Mrs. Hudson’s successful play at London MCR Championship drew everyone's attention, so that even the correspondent of the newspaper "MahjongNews” decided to watch her play. Here is an abstract from the article describing a particular deal:

Mrs. Hudson managed quite quickly to reach a waiting hand. But the most amazing thing is the fact that after each of her moves after getting to the wait (for valid 8+ pts. hand) and until she declares “Hu!” on a discarded tile, Mrs. Hudson’s hand changed and the hand's value increased.”

Question

Please, provide the chain of Mrs. Hudson’s hands under the following conditions:

  • the hand value is counted specifically on a discard tile,
  • the hand value with multiple waits is counted by its minimum value,
  • at least one tile in the hand (part of hand except flower tiles) must changed after each move,
  • none of the tiles taken from the wall by Mrs. Hudson will give mahong to her.

Scoring guidelines:

  • submitting a chain of 4, 5, 6 or 7 hands to Mrs. Hudson’s hand will be scored for 1 SHP (),
  • submitting chain of 8, 9, 10 or 11 hands to Mrs. Hudson’s hand will be scored for 2 SHP (),
  • submitting chain of 12, 13, 14 or 15 hands to Mrs. Hudson’s hand will be scored for 3 SHP (),
  • submitting chain of 16 or more hands to Mrs. Hudson’s hand will be scored for 4 SHP ().

Answer

Let’s consider a list of technical actions carried out upon Mrs. Hudson’s waiting hand for the hand still be on wait and changed (part of hand except flower tiles) after move is finished:

  • drawing one tile from the wall, discarding the other tile,
  • declaring concealed/ opened/ promoted kong, combined with drawing tile from the wall,
  • declaring Flower, combined with drawing tile from the wall,
  • declaring pung,
  • declaring chow.

For draw-and-discard action hand value may be increased by getting points for new scoring elements like wait, voided suit, hand as-a-whole change (external hand, reversible tiles), etc. Flower declaration without change of hand does not work by mystery conditions, hence, we need draw-and-discard action tricks. Kong declaration is ideal for hand value increase due to acquiring additional points from number of kongs in hand. Pung or chow declaration is ineffective.

The general plan for the chain of waiting hands consist of following parts:

  • 3-pung hand converted to 4-pung hand,
  • 4 kongs declarations,
  • 8 flower declarations,
  • tricks around voided suit, external hand and reversible tiles.

How long this chain can be? Out of 144 tiles 13*4=52 tiles always must be placed in 4 players’ hands. Mrs. Hudson’s hand should have 4 extra tiles in kongs and 8 flowers. Thus, 144-52-4-8=80 tiles must inevitably go to discard zone. On a rough count, a chain length can be limited by 80/4=20. Fortunately, any single declaration by other players provide one additional wall tile, altogether up to 4*3=12 tiles may be added to pool increasing chain length to the value of 23. The other possibility to increase length is to neglect hand efficiency issue – pick tile for the wait so that hand value increases while number of available tile may be lesser.

And here is a chain of 27 (!) hands (on the edge of efficiency, increased efficiency when three other players declare chows hence eliminating critical tiles will lessen chain for 4-5 hands) based on pungs/ kongs, flower combos and tricks about pattern groups. Hand value is calculated on discard by mystery conditions. For any Mrs. Hudson’s waiting hand we will count discarded, melded, standing and wall tiles after Mrs. Hudson’s discard, describing if necessary moves of other players before next her move. Round starts with West and follows North, East and South.

1.       Mrs. Hudson is sitting on South and takes first East discard, “Pung!”:
Concealed --
, , ,
Opened -- .   
Hand value = 2*1 (Pung of Terminals) + 2 (Double Pung) + 2 (Two Concealed Pungs) + 2 (Dragon Pung) = 8 points.
Melded = 3, standing=13 (E) + 10 (S) + 13 (W) + 13 (N) = 49, discarded = 1, wall = 91 tiles.

2.       Simple draw-and-discard round, South creates 1 point for wait:
Concealed -- 
,
Opened -- .
Hand value = 2*1 + 2 + 2 + 2 + 1 (Closed Wait) = 9 points.
Melded = 3, standing=13 + 10 + 13 + 13 = 49, discarded = 5, wall = 87 tiles.

3.       Simple draw-and-discard round, all three other players discard . South moves wait, getting External Hand:
Concealed -- 

Opened -- .
Hand value = 2*1 + 2 + 2 + 2 + 4 (External Hand) + 1 (Edge Wait) = 13 points.
Melded = 3, standing=13 + 10 + 13 + 13 = 49, discarded = 9, wall = 83 tiles.

4.       South declares pung on West’s discard, discarding useless :
Concealed -- 

Opened -- .
Hand value = 3*1 + 2 + 2 + 2 + 6 (All Pungs) + 1 (Single Wait) = 16 points.
Melded = 6, standing=13 + 7 + 13 + 13 = 46, discarded = 10, wall = 82 tiles.

5.       Simple draw-and-discard round. First trick with Flower. South takes Flower tile from the wall, declares Flower, takes another Character tile and discards previous Character tile:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 2 + 6 + 1 + 1 (Flower) = 17 points.
Melded = 7 (including 1 Flower), standing=13 + 7 + 13 + 13 = 46, discarded = 14, wall = 77 tiles.

