Short- and long-term tile efficiency

[Mauro]

Let's say a player has this hand, with a called set (which is not relevant to the question):



What would you discard?

On one hand, is clearly unconnected and the way to go if you pursue short-term tile efficiency, since it leaves you with 16 out and two partial sets, but if you close the ryanmen then you are in a one-side wait with 4 outs.

On the other hand, if you cut or , you lose one potential set, but you have 57 tiles that improves your hand, which goes to 40 if you draw , with a chance to a tenpai with ryanmen wait.

Is the improvement in useful tiles worth sacrificing ? If I do, would the hand be much slower could, since on one hand I cut a potential set, but on the other hand I greatly improved my useful tiles?

[Shirluban]

if you cut or , you lose one potential set, but you have 57 tiles that improves your hand

I fail to see which ones.
Let's say you discard :
do improve the hand.
is only slightly better that the initial position.
are questionable whether they really improve the hand, as you don't need three potential pairs.
put you 1-away, but they would have made you tenpai if you had discarded .
Other tiles don't put you back 1-away, and three quarters of them don't even connect to anything.

So overall 20 tiles put you in a better position than discarding .
If you could declare riichi, that would be only 8 tiles.

Assuming the called set is a yakuhai, I would consider folding as an open 1-han hand is not worth pushing to.
(If the called set is anything else, then the hand wouldn't have any yaku...)

If the hand were still closed, it would be better to be tenpai quickly and declare riichi, even with a bad wait, since it incites the other players to break their hand to defend. Riichi + maybe ippatsu, tsumo, ura-doa can bring quite some points.
... but I would still consider folding.

[Mauro]

if you cut or , you lose one potential set, but you have 57 tiles that improves your hand

I fail to see which ones

Not sure what I did to have 57, but I was basing my message on Tenhou which gives 53: https://tenhou.net/2/?q=234788m7p2s445z (white dragon because Tenhou gives you the drawn tile, so I used one that's unconnected).

put you 1-away, but they would have made you tenpai if you had discarded

True, but my doubt was also based on the idea that discarding sou does slow you down, but you could have a tenpai with eight outs instead of four; I'm not sure if/when such a trade-off makes sense, also because as you point out you could slow down your hand and still end up with the same 4-tiles wait.