2, South player's hand
This is a hand that can aim for a manzu honitsu while the dora is still floating.
Discarding the dora immediately here, or discarding first, would both be poor play.
If the honor tiles pair up, they fill exactly the taatsu you need for honitsu,
so it is far too painful to stack into your discard pile from this hand.
Discarding is also premature.
If the dora pairs up, the value is no worse than honitsu;
and if you draw or , then it is better to abandon honitsu.
So overall, I think the reasonable early-hand choice here is to deal with first.
There is a saying: “He who chases two rabbits catches neither.”
But that saying does not always apply to mahjong.
Especially in the early hand, you should play in a way that keeps multiple possibilities alive.
Original Japanese page: http://beginners.biz/dora/dora05.html