In the morning, Sherlock Holmes and Dr. Watson are sitting at the table waiting for Mrs. Hudson to bring them their morning coffee. "Mrs. Hudson is definitely delayed," said Watson. "I will go into the kitchen to see what's the matter."

It turnes out that Hudson is sitting at the table turning tiles back and forth and writing something.

"Mrs. Hudson, what are you doing? We are tired of waiting for our morning coffee!"

After bringing morning coffee, Mrs. Hudson explains:

"I'm trying to determine the maximum value of the mahjong hand for all valid types of structures."

"Well, the maximum value for the hand with a regular structure is known, which is 328 points without flowers, if I am not mistaken. For the hand with Big Three Dragons, All Honors etc.," said Watson.

"As written in the "Green Book" there are three more valid hand structure which are not regular:

  • "Seven Pairs"
  • "Thirteen Orphans"
  • "Lesser/Greater Honors and Knitted Tiles"

said Mrs. Hudson.

"I would also add here one more type -- "Semi-Regular" -- for the hand consisting of three knitted sequences of "Knitted Straight", Chow / Pung / Kong and a Pair," Holmes joined the conversation. "It is easy to distinguish types of hand structures. A regular hand has four times Chow / Pung / Kong and a Pair. This hand is allowed to declare sets, thus I would say it is also allowed to collect the hand  pieces. Three types of irregular hands consisting only of pairs and single tiles do not allow any declarations prior to "Hu". Finally, a Semi-Regular type of hand which allows only one declaration of a set." 

"So, Mrs. Hudson, what's your question?" asked Watson.

"Quite simple, to determine the maximum value of a hand for each hand structure. We speak here specifically about hand value, and not about total points won," said Hudson.

"Part of the issue, definitely, is investigation which fans or combinations of fans related to the winning tiles are applicable," continued Holmes. "Here is a list of those fans":

  • fan #44 Last Tile Draw,
  • fan #45 Last Tile Claim,
  • fan #46 Out with Replacement Tile,
  • fan #47 Robbing The Kong,
  • fan #56 Fully Concealed Hand,
  • fan #58 Last Tile,
  • fan #77 Edge Wait,
  • fan #78 Closed Wait,
  • fan #79 Single Wait,
  • fan #80 Self-Drawn.

 

Question: For each of the following four types of hand structure, please, determine the maximum value for the hand (without Flowers):

  • "Seven Pairs"
  • "Thirteen Orphans"
  • "Lesser/Greater Honors and Knitted Tiles"
  • "Semi-Regular" (three knitted sequences of "Knitted Straight", Chow / Pung / Kong and a Pair)

Note: Correct answers for one or two hand structures will be scored as , three or four as .

 

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

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  • Guest - Jinbi Jin

    Seven Pairs: 164 pts
    for example (of bamboo): 22224444666688, which scores All Green (88), Full Flush (24), Seven Pairs (24), Reversible Tiles (8), Tile Hog x 3 (6), All Simples (2); which combines with Last Tile Draw (8), Fully Concealed Hand (4)

    Honors and Knitted Tiles: 40 pts
    Greater Honors and Knitted Tiles (24); which combines with Last Tile Draw (8), Fully Concealed (4), Last Tile (4)

    Thirteen Orphans: 104 pts
    Thirteen Orphans (88); which combines with Last Tile Draw (8), Fully Concealed (4), Last Tile (4) (in the case of a single-sided wait)

    Semi-regular hand: 44 pts
    for example, as east in east round: (character 147) (bamboo 258) (dots 36), concealed kong of east, green dragon pair; which scores Knitted Straight (12), All Types (6), Concealed Kong (2), Round Wind (1), Seat Wind (1); and which combines with Last Tile Draw (8), Out with Replacement Tile (8), Last Tile (4), Fully Concealed (4)

  • Guest - Jinbi Jin

    Hm, correction on semi-regular case; both Round Wind and Seat Wind should be 2 pts, not 1 (and there may or may not be another error in that computation). So that number of points becomes 48 pts. (Knitted Straight (12) + All Types (6) + Concealed Kong (2) + Round Wind (2) + Seat Wind (2); Last Tile Draw (8), Out with Replacement Tile (8), Fully Concealed (4), Last Tile (4))

  • Guest - Cyrille

    For each hand I propose, the winner cumulates fully concealed hand and last tile draw.

