LONDON - Before a traditional game at 221 B Baker Street, there is a mahjong class. Mrs. Hudson is asking Sherlock Holmes:

"If a complete hand allows multiple ways to score, what is the appropriate way to manage that?"

"According to the "Green Book", after a player declares "Hu", the player should clearly do several things: brake hand into sets with valid a hand structure, indicate clearly which set will be formed with the winning tile, and then score their fan.

Let's consider some interesting hand. Imagine that the player declares "Hu" on his 10th turn with this concealed hand:

winning on discarded .

How to best score this hand? Please note, there are several ways to structure the hand to answer the above stated question.

Question: Please, provide all possible variants of scoring this hand's value (list all fan for the relevant structures).

Note: Two or three correct variants will be scored for , four or more correct variants will be scored for .

 

 

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

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  • Guest - Oh Yong Sing

    11,11,22,22,33,33,44 : Seven Pairs (24), Full Flush (24), Lower Four (12), Reversible Tiles (8), 3 × Tile Hog (3 x 2). Total: 74 points.

    123,123,123,123,44: Quadruple Chow (48), Full Flush (24), Lower Four (12) Reversible Tiles (8), All Chows (2), Concealed Hand (2). Total: 96 points.

    111,222,333,123,44: Pure Shifted Pungs (24), Full Flush (24), Lower Four (12), Reversible Tiles  (8), 3 x Tile Hog (3 x 2), Concealed Hand (2). Total: 76 points.

    11,123,123,234,234: Full Flush (24), Lower Four (12), Reversible Tiles (8), All Chows (2), 2 x Pure Double Chow (2 x 1), Concealed Hand (1). Total: 49 points.

  • Guest - Jinbi Jin

    In the following, I'll indicate the discarded tile by just a *, and mark the parts a hand consists of using parentheses.

    First, note that the waits of this hand are 1, 2, 3, 4, 5 of circles, so no points for the type of wait can be added.

    The only possible irregular hand that can be made is a Seven Pairs hand (11)(1*)(22)(22)(33)(33)(44):
    - this one scores Seven Pairs (24) + Full Flush (24) + Lower Four (12) + Reversible Tiles (8) + Tile Hog x 3 (6) = 74 pts.

    Next, we find all possible configurations of this hand as a regular hand. It is not possible for (22) or (33) to be the pair of this hand, so the only possible pairs are (11) and (44).
    In the first case, there are two possibilities; (11)(123)(*23)(234)(234) and (1*)(123)(123)(234)(234).
    - both of them score Full Flush (24) + Lower Four (12) + Reversible Tiles (8) + Tile Hog x 3 (6) + All Chows (2) + Concealed Hand (2) + Pure Double Chow x2 (2) = 56 pts.
    In the second case, there are three possibilities; (123)(123)(123)(*23)(44), (11*)(222)(333)(123)(44), and (111)(222)(333)(*23)(44).
    - (123)(123)(123)(*23)(44) scores Quadruple Chow (48) + Full Flush (24) + Lower Four (12) + Reversible Tiles (8) + All Chows (2) + Concealed Hand (2) = 96 pts.
    - (11*)(222)(333)(123)(44) scores Pure Shifted Pungs (24) + Full Flush (24) + Lower Four (12) + Reversible Tiles (8) + Tile Hog x 3 (6) + Two Concealed Pungs (2) + Concealed Hand (2) + Pung of Terminals (1) = 79 pts.
    - (111)(222)(333)(*23)(44) scores Pure Shifted Pungs (24) + Full Flush (24) + Three Concealed Pungs (16) + Lower Four (12) + Reversible Tiles (8) + Tile Hog x 3 (6) + Concealed Hand (2) + Pung of Terminals (1) = 93 pts.

    (So the best option among these six is (123)(123)(123)(*23)(44), scoring 96 pts.)

  • Guest - Oh Yong Sing

    Correction on the 3rd variant:

    11,11,22,22,33,33,44 : Seven Pairs (24), Full Flush (24), Lower Four (12), Reversible Tiles (8), 3 × Tile Hog (3 x 2). Total: 74 points.

