Question (): Provided Watson did not play while sleeping and the deal has been continued as long as it possible without disturbing Watson please tell how many dreams Dr. Watson has seen during his sleep?

Note: One dream corresponds exactly to one successful declaration: "Flower", "Chow", "Pung", "Kong", "Hu" (no false "Hu" counts for successful declaration for clarity).

 

Answer: To start with, Dr. Watson can seat at any wind except East, let's assume it is North. The key issue to solve for continuing deal is to not let West's discard remain unclaimed, otherwise the game will stall. So, every West's discard must be punged or konged by East or South. East can claim only pungs and kongs, while South and West can declare those plus also chow. "Hu" can be declared by any of the three players. Flowers can be declared by everybody except North, and to maximize the number of calls, none of flowers should be declared during the flowers replacement phase (right after the dealing of the tiles).

One more crucial point about kongs - concealed kongs only take one declaration, while promoted kongs take two declarations: pung,  and then kong. South and West can declare promoted kong over the span of two turns: pung from a discard and kong after a taking tile. In fact, this process requires two turns due to a rule from the "Green Book" (see p. 3.6.8): "You may not kong in the same turn as one in which you have melded a chow or a pung". One IS allowed, however, to declare a second kong after declaring a first kong and then self-drawing a supplemental tile from the wall.

So, the chain of events may look like (numbers in brackets show total number of declarations = Watson's dreams):

  • dealing tiles,
  • no Flowers replaced,
  • Watson falls asleep,
  • East discards,
  • South declares Pung then discards (1),
  • West declares Pung then discards (2),
  • East declares Pung then discards (3),
  • South declares Pung then discards (4),
  • West declares Pung then discards (5),
  • East declares Pung then discards (6),
  • South declares Pung then discards (7),
  • West declares Pung then discards (8),
  • East declares Pung then discards (9),
  • South declares Pung then discards (10),
  • West declares Pung then discards (11),
  • East declares Melded Kong (12),
  • East declares Promoted Kong, which repeats three times (15)
  • South takes a tile from the wall and declares Flower, it repeats four times (19),
  • South takes tile from the wall and declares Promoted Kong, which repeats four times (23),
  • West takes tile from the wall and declares Flower, it repeats four times (27),
  • West takes tile from the wall and declares Promoted Kong, it repeats four times (31),
  • West discards, East declares "Hu" (32),
  • Watson wakes up.

So, Watson has seen as many as 32 mahjong dreams.

P.S. If unsuccessful declarations are to be counted, then there might be the possibility of chow-declarations being bumped by pungs, and multiple "Hu".

 

Prizes generously provided by the publishers of Mahjong Collector Magazine, and by Holiday Mahjong Online.