Atozuke
Atozuke 「後付け」 describes a "yakuless" tenpai which gains yaku upon winning. In other words, the current state of the hand does not produce yaku while tenpai. This typically involves an open hand, but can also apply to closed hands without riichi. It is also called sakizuke 「先付け」.
When a hand is subject to atozuke, it may still win if it draws the "higher value" tile. However, it is normally unable to win off the "lesser" tile, since it would lack yaku. If the lesser tile is drawn, the hand may be subject to furiten.
Atozuke is subject to rule variations. When the atozuke rule is disabled ("atozuke nashi"), you must have a confirmed yaku before winning (and sometimes, before making any call). The more common rule, by far, is to allow atozuke.
Examples
Note: as with any "yakuless" hand, a hand subject to atozuke may win from the lesser tile by gaining haitei, houtei, rinshan, or chankan. Closed hands can also win by mentsumo. If a hand in atozuke does not gain one of these conditional yaku, though, it cannot win by the lesser tile.
Yakuhai
This hand uses a shanpon tenpai for two tiles. Winning with the haku gives a yaku through yakuhai, but winning with the 9-pin gives nothing. As this is a closed hand, it can win with mentsumo regardless of winning tile, but it can only ron off the haku (unless it gains a conditional yaku like houtei).
This time, the same tiles from the above hand has an open call. At it stands, it needs the haku in order to win (or a conditional yaku like houtei).
Tanyao
Agari:
Tanyao can only be achieved when won with 6-sou.
Sanshoku
This hand has an apparent yaku of sanshoku doukou. However, the latter wait of 3-sou would create a sequence of 1-2-3 sou, as it triggers the effect applied by the lesser valued tile. Thus, it only has a yaku when won with the 2-sou.
Sanshoku is hinted at, however, the extended nobetan wait of 1-4-7s in the hand can ruin sanshoku if won from the 1s (it would become 11 - 234 - 567).
Counter examples
In these examples, atozuke is not used. In these cases, the hands may win on any of the waiting tiles. They each have valid yaku already embedded into the hand, regardless of their winning tiles.
The open call on the green dragon instantly gives the hand a yaku via yakuhai.
Sanshoku is already embedded in the hand.
This hand employs honitsu.
Atozuke disabled
When the atozuke rule is disabled, the hand must have a confirmed yaku before winning and before calling any tile. Therefore, a hand that could always win under atozuke enabled may not be allowed to win in atozuke disabled.
If this hand wins from 6-sou, it gains iipeikou. If it wins from 9-sou, it gains sanshoku.
- When the atozuke rule is enabled, this hand can win no matter what. Both winning tiles give a yaku, so it always has a yaku, so it can win regardless of the tile.
- When the atozuke rule is disabled, this hand cannot win. Neither iipeikou nor sanshoku are confirmed. Because this hand does not guarantee "iipeikou", "sanshoku", or any other specific yaku in its current state, it cannot win. (Of course, since this is a closed hand, you can just call riichi.)
This hand would gain a yakuhai triplet if it wins off the haku or chun. However, it does not have any yaku in the current state, and so it cannot win if atozuke is disabled (until riichi is declared).
This hand has a confirmed yaku through the triplet of hatsu. However, it did not have any yaku when calling the 789-sou. Therefore, this hand cannot win with atozuke disabled.
When the hatsu triplet is closed, the hand can always win. (Even if the hatsu triplet was not there when 789-sou was called, there would be practically no way to enforce it, so "drawing the hatsu triplet after calling" play is technically allowed.)
Note: for whole hand yaku, like honitsu, the yaku can be scored even if you had different suit tiles at the time of calling. Calling for chanta/junchan is allowed so long as your final wait guarantees the yaku.
To repeat, the atozuke rule is most often enabled. When atozuke is enabled, all these types of hand can win without issue.
Strategy
When atozuke is enabled, players may deliberately enter the state of atozuke, depending on the starting hand. Calling tiles helps develop the hand faster, even if there's a chance you may not win later. For example, with a yakuhai pair, you may want to call early and hope someone discards the needed yakuhai later.
Risk of furiten
- Draw:
Open hands under atozuke run the risk of furiten. If this hand draws the 9-pin, it enters furiten. If this happens, it is possible to change waits, or win by drawing needed tile. Or you can stay tenpai until exhaustive draw to gain the tenpai payment.