    123,123,123,123,44: Quadruple Chow (48), Full Flush (24), Lower Four (12) Reversible Tiles (8), All Chows (2), Concealed Hand (2). Total: 96 points.

    111,222,333,123,44: Pure Shifted Pungs (24), Full Flush (24), Three Concealed Pungs (16), Lower Four (12), Reversible Tiles  (8), 3 x Tile Hog (3 x 2), Concealed Hand (2). Total: 92 points.

    11,123,123,234,234: Full Flush (24), Lower Four (12), Reversible Tiles (8), All Chows (2), 2 x Pure Double Chow (2 x 1), Concealed Hand (1). Total: 49 points.

  • Guest - Cyrille

    All my propositions will include full flush(24), lower four (12) and reversible (8), that makes already 44 points.

    a) 123 123 234 234 11
    I add concealed(2), all chows(2), 2*pure double chow(2), 3*tile hog(6). Total = 56 points

    b) 11 11 22 22 33 33 44
    I add seven pairs(24) and 3*tile hog(6). Total = 74

    c) 111 222 333 123 44 (winning tile is used for 123).
    I add concealed(2), 3*tile hog(6), terminal pung(1),3 pure shifted pungs(24), 3 concealed pungs(16). Total = 93 points

    d) 123 123 123 123 44
    I add concealed(2), all chows(2), quadruple chow (48). Total = 96 points

  • Guest - Oh Yong Sing

    Correction on my 4th variant:

    11,123,123,234,234: Full Flush (24), Lower Four (12), Reversible Tiles (8), 3 x Tile Hog (3 × 2), All Chows (2), 2 x Pure Double Chow (2 x 1), Concealed Hand (2). Total: 56 points.

  • For starters, clearly, the player has no kongs.

    As this is the player’s tenth turn, we can assume (?) that the winning tile is not the last discard in the game.

    This hand is a valid seven pairs hand: 11 11 22 22 33 33 44.

    This hand does not qualify for thirteen orphans or for knitted tiles. The only thing that’s left is a normal hand with chows, pungs and a single pair.

    Consider the 44: either this is a pair or each 4 is part of a chow, which can only be 234, as there is no 5 in the hand.

    If 44 is a pair, then the remainder of the hand is 111122223333. Consider the threes: 33 cannot be a pair (as we already have one), so the threes either form a pung (??3 333) or are all part of chows (123 123 123 123). In the latter case, we already know the whole hand: 123 123 123 123 44. On the other hand, if we do have a 333 pung, then the remaining 3 must be part of a 123 chow and we have 111222 left over, which can only be two pungs: 111 222 123 333 44.

    If the fours do not form a pair, then we have 11112233 234 234. If 22 or 33 is a pair, then the other must be a pair too, which is impossible (as we need only one pair). So 11 is a pair and we’re left with 112233, which can only be a pair of chows: 11 123 123 234 234.

    In total, there are exactly four possible decompositions of this hand:

    • 11 11 22 22 33 33 44
    • 123 123 123 123 44
    • 111 222 123 333 44
    • 11 123 123 234 234


    Now, let’s see what fan they score.

    Regardless of the interpreted hand composition, this hand qualifies for full flush (24), lower four (12), reversible tiles (8), concealed hand won by discard (2).

    In addition to this, the individual interpretations of the hand score:
    • 11 11 22 22 33 33 44: seven pairs (24), tile hog (2) = 72 total
    • 123 123 123 123 44: quadruple chow (48), all chows (2) = 96 total
    • 111 222 123 333 44: three pure shifted pungs (24), two concealed pungs (2), tile hog (2), pung of terminals (1) = 75 total
    • 11 123 123 234 234: tile hog (2), pure double chow (1) twice = 50 total

  • For starters, clearly, the player has no kongs.

    As this is the player’s tenth turn, we can assume that the winning tile is not the last discard in the game: the number of used wall tiles is certainly no more than 8 flower replacements + 4 kong replacements per player * 4 players + 4 wall tiles per go-around * (10 turns + 4 melds that interrupt turn order per player * 4 players) = 128, while the total number of tiles in the wall is 144, so there are definitely still tiles left in the wall.

    This hand is a valid seven pairs hand: 11 11 22 22 33 33 44.

