Necessary and Unnecessary Tiles

A tool for calculating necesaary tiles and unnecessary tiles for winning hands in Japanese mahjong.

Read this in Japanese (日本語).

What are necessary tiles and unecessary tiles in mahjong ?

• Necessary tiles:
  • the tiles needed to win with least number of exchanges.
  • decrease the shanten number when one of them is drawn.
  • called "yuukouhai" or "ukeire" in Japanese.
• Unnecessary tiles:
  • the tiles unneeded to win with least number of exchanges.
  • keep the shanten number unchanged when one of them is discarded.
  • called "yojouhai" in Japanese.

Usage

1. Prepare a std::vector<int> array representing a hand.

• The n th element stores the number of n th tiles.

	1	2	3	4	5	6	7	8	9
Manzu	0	1	2	3	4	5	6	7	8
Pinzu	9	10	11	12	13	14	15	16	17
Souzu	18	19	20	21	22	23	24	25	26
Jihai	27 (East)	28 (South)	29 (West)	30 (North)	31 (White)	32 (Green)	33 (Red)

• For example, if you have manzu tiles (1, 2, 3), pinzu tiles (2, 4, 5, 7, 7, 9), and jihai tiles (East, West, White, White, White), define the following array.

std::vector<int> hand = {
  1,1,1,0,0,0,0,0,0, //Manzu
  0,1,0,1,1,0,2,0,1, //Pinzu
  0,0,0,0,0,0,0,0,0, //Souzu
  1,0,1,0,3,0,0 //Jihai
};

2. Calculate the shanten number, necessary tiles and the unnecessary tiles.

std::tuple<int,int,std::int64_t,std::int64_t> CalshtDW::operator()(const std::vector<int>& hand, int m, int mode)

NOTE: Normally, substitute the value obtained by dividing the number of tiles by 3 into m.

NOTE: mode specifies for which winning pattern calculate shanten number. When the pattern is "General Form", mode is 1, when "Seven Pairs": 2, "Thirteen Orphans": 4. When calculating the Shanten number for multiple winning patterns, specify the logical sum of them.

NOTE: This method returns the value of shunten number + 1, mode, necessary tiles, unnecessary tiles. The mode indicates which winning pattern (General Form, Seven Pairs, Thirteen Orphans) has the minimum shunten number. Each valid/unnecessary tile is represented by a 64-bit integer. Whether 1 or 0 of the i-th bit indicates whether the i-th tile is a necessary tile (or an unnecessary tile) or not.

For example, calculate the necessary tiles and unneccessary tiles of the hand defined above. It requires one of manzu tiles (1 to 9) or one of jihai tiles (East, West) for winning, however one of manzu tiles (2, 4, 5, 7, 9) or one of jihai tiles (East, West, White) is uneeded. The source code is as follows:

#include <iostream>
#include <bitset>
#include <vector>
#include "calsht_dw.hpp"

int main()
{
  CalshtDW calsht;

  // Set the location of shanten tables
  calsht.initialize(".");

  std::vector<int> hand = {
    1,1,1,0,0,0,0,0,0,// manzu
    0,1,0,1,1,0,2,0,1,// pinzu
    0,0,0,0,0,0,0,0,0,// souzu
    1,0,1,0,3,0,0// jihai
  };
  unsigned long long int disc;
  unsigned long long int wait;

  auto [sht, mode, disc, wait] = calsht(hand, 4, 7);

  std::cout << sht << std::endl;
  std::cout << mode << std::endl;
  std::cout << std::bitset<K>(disc) << std::endl;
  std::cout << std::bitset<K>(wait) << std::endl;

  return 0;
}

Output:

3
1
0010101000000000101011010000000000
0000101000000000111111111000000000

Sample Program

This program simultes single player mahjong. In each round, it discards one of unnecessary tiles, and then maximize the number of necessary tiles.

Build

• Debug mode

$ mkdir build
$ cd build
$ cmake .. -DCMAKE_BUILD_TYPE=Debug
$ make

• Release mode

$ mkdir build
$ cd build
$ cmake .. -DCMAKE_BUILD_TYPE=Release
$ make

NOTE: A compiler compatiable with C++11 or higher is needed.

Execute

$ ./sample [number of rounds (e.g. 1000000)]
$ cat result.txt
Number of Tiles         14
Total                   1000000
Time (msec.)            106499

Turn    Shanten Number (-1 - 6)                                         Hora    Tempai  Exp.
0       4       689     23224   194623  439207  285376  55254   1623    4e-06   0.000693        3.1576
1       36      3139    60055   312301  436206  169174  18856   233     3.6e-05 0.003175        2.76561
2       165     9550    118653  409619  368079  87961   5939    34      0.000165        0.009715        2.42371
3       575     22236   193284  461052  278799  42243   1805    6       0.000575        0.022811        2.12924
4       1585    43455   270484  467989  196448  19497   539     3       0.001585        0.04504 1.87492
5       3557    73558   341680  439988  132134  8916    167     0       0.003557        0.077115        1.651
6       7014    111731  397628  393033  86425   4115    54      0       0.007014        0.118745        1.45269
7       12342   155439  437312  337357  55610   1918    22      0       0.012342        0.167781        1.2743
8       19769   202505  460160  281105  35463   991     7       0       0.019769        0.222274        1.11299
9       29749   250970  466746  229544  22484   502     5       0       0.029749        0.280719        0.96557
10      42291   298561  460318  184296  14284   247     3       0       0.042291        0.340852        0.830474
11      57229   343412  444338  145635  9257    128     1       0       0.057229        0.400641        0.706667
12      74977   383949  420945  114180  5875    74      0       0       0.074977        0.458926        0.592249
13      94703   420040  392750  88629   3832    46      0       0       0.094703        0.514743        0.486985
14      116313  450680  362048  68448   2487    24      0       0       0.116313        0.566993        0.390188
15      140202  475546  330180  52435   1622    15      0       0       0.140202        0.615748        0.299774
16      165530  494708  298847  39820   1087    8       0       0       0.16553 0.660238        0.21625
17      192032  508775  268240  30169   780     4       0       0       0.192032        0.700807        0.138902

• The first line shows the number of hand tiles, the second line shows the number of games, and the third line shows the execution time (milliseconds).

• The sixth line onward shows the ratio of each shanten number (-1 to 6), winning ratios, tempai ratios, expected values of shanten numbers from left to right. The final line shows that the winning rate in single player mahjong is about 19%.

• The graph belows shows the ratios and expected values of shanten number in each round.

Three Player Mahjong mode

Enable THREE_PLAYER.

Example:

$ cmake .. -DCMAKE_BUILD_TYPE=Release -DTHREE_PLAYER=on

Building tables (Unneeded)

Build tables of parameters required for calculating necesaary tiles and unnecessary tiles. Make "index_dw_h.txt" and "index_dw_s.txt".

$ ./mkind2.out

License

GNU General Public License v3.0.