By the final session of the London MCR Championship, Professor Moriarty has taken the first position with a tremendous lead of 4 table points and 100 game points above second place, who is Sherlock Holmes. Sherlock can win the championship only under the rarest of circumstances: Sherlock must win his last table, and Moriarty must lose it. Luckily for Holmes, the two meet at the same table.

Before the last deal of the table, and of the whole championship, a miracle for Sherlock was beginning to take shape. Sherlock (East) has +90, Moriarty (South) has -39, Mrs. Hudson (West) has -21, and Moran (North) has -30 points. Sherlock, after winning first deals, has focused entirely on calling mahjong against Moriarty's discards in order to secure his position.

By the middle of a deal, Sherlock is waiting with this concealed hand -- , melded -- four flowers. Moriarty, on the right, has melded three sets including a dragon pung.

The situation is very clear: Sherlock can win from the wall with any hand, from Mrs. Hudson with a hand which scores no more than 17 points, or from Moran with a hand which scores no more than 8. If Sherlock wins from Moran any more than 8 points, Moriarty will bump up to 3rd place, earning him 1 TP, and winning him the championship. Sherlock's chances to win also include a "Hu" by either Moran or Mrs. Hudson, but only if they win with a small hand.

Suddenly, Mrs. Hudson discards . Sherlock cannot declare "Hu" at this time since his hand worth 26 points, and that against Mrs. Hudson would be too upsetting. With Mrs. Hudson sitting at North, then the best choice would be to declare Chow , discard  and wait for a future opportunity. So, Sherlock passes. In one turn Moriarty melds another set so he has four melded sets with two clear points, so he can now clearly win on any discard. In two moves, thunder and lightning struck: Moran on the left of Sherlock discards  and Moriarty on the right declares "Hu".

"So, the London Championship was won by Moriarty?" asked Watson at home.

"No way," Sherlock replied, showing the Champion's Cup.

"But how?"

"The player should know the "Green Book", it is the Bible and the law for the mahjong player."

Question (): Please, explain what happened, and how Sherlock managed to win championship?

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  • Guest - Oh Yong Sing

    Holmes can declare:

    Concealed Hand (2), All Chows (2), 2 x Short Straight (2 x 1), Mixed Double Chow (1), Close Wait (1).

    He can use his flower tiles for the counting, which would make them invalid to be added to the total points.

  • Guest - Sylvain MALBEC

    Sherlock declared Hu on Moran's discard.
    Since he's closer in turn order, Moriarty's Hu is voided and Sherlock wins the hand.
    Then Sherlock intentionally under-scored is hand as such:
    Two Terminal Chows (1)
    Short Straight (1)
    Concealed Hand (2)
    All Chows (2)
    Mixed Double Chow (1)
    Closed Wait (1)
    No flower
    TOTAL: 8 points

    Total for the table:
    Sherlock: +90 +32 = 122 (1st +4TP)
    Moriarty: -39 -8 = -47 (4th +0TP)
    Mrs. Hudson: -21 -8 = -29 (2nd +2TP)
    Moran: -30 -16 = -46 (3rd +1TP)

    Sherlock and Moriarty are tied on table points, so the victory goes to the one having the most game points.
    Sherlock earned +122 GP, and Moryarti lost -47 GP, so Sherlock closed the 100GP gap and wins the tournament.

  • This is hard!

    Do I understand correctly that Sherlock did not have a chance to change his hand? Hudson discarded 2, then Moran discarded something and Moriarty claimed the discard (skipping Sherlock’s turn), then Hudson discarded something and then Moran discarded 2 and Moriarty called hu; right?

    I am also assuming that Moriarty knew what he was doing and did not commit a foul of any kind with his hu declaration.

    So, Sherlock has three options: do nothing, declare hu, or misbehave.

    If he does nothing, then Moriarty wins off Moran with a hand worth at least 8 points (Melded Hand + Dragon Pung), which brings him up to at least -7 and Hudson and Moran down to at least -29 and -46 respectively. Moriarty finishes in second place (at least) and stays 2 table points ahead of Sherlock. Clearly, this does not work.

    If he declares hu, then Moriarty’s hu is invalidated and Sherlock wins off Moran with a hand worth 26 points (Pure Straight + All Chows + Concealed Hand + Mixed Double Chow + Closed Wait + 4 Flower Tiles), which brings Hudson, Moriarty and Moran down to -29, -47 and -64 respectively. Moriarty finishes in third place and stays 1 table point ahead of Sherlock. Clearly, this does not work either.

