(11C) Mahjong scores

[Rogier]

This is not the puzzle-style Mahjong. It's quite a complex game, with a lot of rules but it's fun. I will try and explain it in brief.

In this game the tiles are laid out in a square forming four walls 18 tiles long an 2 tiles high. By throwing dice the player who will be EAST for the first game is established and this player trhows dice to determine in which wall dealing will begin. The ' owner' of that wall throws dice te determine at which spot the dealing of tiles will begin.

Three players start out with 13 tiles, East starts out with 14. He will discard the fist tile. After that the players take turns drawing a tile. You may take a tile from the wall, but under circumstances you may also claim a discarded tile.

• You may claim a discarded tile from any player to complete a pung (see below) or to win the game.
• Under conditions, you may also claim a tile to complete a kong (see below).
• A Tsjou (see blow) may only be completed by a tile discarded by your left-hand neigbour, or to win the game.
  

If you can't make a winning combination with the tile you took, you discard a tile of your choice (call it's name and place it on the table).

A winning combination is a combination of 14 tiles consisting of 4 triplets and 1 pair of identical tiles. If all players agree you can also accept other combinations as winning, like 7 "twins". Winning games have all sorts of beautiful Chinese names, which I don't know.
Triplets can be a combination of 3 identical tiles (like 3 times 3 bamboo) of 3 different tiles of the same colour and in ascending order (eg sign3-sign4-sign5). The first variety is called Pung, the second is called Tsjou. In some cases a Pung may be extended to a quadruplet, called Kong. In that case the player must take 1 extra tile from the wall (otherwise you can't win anymore).
If the tile completing a pung/kong was discarded by another player, the pung/kong is laid out on the table. Ifs the player took the tile from the stock, the tiles are kept hidden.
A tsjou scores no points, a kong scores double what a pung would do, hidden pungs and kongs score double points.

Example. WEST wins with this hand:
3X 7 of signs (in the hand)
3X 2 of signs (on table)
3X West wind (in the hand)
3X Red dragon (on the table)
2X North wind
The winning tile was North wind, discarded by another player

This would score:
2 points for the 2's of signs
4 points for the 7's of sings (hidden scores double)
4 points for the Red dragons (dragons and winds score double)
8 points for the West winds (hidden scores double)
Bonus for only way to win: 2 points
Bonus for winning: 20 points
Total so far: 40 points

This score is doubled for:
Pung of Red dragon: 1 (pungs and kongs of dragons do that)
Only one suit (so: no circles or bamboos) + honours (winds and dragons): 1
Pung of West wind: 1 (but only because our winner is WEST.)

So final score = 8x40 points = 320 points.

Now for the whole table:
EAST: 8 points
SOUTH: 20 points
WEST: 320 points (Winner)
NORTH: 64 points

Result (and this is what the program takes care of):
> SOUTH and NORTH pay WEST 320 points, EAST pays WEST 640 points
> SOUTH receives 2x(20-8) = 24 points from EAST
> SOUTH pays 64-20 = 44 points to NORTH
> EAST pays 2x(64-8) = 112 points to NORTH
EAST did not win, so the winds rotate. In the next game our winner will be SOUTH.

There are numerous game variants and various ways of scoring, but this is the system we use.
See also: https://en.m.wikipedia.org/wiki/Mahjong

BTW: you are right about the total points. It's a closed system, so knowing 3 players should be enough, but only for the 'grand totals'. Points scored per game is not a closed system. I found it easier to keep the values for all 4 players. If I want to check a ' credit status' I just Rcl 1-4. If I only kept score on 3 players I would need an extra piece of code to calculate the fourth.