and are 1 each, open or closed. Haitei is a tsumo on the last tile of the live wall. Houtei is a on the discard that follows it, the last discard of the hand.
The full names are haitei raoyue and houtei raoyui. Tenhou's rules and Mahjong Soul write them 海底摸月 and 河底撈魚. This site's glossary spells haitei 海底撈月 and lists the pair as Last Tile from Wall and Last Discard.
Which tile is the last
In a four-player game the always holds 14 tiles. Each takes one more tile from the end of the live wall to keep it at 14, so every kan moves the last draw one tile earlier. The EMA 2016 rules spell that out under each kind of kan.
The player who draws the last tile can win on it by tsumo. That's haitei. If they don't win, they discard, and that tile is the last discard. Anyone waiting on it can ron. That's houtei. Nobody can , , or kan it: the EMA 2016 rules let the last discard be claimed only for a win. They also forbid a closed kan on the last tile.
If nobody wins, the hand ends in an .
An open hand with no other yaku
You called pon on 9 man: 
. These ten tiles are still in your hand.
The hand waits on 
or 
, from both sides. It has no yaku. The 1s and 9s rule out , 9 man isn't a value tile, and the 456 man rules out . During the hand, neither tile can win.
On the last tile, either one can. Draw it as the last tile and haitei is the yaku. The fu are the base 20, plus 2 for the tsumo, plus 4 for the open triplet of 9 man. 26 rounds up to 30. At 1 han 30 fu, a collects 300 from each other non-dealer and 500 from the dealer. A dealer collects 500 from each player.
Ron it as the last discard and houtei is the yaku. An open hand gets no 10 fu for a ron, so the count is 20 plus 4. 24 rounds up to 30. At 1 han 30 fu, a non-dealer collects 1,000. The dealer collects 1,500.
On a riichi hand
After this hand waits on 
only, a .
Draw it as the last tile: riichi, menzen tsumo, and haitei make 3 han. The fu are 20, plus 2 for the tsumo, plus 2 for the middle wait. 24 rounds up to 30. At 3 han 30 fu, a non-dealer collects 1,000 from each other non-dealer and 2,000 from the dealer. A dealer collects 2,000 from each player.
Ron it as the last discard: riichi and houtei make 2 han. The fu are 20, plus 10 for a closed ron, plus 2 for the middle wait. 32 rounds up to 40. At 2 han 40 fu, a non-dealer collects 2,600. The dealer collects 3,900.
Those payments have no , no , and no riichi sticks. The scoring guide counts fu like these line by line.
Haitei and rinshan kaihou
A kan on the second-to-last draw makes the the last tile. The EMA 2016 rules say so. A win on that replacement tile is rinshan kaihou and not haitei as well: Tenhou's rules and the EMA 2016 rules both say the two don't combine.
Tenhou, Mahjong Soul, and EMA 2016
Tenhou lists 海底摸月 and 河底撈魚 at 1 han each, with no mark for a , so an open hand scores them too.
Mahjong Soul's Japanese FAQ defines haitei as a tsumo on the hand's last drawn tile and houtei as a ron on its last discard.
The EMA 2016 rules have both at 1 han, with no closed-hand condition.
Common mistakes
- Calling chi or pon on the last discard. Only a ron can take it.
- Counting from the original wall. Each kan moves the last tile one draw earlier.
- Adding haitei to a win on the last tile. The two don't combine.
- Thinking a yakuless open hand can't win. On the last tile, haitei or houtei is its yaku.
- Mixing them up. Haitei is your own draw. Houtei is someone else's discard.
What sits with it
Haitei is a tsumo, so a closed hand adds menzen tsumo. Houtei is a ron, so it never does. Either one stacks with riichi, tanyao, and anything else the tiles hold.
Price a last-tile win
The score calculator turns 2 han 40 fu, riichi and houtei on a middle wait, into 2,600 or 3,900. On an open hand with no other yaku, houtei alone makes the win.
Open the score calculator