    Sherlock can try to commit a foul or “help” Moriarty commit one:

    • Sherlock could make a false hu declaration, but then he would forfeit 20 points to each of the remaining players as well as his right to win the hand. This would reduce the contest point spread between him and Moriarty to 49, so even if the game ended with Sherlock in first and Moriarty in last place, Moriarty would still be 51 contest point ahead and win the championship. So again, this does not work.
    • Sherlock could declare hu correctly but also knock over some of Moran’s tiles. He would forfeit “5–60 points to [Moran] according to the umpire’s discretion”, and the umpire would get to decide whether Sherlock continues to play. If the umpire decided to fine Sherlock anywhere between 18 and 60 points while allowing Sherlock’s hu, then Moran would reclaim his third place at the table, and Sherlock would keep his 127+ score point lead ahead of Moriarty and win the championship. This could work.
    • Reading the Green Book very literally, it appears that this may work: Sherlock declares hu (which invalidates Moriarty’s hu), but then he “forgets” to reveal his concealed tiles and discards a tile instead (see §3.11.6.11 paragraph 3). This seems very odd, and I doubt the rules were intended this way. If this were true, anyone could freely invalidate anyone else’s hu declaration made on a discard. This is probably a case of bad phrasing, bad translation or insufficient detail in the rules.
    • Sherlock could declare hu correctly but fail to tally his hand’s points using the tiles on the table; specifically, he could mix the tiles from his winning hand with other tiles on the table (see §3.11.6.11 paragraph 6). Apparently, this results in his win being invalidated and play resuming. Presumably, Moriarty’s win has been invalidated by this time (by Sherlock’s originally correct hu). Then, Sherlock hopes to end the game without Moriarty winning for the second time. This could work.
    • Sherlock could let Moriarty declare hu correctly and then “help” Moriarty mix the tiles in his hand with other tiles on the table. This would invalidate Moriarty’s win and resume the game, giving Sherlock another chance at winning. This could work, but this is close to cheating and could get Sherlock a harsher penalty.


    Finally, Sherlock could stall for time. The Green Book states that when the time allotted for the game runs out, play immediately stops and nobody gets any extra points. I am not sure that this applies to hands that have already been declared won, but maybe. The specific wording used in the Green Book is “any hand in play at that moment”. Sherlock could delay the process of Moriarty scoring his hand, or of Sherlock himself declaring hu, revealing and scoring his own hand, until the time limit bell rang. If the Green Book does mean that no points would be earned for the last hand in this case, then this could work. I have not found any specific penalties in the Green Book for stalling for time. However, if there is too much time remaining and Sherlock stalls too obviously, then he will probably be penalized for obstruction at the umpire’s discretion. It is possible that he gets a penalty that does not affect his final standing, but this is not guaranteed.

  • Guest - Jinbi Jin

    (This solution leaves the question why Sherlock didn't do this off Mrs. Hudson's hand...)

    Sherlock calls Hu as well, and since he's the player downstream from Moran, Sherlock's Hu takes priority. He then proceeds to rely on his freedom of choice of scoring to score as follows:

    Concealed Hand (2) + All Chows (2) + Mixed Double Chow (123d, 123b) (1) + Two Terminal Chows (123b, 789b) (1) + Short Straight (456b, 789b) (1) + Single Wait (1), for 8 points, simply neglecting the 4 flowers he has melded.

    The end result then becomes:
    Sherlock +122, Hudson -29, Moran -46, Moriarty -47, and Sherlock wins the tournament by 69 game points.

  • (In fact, even if Sherlock could have changed his hand, he still couldn’t just declare hu and win. He has four flowers, so his hand would either be worth too much with the flowers for Moriarty to stay last or too little without the flowers for Sherlock to be allowed to declare hu.)

    Okay, here’s a specific, full scenario of what may have happened:

    Moran discards 2 bamboo.
    Moriarty: “Hu!”
    Sherlock: “Hu! Sorry, I’m closer to the discarder, so it’s my win.”
    Sherlock reveals his tiles and counts his points using tiles from the discard pool.
    Sherlock: “Pure Straight, All Chows, Concealed Hand, Mixed Double Chow, Closed Wait, 4 Flower Tiles. 26 points.”
    All other players at the table agree. They expect the following final score at the table: Sherlock +140, Hudson -29, Moriarty -47, Moran -64.
    Sherlock: “So what did you have there, Moran?”
    Before anyone can say anything, Sherlock leans towards Moran and knocks over all his concealed tiles for all to see.
    Moran: “Hey! You can’t do that! Umpire! Holmes has just exposed tiles from my hand.”
    Umpire: “Oh wow, the whole hand? Mr Holmes, even if you’re famous and currently leading the championship, you can’t just expose other players’ tiles. You exposed the entire hand, so I have to impose the harshest penalty on you: you must give 60 points to Mr Moran.”
    Sherlock pretends to look shocked and saddened.
    Final score at the table: Sherlock +80, Moran -4, Hudson -29, Moriarty -47. Sherlock gets 4 table points, while Moriarty gets 0.
    Final standing in the championship: Sherlock and Moriarty have the same amount of table points, and Sherlock has 27 contest points more than Moriarty, so Sherlock Holmes is declared champion.