    This hand does not qualify for thirteen orphans or for knitted tiles. The only thing that’s left is a normal hand with chows, pungs and a single pair.

    Consider the 44: either this is a pair or each 4 is part of a chow, which can only be 234, as there is no 5 in the hand.

    If 44 is a pair, then the remainder of the hand is 111122223333. Consider the threes: 33 cannot be a pair (as we already have one), so the threes either form a pung (??3 333) or are all part of chows (123 123 123 123). In the latter case, we already know the whole hand: 123 123 123 123 44. On the other hand, if we do have a 333 pung, then the remaining 3 must be part of a 123 chow and we have 111222 left over, which can only be two pungs: 111 222 123 333 44.

    If the fours do not form a pair, then we have 11112233 234 234. If 22 or 33 is a pair, then the other must be a pair too, which is impossible (as we need only one pair). So 11 is a pair and we’re left with 112233, which can only be a pair of chows: 11 123 123 234 234.

    In total, there are exactly four possible decompositions of this hand:

    • 11 11 22 22 33 33 44
    • 123 123 123 123 44
    • 111 222 123 333 44
    • 11 123 123 234 234


    Now, let’s see what fan they score.

    Regardless of the interpreted hand composition, this hand qualifies for full flush (24), lower four (12), reversible tiles (8), concealed hand won by discard (2).

    In addition to this, the individual interpretations of the hand score:
    • 11 11 22 22 33 33 44: seven pairs (24), tile hog (2) thrice = 76 total
    • 123 123 123 123 44: quadruple chow (48), all chows (2) = 96 total
    • 111 222 123 333 44 where the winning tile completes 111: three pure shifted pungs (24), tile hog (2) thrice, two concealed pungs (2), pung of terminals (1) = 79 total
    • 111 222 123 333 44 where the winning tile completes 123: three pure shifted pungs (24), three concealed pungs (16), tile hog (2) thrice, pung of terminals (1) = 93 total
    • 11 123 123 234 234: all chows (2), tile hog (2) thrice, pure double chow (1) twice = 56 total

  • Er, disregard my calculation of the number of tiles left in the wall in the last comment. I forgot to subtract the number of tiles in the players’ hands from the total number of tiles.

    Still, even if it might be possible that this is the last discard, that would add 8 points (last tile claim) to every possible interpretation of the hand and would not vary based on the interpretation.

  • Another attempt at proving that last tile claim is in fact impossible: the number of used wall tiles is certainly no more than 13 initial tiles per player * 4 players + 8 flower replacements + 4 kong replacements per player * 3 players with kongs (the winner has no kongs) + 4 wall tiles maximum per go-around * 10 turns in which the winner got a tile + 2 wall tiles maximum per go-around in which the winner didn’t get a tile (someone else must have claimed a discarded tile, and so neither the winner nor the claiming player got a fresh tile from the wall) * 4 melds per player * 3 players with open hands (the winner has a closed hand) = 136, while the total number of tiles in the wall is 144, so there are definitely still tiles left in the wall.

  • Guest - Massimo

    The best hand scoring is 102 points (without flowers).

    Variant 1: 123 - 123 - 123 - 123 - 44
    full flush (24) + concealed hand (2) + tile hog (2) * 3 + lower four (12) + reversible tiles (8) + quadruple chow (48) + all chows (2) = 102 points

    Variant 2: 111 - 222 - 333 - 123 - 44
    full flush (24) + concealed hand (2) + tile hog (2) * 3 + lower four (12) + reversible tiles (8) + three coanceled pung (16) + pure shifted pungs (24) + no honors (1) = 93 points

    Variant 3: 11 - 11 - 22 - 22 - 33 - 33 - 44
    full flush (24) + concealed hand (2) + tile hog (2) * 3 + lower four (12) + reversible tiles (8) + seven pairs (24) + no honors (1) = 77 points

    Variant 4: 123 - 123 - 234 - 234 - 11
    full flush (24) + concealed hand (2) + tile hog (2) * 3 + lower four (12) + reversible tiles (8) + pure double chow (1) + pure double chow (1) + all chows (2) = 56 points

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