Once upon a time an associate of the Lee family approached me. "Would you join us for a game of Mahjong?" they asked. I agreed, flattered and nervous by such an invitation. The date was set and I arrived on an unassuming street at an unassuming door. I entered.
What then transpired was a night of wonder, amazement, and my introduction to the great and terrible world of Mahjong scoring!
Let me give you two choices - would you like a max score of 10 or of 100,000+?
Hong Kong Style (at least, the variant I play) awards individual points for particular rules:
+1 if you have no flowers or seasons
+1 if you have your flower
+1 if you have your season
+1 for concealed
+1 for self draw
+1 for every pung of dragons (up to +3)
+1 for a pung of the wind of the round
+1 for a pung of your wind (If yours is the wind of the round, you get both points.)
And then hand bonuses:
+1 point if all Chow
+3 points if all Pung
+3 points if 1 suit + honor tiles (semi-pure).
+6 points if all same suit (pure)
Once you do the math you add all these up to your score.
BUT THEN you convert the points into chips (and then on to money, if ye be the wagering sort).
The winner is paid either by the person who threw the 14th tile for their hand, giving them 1x, or every player pays them if they self-drew (on top of the point boost for self-drawing) for a total of 3x. Payout rules vary house to house.
Well... Remember when I mentioned variants? The scoring used that night at the Lee's was a type of Chinese Classical. I went on to learn Vanilla Western which is itself a modification of CC.They score like this:
20 points to the player who went out, and:
+2 if 14th completes Chow in only possible place
+2 if 14th completes pair
+2 if 14th is self draw
+4 points for every flower or season
+2 for any pairs of dragons, player's wind, or wind of round.
+2 if you grabbed the first discard of the game
+2 points for every Pung. For each pung, double value if:
if made of Honor Tiles OR 1 OR 9
x4 if made into kong
(these all multiply, so a concealed kong of #1 is worth 32 points. 2x2x2x4 = 32)
Okay, so your're likely sitting on 20-50 points. This is your Ground Score. Now Let's get Weird.
Player who won:
Score x2 if all tiles concealed.
Score x2 if just last tile drawn from wall
Score x2 if last tile was the last tile of the wall
Score x2 if last tile robbed a kong.
Player who won and all players who were waiting on just one tile
Score x2 if hand is semi-pure (all same suit + honors)
Score x2 if no Chows
Score x2 for EACH Pung/Kong of Dragons
Score x2 for Pung/Kong of own wind
Score x2 for Pung/Kong of wind of the round
Score x2 for having own flower
Score x2 for having own season
Score x4 if you hold all four seasons
Score x4 if you hold all four flowers
Score x8 if entire hand is pure (all one suit, no honor tiles)
Score x8 if entire hand IS all honor tiles.
So how do we get to 63,000? Check this out:
Let's say I win with Own flower, own season, 2 pung of dragon, pung of own wind, pung of wind of the round, pair of third wind. Assume 2 pung were exposed, 2 concealed.
Going out: +20
+8 for own flower and season
+8 concealed pung 1
+8 concealed pung 2
+4 pung 3
+4 pung 4
Ground score is 52. Now we double.
x2 for no Chow
x2 for dragon 1
x2 for dragon 2
x2 for own wind
x2 for wind of the round
x2 for own flower
x2 for own season
x8 for all honor tiles
That's a multiplier of 10 doubles, or 2048 times base = 106,496. If I had self-drawn? Double again for 212,992. If I converted one of the concealed pung into an exposed kong? That increases the base score by 8 - which scales up to be worth 32,768 points for 245,760.
If you got really crazy, the theoretical max is somewhere around 1.8 Trillion. (4 kongs of 3 dragons plus your own wind which is wind of the round, all hidden, plus pair of any other wind. 128 + 4 (pair, self draw) +64 (all flowers, seasons) + 20 for going out = 216 Base. Doubles: 33. Total: 1,855,425,871,872.
Remove the 16 doubles for all flowers and seasons as that is pretty ridiculous and you get 83,886,080 (assume only two self - 160 base and 19 doubles)
The book that I got this from (Thompson & Maloney) suggests one should cap the max score at 300-1000 at the start of the game. To which I say - if you're going to use a broken scoring system, why cushion it? Go all of the way! But I'd never play an uncapped game of Western Vanilla for money. Mathematicians THIS IS WHY YOU CHECK EDGE CASES.