You might not have quite got it completely (maybe you have!), for the first picture there are (more than) two different paths you should take and that's why I said it's preferential and not a definite answer. Also when I talk about discard, I never take into account what actually happened (before or after) but what is best for that certain situation so drawing
and kanning it in the second picture is irrelevant to my advice for the first part (going to tanyao) so think of the two parts of my answer as separate answers to the question.
I will explain the first picture in more detail.
, you technically have two choices if you want to increase your chances of winning the hand. The first choice is discarding
, this is because you can go to tanyao, and as I have said
is quite easy to pon. lets say you pon the
, you get
, from here you can pon
) , or get the tiles yourself to get tenpai. ( you might get other tiles which may make the hand or wait better as well) so the speed is there. You do however lose some defense in the process which is a down side but you have a good chance of getting tenpai quite quickly. also there is some flexibility in the wait itself in this route in the sense that if you don't want to throw the
(as you have mentioned), you can still get tenpai with a good probability by still holding onto the
(although you have to remember that you don't know if the kamicha wants the
or not in that current situation)
The second choice is not discarding
because of the furiten but actually discarding the
. This is due to the lack of
as there is already two out (if there were no
on board, I would probaly advise discarding
) and it is almost certain that you are going to use the
as the pair or jyantou therefore leaving 3 pairs with either
discard is not optimal (3 pair theory ( it means having two pairs will complement each other and increase the tile efficiency by 4 tiles but increasing the number of pairs from two to three only increases the tile efficiency by 2 tiles and therefore in this case it's better to leave a kanchan which gives your 4 tiles to tenpai then leaving a pair which gives you in this case no additional tiles because
is dead!) you don't throw the
using the same theory because of furiten. The reason you don't get rid of the
wait even though it's furiten is because that is still 5 tiles you can draw to get tenpai so it's worth leaving just incase you draw it first
this route is not too great in the sense that you have the
wait furiten and the
which can lead to awkward waits such as
wait ) and even if you avoid furiten
wait which is far from ideal)
The greatest advantage to this route is being able to hold onto the two
which is a definite safe tile in which you can use to defend against riichi.
I find the
discard somewhat of an intermediate to the two choices I mentioned above and feel like it's a bit indecisive on the approach that you want to take with your hand.