6.       East declares pung on South’s discard of . South creates 1 point for voided suit:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 2 + 6 + 1 + 1 (One Voided Suit) + 1 = 18 points.
Melded = 10, standing=10 + 7 + 13 + 13 = 43, discarded = 16, wall = 75 tiles.

7.       East declares pung on South’s discard of . South declares concealed kong:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 2 + 6 + 1 + 2 (Concealed Kong) + 1 = 19 points.
Melded = 17 (added pung and 4 tiles in concealed kong), standing=7 + 4 + 13 + 13 = 37, discarded = 18, wall = 72 tiles.

8.       East declares pung on South’s discard of . South creates 1 point for voided suit:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 2 + 6 + 1 + 2 + 1 (One Voided Suit) + 1 = 20 points.
Melded = 20, standing=4 + 4 + 13 + 13 = 34, discarded = 20, wall = 70 tiles.

9.       South declares opened Kong on West’s discard of :
Concealed -- 

Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 6 (Opened and Concealed Kong) + 6 + 1 + 1 = 21 points.
Melded = 24 (added 4 tiles in opened kong), standing=4 + 1 + 13 + 13 = 31, discarded = 21, wall = 68 tiles.

10.   East declares pung on South’s discard of . South creates 1 point for voided suit:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 6 + 6 + 1 + 1 (One Voided Suit) + 1 = 22 points.
Melded = 27, standing=1 + 1 + 13 + 13 = 28, discarded = 23, wall = 66 tiles.

11.   North declares pung on South’s discard of . South goes for Reversible Tiles:
Concealed -- 
,
Opened -- , 1 Flower.
Hand value = 3*1 + 2 + 2 + 6 + 6 + 1 + 8 (Reversible Tiles) + 1 = 29 points.
Melded = 30, standing=1 + 1 + 13 + 10 = 25, discarded = 26, wall = 63 tiles.

12.   Simple draw-and-discard round. Second trick with Flower. South declares Flower and chooses new Reversible tile. For the subsequent moves (with simple draw-and-discard round) South will try to choose for Single Wait Reversible tile (from , , , , , , , ) with better chances to win, decision is based on chances and game flow.
Concealed -- 

Opened -- , 2 Flowers.
Hand value = 3*1 + 2 + 2 + 6 + 6 + 1 + 8 + 2 (Flowers) = 30 points.
Melded = 31, standing=1 + 1 + 13 + 10 = 25, discarded = 30, wall = 58 tiles.

18.   Eighth trick with Flower:
Concealed -- 

Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 6 + 6 + 1 + 8 + 8 (Flowers) = 36 points.
Melded = 37, standing=1 + 1 + 13 + 10 = 25, discarded = 54, wall = 28 tiles.

19.   North declares pung on South’s discard of . South declares first promoted kong:
Concealed -- 

Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 32 (Three Kongs) + 6 + 1 + 8 = 54 points.
Melded = 41, standing=1 + 1 + 13 + 7 = 22, discarded = 57, wall = 24 tiles.

20.   North declares pung on South’s discard of . South creates 1 point for voided suit:
Concealed -- 
,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 32 + 6 + 1 + 1 (One Voided Suit) + 8 = 55 points.
Melded = 44, standing=1 + 1 + 13 + 4 = 19, discarded = 60, wall = 21 tiles.

21.   West declares pung on South’s discard of . South goes for Reversible Tiles:
Concealed -- 
,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 32 + 6 + 1 + 8 (Reversible Tiles) + 8 = 62 points.
Melded = 47, standing=1 + 1 + 10 + 4 = 16, discarded = 56, wall = 25 tiles.

22.   Simple draw-and-discard round. South goes for All Terminals or Honors:
Concealed -- 
,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 32 + 32 (All Terminals or Honors) + 1 + 8 = 80 points.
Melded = 47, standing=1 + 1 + 10 + 4 = 16, discarded = 60, wall = 21 tiles.

23.   West declares pung on South’s discard of . South creates 1 point for voided suit:
Concealed -- 
,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 32 + 32 + 1 + 1 (One Voided Suit) + 8 = 81 points.
Melded = 50, standing=1 + 1 + 7 + 4 = 13, discarded = 63, wall = 18 tiles.

24.   South’s discard of  was claimed for chow   , West’s discard of  was claimed for chow   . South declares second promoted Kong changing wait for better chances:
Concealed -- 
,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 88 (Four Kongs) + 8 = 103 points.
Melded = 57, standing=1 + 1 + 4 + 1 = 7, discarded = 65, wall = 15 tiles.

25.   Simple draw-and-discard round. South creates 1 point for voided suit:
Concealed -- 

Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 88 + 1 (One Voided Suit) + 8 = 104 points.
Melded = 57, standing=1 + 1 + 4 + 1 = 7, discarded = 69, wall = 11 tiles.

26.   West declares pung on South’s discard of . South goes for Reversible Tiles:
Concealed -- 
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 88 + 8 (Reversible Tiles) + 8 = 111 points.
Melded = 60, standing=1 + 1 + 1 + 1 = 4, discarded = 72, wall = 8 tiles.

27.   Simple draw-and-discard round. South goes for All Terminals or Honors:
Concealed -- ,
Opened -- , 8 Flowers.
Hand value = 3*1 + 2 + 2 + 88 + 32 (All Terminals or Honors) + 1 (One Voided Suit) + 8 = 136 points.
Melded = 60, standing=1 + 1 + 1 + 1 = 4, discarded = 76, wall = 4 tiles.

West discards  and Mrs. Hudson declares “Hu!” for 136 points.