  • Guest - Menno Deij

    Hi Vitaly,

    What may have happened is that Moriarty declared an invalid Hu. In that case, he loses 60 points, 20 to each opponent. The new point distribution is then 110 for Holmes, -99 for Moriarty, -1 for Hudson and -10 for Moran. As there are two more winning tiles in the wall, Sherlock decided not to make Hu and waited for the next opportunity.

  • Guest - Anh-Vu Tran

    Hello,

    We know that Holmes didn't do the chow 123b, because the player right before him is Moran, not Mrs. Hudson.
    It means that Holmes still holds the same concealed hand and is waiting for 2b to win.
    Now let me quote one paragraph from the Green Book:

    3.7.2.4. Only one player can win current hand. When more than one person declares "Hu" on a discard, the nearest next player following the discarder is the winner.


    When Moran discards the 2b tile Moriarty is waiting on, Holmes can also claim Hu, and he is the nearest next player following the discarder. If Holmes declares a valid Hu, then Moriarty cannot win that hand.
    This is only the first part why Holmes wins the tournament. Unfortunately, if he declares 26 points, Moran would lose too many points, Moran finishes at 4th place, Moriarty is 3rd with 1 table point and is still ahead for the tournament.
    Now comes another quote from the Green Book:

    3.9.1.6 (4) Freedom to Choose the Highest Points ("the High- versus- Low Principle") : If you can use a set to form both a high-score fan and a low-score fan, it is your right to choose the high-score fan.


    A player is free to choose the highest fan, he is also free not to choose it too ! Holmes can declare the following fans:
    Concealed Hand (2pts) + All Chows (2pts) + Mixed Double Chow 123 (1pt) + Short Straight 123456b (1pt) + Short Straight 456789 (1pt) + Closed Wait (1pt) = 8 pts
    He forgets the flowers. 8pts from Moran discard is exactly what Holmes needed to have 4 tables points and Moriarty 0 table point.

    Finally Holmes and Moriarty have same total table points. But Holmes makes more than 100 game points more than Moriarty at the last table. Holmes has the highest total game points and wins the championship.

    Anh-Vu

  • Guest - Menno Deij

    Hi Vitaly,

    As the rules state that the player is the only one who is counting fans, Sherlock can declare hu and count his hand as follows:
    Concealed hand 2, all chows 2, two mixed chows 1, two terminal chows 1, closed wait 1 and short straight 1 to get exactly 8 points from Moran. The other players can only check, and the referee can only confirm. This way Sherlock can win the tournament by not counting the full straight.

  • Assuming that Holmes actually did win the last hand, we must find a way for Moran to gain a few extra points or for Moriarty to lose a few extra points. (Even if Holmes could change his hand’s value, the absolute cheapest he can get is 12 points, as he has four declared flowers.) The only way for Moran to gain points that I see is for someone to knock over his tiles, which I have tried in a previous answer. For Moriarty to lose points, he must commit a foul.

    Perhaps Moriarty has already committed a foul such as a late pung call. But this would make the problem trivial, and Holmes’s reasoning given in the problem statement implies this not to be the case.

    The only foul I can see in the rules that Moriarty could commit right after declaring hu that would result in him losing points is exposing his hand after Holmes declares his own hu and breaking the wall such that play cannot continue, which costs him 30 points per each of the remaining players, as per §3.11.6.7.2. The English version of the green book is very unclear on when this penalty applies, and you could even argue that it applies even if Moriarty merely showed his hand and Holmes’s win was recognized:

    1. Moriarty declares hu and immediately flips over his last concealed tile.
    2. Holmes declares hu. Moriarty hears this but is too late to stop his tile from becoming visible.
    3. Holmes’s win is scored. Moriarty gives 30 points to each player as penalty for unduly exposing his hand.

    This contradicts common sense, which says the penalty should not be paid if Holmes’s win is confirmed to be valid. The Chinese version of the rules sounds even more sensible: the penalty applies only if play should continue (i. e. Holmes’s win turns out to be invalid—and this is assuming Moriarty’s hu wouldn’t be recognized instead, which I’m not sure about) but cannot continue because Moriarty has exposed or moved too many tiles, in particular tiles from the wall. Here is the Google translation I base this reasoning on: http://bit.ly/2oHwMug

  • Guest - Cédric

    Holmes claimed for the winning tile and counted exactly 8 points in his winning hand.

    Holmes had not claim the 2 bamboo discarded by Mrs. Hudson (North). So he was still waiting for this tile. When Moran (East) discarded it, Holmes (South) intercepted and said Hu at the same time as Moriarty (West).
    Holmes has then counted: concealed hand (2), all chows (2), single wait (1), two short straights from 1 to 6 and 4 to 9 (2) and a double chow (1) for a total of 8 points. He volontarily forgot the flowers.
    Final scores :
    Holmes : +90 + 32 --> +122
    Mrs Hudson : -21 -8 --> -29
    Moran : -30 -16 --> -46
    Moriarty : -39 -8 --> -47

    Holmes won the Championship for only 71 game points ahead Moriarty.

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