    1) Seven pairs. Bamboos 22 22 44 44 66 66 88
    7 pairs(24), all green(88), full flush(24), reversible(8), 3*tile hog(6), all simples(2), fully concealed(4), last tile draw(8). Total : 164 points

    2) 13 orphans (the winning tile is not the pair)
    13 orphans (88), last tile(4), fully concealed(4), last tile draw(8). Total : 104 points

    3) Knitted
    Greater honors and knitted tiles (24) or lesser honors+knitted straight, last tile(4), fully concealed(4), last tile draw(8). Total : 40 points

    4) Semi-regular
    147 258 369 EEEE RR (East is table and player wind and winning tile is one of the straight, on replacement tile)
    Knitted straight(12), all types(6), wind(2+2), concealed kong(2), out with replacement tile(8), last tile(4), fully concealed(4), last tile draw(8). Total : 48 points

  • Guest - Timur Hahn

    -Structure 1, "Seven Pairs": 2B 2B 4B 4B 4B 4B 6B 6B 6B 6B 8B 8B 8B 8B, going out by self-draw on the last tile of the wall (not important which of the tiles finishes the hand). All Green (88), Seven Pairs (24), Full Flush (24), Reversible Tiles (8), All Simples (2), Last Tile Draw (8), Fully Concealed (4), Flower (8) = 166 points. Tile hog does not combine with All Green/Seven Pairs.

    -Structure 2, "Thirteen Orphans": 1B 9B 1C 9C 1D 9D E S W N R GG, going out on Wh, the last tile of its kind drawn as the last tile from the wall. Thirteen Orphans (88), Last Tile (4), Last Tile Draw (8), Fully Concealed (4), Flowers (8) = 112 points.

    -Structure 3, "Honors and Knitted Tiles": 1C 4C 2B 5B 8B 3D 6D 9D E S W N G (or analogous), going out by self-drawing the fourth 7C as the last tile from the wall. Lesser Honors and Knitted Tiles (12), Knitted Straight (12), Fully Concealed (4), Last Tile Draw (8), Last Tile (4), Flowers (8) = 48 points.

    -Structure 4, "Semi-regular Knitted Straight": 1C 4C 7C 2D 5D 8D 3B 9B EEEE (concealed kong) GG (with E as your seat wind and the prevalent wind), going out on self-drawn 6B as the last tile in the wall and the last tile of its kind, as the kong replacement tile. Knitted Straight (12), All Types (6), Fully Concealed (4), Last Tile Draw (8), Out with Replacement Tile (8), Pung of Seat Wind (2), Pung of Prevalent Wind (2), Concealed Kong (2), Last Tile (4), Flower (8) = 56 points.

  • Guest - Sylvain MALBEC

    Hello.
    I hope I haven't overlooked any point.

    "Seven Pairs"
    22 22 44 44 66 66 88bam
    Seven Pairs (24)
    All Green (88)
    Full Flush (24)
    Reversible Tiles (8)
    All Simples (2)
    Tile Hog (2 x3)
    Last Tile Draw (8)
    Fully Concealed Hand (4)
    TOTAL = 164

    "Thirteen Orphans"
    This one is pretty straightforward, since 13 of the 14 tiles are engraved in stone.
    Thirteen Orphans (88)
    Last Tile Draw (8)
    Fully Concealed Hand (4)
    Last Tile (4)
    TOTAL = 104

    "Lesser/Greater Honors and Knitted Tiles"
    Greater Honors and Knitted Tiles (24)
    Last Tile Draw (8)
    Fully Concealed Hand (4)
    Last Tile (4)
    TOTAL = 40

    "Semi-Regular"
    147bam 258dot 369wan EEEE R + R
    Knitted Straight (12)
    All Types (6)
    Prevalent Wind (2)
    Seat Wind (2)
    Concealed Kong (2)
    Out with Replacement Tile (8)
    Last Tile Draw (8)
    Fully Concealed Hand (4)
    Single Wait (1)
    TOTAL = 45

  • Guest - Menno Deij

    Ok, my latest attempt :o

    I've indicated by * the changes I made for your easy review

    1) Maximum score for 7 pairs
    hand: b22 b22 b44 b44 b66 b66 b8
    Assume the player makes mahjong by drawing the winning tile b8 as the last tile from the wall
    All green 88
    7 pairs 24
    Reversible tiles 8
    LTD 8
    FC 4
    tile hog x3 6
    *Full Flush 24
    *All Simples 2
    total 164

    4) Maximum score for knitted straight
    hand: b147 p258 m36 EEE GG
    Assume that the player is east in the east round, a pung of m9 is on the table, and the player draws as the penultimate tile from the wall the 4th east wind and makes a concealed kong. Then, as the replacement tile for making this kong, the player draws the last tile from the wall and it is the fourth m9 to make mahjong.

    Knitted straight 12
    Concealed kong 2
    Pung own wind 2
    Pung round wind 2
    Out with replacement tile 8
    LTD 8
    FC 4
    *All Types 6
    *Last Tile 4
    total 48

  • After first day twelve contestants have sent their solutions. Remarkably, all nine contestants with full score after mystery #4 have sent their correct answers. So the list of "Top Nine" stay although reshuffled by timestamp.

