Haitei raoyue and houtei raoyui
Win by last draw|
Win by last discard
Haitei raoyue 「海底撈月」 or simply Haitei is a standard yaku, where a player wins with the tsumo on the haiteihai, the last drawable tile from the live wall. As such, this yaku is only accessible via tsumo.
Houtei raoyui 「河底撈魚」 is the ron variant to haitei, which is dependent on the last discarded tile of a hand. So, players making the last discard of the hand must take extra care not to play into another player's hand in this case.
The last tile draw and discard is defined by the dead wall. By rule, the dead wall must retain 14-tiles at all times; and this includes any revealed dora indicators. Naturally, to score either haitei or houtei, a player must be at tenpai at the end of the hand just before ryuukyoku. Finally, hands may definitely be declared for a win, if either haitei or houtei is the only yaku of the hand.
Haiteihai and houteihai
Haiteihai 「海底牌」 is the very last tile that can be drawn from the regular wall. This is clearly indicated as the 15th tile left, counting the tiles of the dead wall including the dora indicator. Typically, this tile resides as the lower of two tiles next to the back end of the dead wall. Earlier calls for kan may "alter" the designation of the last tile, as that same bottom tile gets shifted into the dead wall to maintain fourteen tiles after the rinshan draw. In some groups, the tile may physically be moved form the live wall into the dead wall to make it more clear when the hand ends, but this generally not done in advanced play.
Likewise, the very last discard is called houteihai 「河底牌」, which is subject to the call of "ron" for the houtei raoyui yaku and nothing else. Tile calls of chii, pon, or kan cannot apply to it.
If a player calls a kan when there is only one tile left in the live wall, the rinshanpai will be the last draw of the game. In this situation, the rinshanpai is not considered to be the haiteihai, and if the player calling kan wins off of that tile, it will be eligible only for the rinshan kaihou yaku and not for haitei. The final discarded tile is, however, considered to be the houteihai and is subject to the same rules as normal, including the prohibition on tile calls and the eligibility for the houtei yaku.
A player cannot call a kan after drawing the last tile (either normally or as a result of a kan), because they would need to draw a rinshanpai and doing so would bring the dead wall down to 13 tiles.
Haitei and houtei are mutually exclusive with each other, with chankan, and with rinshan kaihou. Each of these yaku requires the winning tile to come from a different location (the live wall, a tile added to make a shouminkan, and the dead wall, respectively). Houtei cannot combine with mentsumo because it is only winnable via discards.
As for ippatsu, it is impossible for the player calling riichi to have the last discard occur within one turn, because there must be at least 4 tiles left in the live wall when calling riichi. If an intervening call was made, which might mean that the player calling riichi would not get another draw, that call alone would disqualify an ippatsu. It is possible, however, for a player to call riichi with exactly four tiles left in the live wall and subsequently get both ippatsu and haitei on their next draw.
Setting up haitei raoyue or houtei raoyui
Like any hand, either yaku requires tenpai at the very last draw and/or discard to even have a chance of winning. At this point, the hand can be any hand, even an open hand. Haitei or houtei would qualify for yaku on each of their own right.
The term haitei raoyue translates literally as "scooping up the reflection of the moon from the bottom of the sea." It is a figurative Chinese expression (sometimes used in Japanese as well) use to mean a futile task. houtei raoyui is a pun on this, translating literally as "catching fish from the bottom of the river." The kanji 河 is the term kawa, meaning the discard pond. Hence houtei is a pun referring to both haitei, and the act of catching a fish from the bottom of the discard river.
- Haitei raoyue in Japanese Wikipedia.
- Houtei raoyui in Japanese Wikipedia.