Tanyao
The biggest selling point of Tanyao comes down to one thing:
you can still win with it after calling.
Especially in modern free-play rules packed with red fives all over the place, open Tanyao is extremely powerful.
Hands like “Tanyao, dora, red-red for 8000!” happen all the time.
It is annoying when someone wins with it, and you even get pathetic situations where you have to fold to open Tanyao.
At some parlors red fives even come with chip bonuses, so open Tanyao is becoming one of the strongest yaku in the game.
1. Play Toward Tanyao
Tanyao is easy to make, and it combines well with many other yaku.
That is why it is important to keep its possibilities in mind while discarding.
Example 1
In Example 1, you should drop the pair of .
If you draw 
, you can aim for Tanyao-Pinfu;
and if you draw 
or 
,
Tanyao Sanshoku also comes into view.
Example 2
In Example 2, you should switch the roles of and .
That is because if you draw or ,
the hand turns into Tanyao.
2. Locking Tanyao In
Example 3
The diagram above is a so-called meld-overload shape.
In a hand like this, the standard answer is to drop .
Even if you later draw 
,
it would only give you a simple Riichi-only hand anyway.
Example 4
If you only look at immediate acceptance, then yes, discarding is the widest choice.
But in real play, most people would normally cut .
That is because Tanyao becomes guaranteed, which means calling is now available;
and in this hand, 456 or 567 Sanshoku is also still in play.
3. Thinking From the Perspective of Calling
Example 5
If you only look at pure acceptance, the widest discard here is a tsumogiri of .
But in the actual game, the discard was .
This was the final hand, the player was dealer, and currently in fourth place.
In a spot like that, you have to win no matter what, so you must also factor in open Tanyao.
If you cut ,
then after ponning or ponning , the hand becomes a one-sided win shape.
Cutting avoids that.
Chi 
Ron
As a result, the hand won for 5800.
Original Japanese page: http://beginners.biz/teyaku/teyaku05.html