  • Guest - Anh-Vu Tran

    Hello,

    Here is my answer for this mystery.

    Maximum hand with Seven Pairs
    =============================

    An example hand with a lot of points, including Seven Pairs is: 2222444466668b win on 8b Last Tile Draw.
    Total points is: All Green (88) + Seven Pairs (24) + Full Flush (24) + Reversible Tiles (8) + Last Tile Draw (8) + Fully Concealed Hand (4) + Tile Hog (3*2) + All simples (2) = 164 pts
    Who would think that it is better than Seven Shifted Pairs !?

    Maximum hand with Thirteen Orphans
    ==================================

    The idea is to wait on a single tile (MCR allows player to have the pair in his/her hand) which is also the Last Tile Draw and Last Tile, e.g. wait on red dragon while a pung of red dragons is already melded.
    Robbing The Kong does not yield maximum points because it has same number of points as Last Tile Draw but cannot combine with Last Tile.
    Last Tile Claim does not yield maximum points too because it cannot combine with Fully Concealed Hand.
    Total points is: Thirteen Orphans (88) + Last Tile Draw (8) + Last Tile (4) + Fully Concealed Hand (4) = 104 points

    Maximum hand with Knitted tiles
    ===============================

    Like Thirteen Orphans, the player waits on a single tile which is also the Last Tile Draw and Last Tile.
    Total points is: Greater Honors and Knitted Tiles (24) + Last Tile Draw (8) + Last Tile (4) + Fully Concealed Hand (4) = 40 points

    Maximum hand with Knitted Straight
    ==================================

    In order to maximize hand, the player waits on the pair tile, with replacement of his/her kong, which is also the last tile draw.
    The kong shall be both the Seat Wind and the Prevalent Wind. The pair is a dragon, therefore the player can count the All Types fan.
    Total points is: Knitted Straight (12) + Out With Replacement Tile (8) + Last Tile Draw (8) + All Types (6) + Fully Concealed Hand (4) + Seat Wind (2) + Prevalent Wind (2) + Concealed Kong (2) + Single Wait (1) = 45 points

    Anh-Vu

  • Guest - Quentin

    Seven Pairs allows the highest irregular scoring: 164 points with e.g. Bams 22 22 44 44 66 66 88, drawing last tile of the Wall.
    Scores 7 pairs, All Green, Full flush, Reversible tiles, All Simples, 3 * Tile Hog, Fully concealed and Last draw.

    104 points is the highest value a 13 Orphans hand may reach, through either Fully concealed, Last Tile and Last draw, or Robbing Kong and Last claim which both grant 16 points.

    The same process applies for "knitted Hands", whatever 7+7 (Greater knitted) or 5+9 (Lesser knitted + Knitted straight): to the classical 24 can be added 16 "lucky" points, hence a maximum of 40 points for knitted hands.

    In case of Knitted straight the maximum scoring can be reached such: get ready with 8 tiles of the knitted straight, a pair of any Dragons and a triplet of "double Wind" (aka seat + prevailing). Wait three tiles like the winning one to be visible, draw last but one tile of the Wind to Kong it (concealed one), draw last tile of the wall as replacement tile and Hu.
    Then you get Knitted Straight, All types, Seat and prevailing Wind, Concealed Kong, Last tile, Last draw, After a Kong, Fully concealed hence 48 points.

  • Guest - Massimo

    "Seven Pairs" type: 2b2b 2b2b 4b4b 4b4b 6b6b 6b6b 8b + 8b
    seven pairs (24) + all green (88) + reversible tiles (8) + all simples (2) + last tile draw (8) + fully concealed hand (4) + tile hog (2) + tile hog (2) + tile hog (2) + full flush (24) = 164pt

    "Thirteen Orphans" type: SWNRBG1c9c1d9d1b9b9b + E
    thirteen orphans (88) + last tile draw (8) + last tile (4) + fully concealed hand (4) = 104pt

    "Lesser/Greater Honors and Knitted Tiles" type: 1c2b3d 7c8b9d ESWNRBG + 5b
    greater honors and knitted tiles (24) + last tile draw (8) + last tile (4) + fully concealed hand (4) = 40pt

    "Semi-Regular" type: 1c2b3d 4c6d 7c8b9d EEEE RR + 5b
    knitted straight (12) + last tile draw (8) + fully concealed hand (4) + out with replacement tile (8) + last tile (4) + closed kong (2) + all types (6) + pung of seat wind (2) + pung of prevalent wind (2) = 48pt

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