MeowCaTS won the Mahjong tournament

1. Introduction

The Mahjong tournament of the 2023 Computer Olympiad took place between August 22 and 24, 2023. In the tournament, a total of five programs participated, with one team from Japan and four teams from Taiwan. The information about these teams is listed in Table 1. The rules of Mahjong have many variants around the world. In this tournament, Taiwan Mahjong was adopted as the primary reference for the rules. Detailed rules can be found in (Chen, Tang and Wu, 2022) and (Shan et al., 2014).

Given the participation of five teams this year, there were a total of five matches, with each team having a bye in each match. A match consisted of 192 games. The score for a game was set to 1000/500, indicating that the winner received a base score of 1000 points along with an additional 500 points per tai, as described in (Shan et al., 2014). The team with the highest accumulated scores was the winner of the tournament. The tournament adopted the game-playing platform developed by Jr-Chang Chen’s team (Chen, 2022). In order to reduce the influence of randomness, the platform implemented the fair mode, which involved using the same random seed to generate the initial wall four times. When a game was over, the initial hand was shifted to the next player to ensure that each player played the same initial hand once. A time limit of three seconds per ply was imposed on each program. When a program exhausted its allocated time, a dummy program would automatically take over the gameplay until the end of the game.

The final rankings and the scores for each match are listed in Table 2. Congratulations to MeowCaTS. This team won 270 games and 272.5k points, achieving the highest scores among all teams, and was awarded the gold medal. SimCat demonstrated a competitive performance, closely following MeowCaTS. However, SimCat won 67.0k points in Match 3, which was lower than 93.5k points of MeowCaTS in Match 2. As a result, SimCat received the silver medal with a total of 226.0k points. Golem won the highest points in Match 2 and Match 3; however, its performance in Match 1 and Match 4 was less impressive. Finally, Golem received the bronze medal with a total of 205.0k points.

MeowCaTS and SimCat were both excellent at quickly forming a ready hand, a key strategy for winning in Mahjong. Golem sometimes tended to make a high-scoring hand, as observed. In Match 1 and Match 4, MeowCaTS and SimCat consistently outpaced Golem in building winning hands. This made a notable gap between Golem and the two programs, despite Golem’s superior performance in Match 2 and Match 3. Surprisingly, the 2022 champion, VeryLongCat, struggled in Match 1, demonstrating a performance that was less impressive compared to its past achievements.

The search algorithms used by the teams are described as follows. MeowCaTS used Monte-Carlo Tree Search to simulate its hand and chose the move based on the highest visit count. It also incorporated importance sampling and the transposition table to enhance the quality of the search. SimCat used Monte-Carlo sampling to compute the win rate in a simplified model (Chen, Tang and Wu, 2022). Golem opted to retain the tile with the most types of possible combinations while keeping the lowest deficiency number (Huang, 2023). VeryLongCat used Expectimax tree search to compute the win rate in a simplified model and applied expert knowledge for pruning (Chuang, 2015). The newcomer, Asura, always discarded the leftmost tile in its hand.

This report comments on two selected games. The first is Game 62 from Match 2, where Golem won 11,000 points, and the second is Game 119 from Match 4, where MeowCaTS won 7,500 points. These games are chosen because both winners have the opportunity to create a special winning hand known as All Triplet, which includes 5 triplets and 1 pair in the hand. In the first game, Golem decided to pursue All Triplet, which was more challenging to win but offered higher points if achieved. In the second game, MeowCaTS gave up to accomplish All Triplet and instead aimed for a hand that was easier to win. We can observe the distinct playing styles among these players.

The format of game logs is described briefly as follows. The first line records the game’s wind (E: east, W: west, S: south, N: north), the player’s wind, start taking tile from which part of the wall (does not effect in this tournament), and the number of consecutive wins for the dealer. The second line lists the scores of the four players. The third line lists the IDs of the initial tiles in the wall in order. Note that the flowers are not used, so there are 136 IDs. The forth line records all moves in the game. Each move consists of a character indicating the player (E, W, S, N) who makes the move, a string indicating the type of the move (M: pick a.k.a. mo, MD: discard the picked tile, HD: discard from the hand, E: eat, P: pong, K: kong (exposed kong), DK: concealed kong, UK: upgraded kong, H: win by a discarded tile, SM: self-drawn win), and the numbers indicating the IDs of the tiles related to the move.

Game 1: Asura vs. MeowCaTS vs. Golem vs. VeryLongCat

WIND N S 3 0

Score −3500 −4000 11000 −3500

SQRWALL 340 170 162 370 172 151 430 221 420 311 461 283 333 282 163 462 371 250 360 291 452 382 362 152 473 230 351 383 242 331 292 251 393 353 380 183 213 120 453 182 252 193 423 343 293 142 263 260 181 140 320 243 450 443 113 270 212 411 441 290 231 161 261 310 470 232 191 361 130 123 222 390 391 241 372 410 332 280 381 253 413 173 431 323 322 180 471 223 422 150 352 211 210 240 220 122 363 350 330 463 111 131 141 112 160 273 440 412 132 442 110 312 460 341 313 153 233 432 392 272 192 472 451 190 143 373 421 171 342 133 121 262 281 433 271 321

1. S HD 430 2. W M 232 3. W HD 473 4. N M 191 5. N HD 423 6. E M 361 7. E HD 212 8. S M 130 9. S HD 420 10. W M 123 11. W HD 452 12. N M 222 13. N HD 453 14. E M 390 15. E HD 261 16. N P 261 260 263 17. N HD 293 18. W P 293 291 292 19. W HD 123 20. N M 391 21. N HD 252 22. W P 252 250 251 23. W HD 152 24. N M 241 25. N HD 213 26. E M 372 27. E HD 361 28. W P 361 360 362 29. W HD 393 30. N M 410 31. N MD 410 32. E M 332 33. E HD 443 34. S M 280 35. S HD 311 36. W M 381 37. W HD 242 38. N M 253 39. N HD 222 40. E M 413 [E E] 41. E HD 332 42. S M 173 43. S HD 221 44. W M 431 45. W MD 431 46. N M 323 47. N MD 323 48. E M 322 49. E HD 290 50. S M 180 51. S HD 130 52. W M 471 53. W MD 471 54. N M 223 55. N MD 223 56. E M 422 [E E] 57. E HD 161 58. S M 150 [S P,S E] 59. S HD 180 60. W M 352 [N G,N P] 61. W HD 331 62. N EL 343 331 353 63. N HD 120 64. E M 211 65. E HD 450 66. S M 210 67. S MD 210 68. W M 240 69. W MD 240 70. N M 220 71. N MD 220 72. E M 122 [E E] 73. E MD 122 74. S M 363 75. S HD 170 76. W M 350 77. W SM 230 232 351 352 381 382 383 350 Self-drawn, 3 Golem won

At the 22nd ply, as shown in Fig. 1a, Golem decided to pong 5-tong, transforming the sequence 345t into an unchangeable triplet of 555t. This decision created an opportunity to accomplish All Triplet since there were already two pairs of 66s and 88s, allowing to form two additional triplets. However, it also missed the opportunity to pick a tile from the wall and potentially transform the tiles 33455t into a better combination, such as 23345t or 34556t. This pong move made the hand more difficult to win but promised more points if successful. Finally, Golem won the game with 11,000 points by self-drawing 5-sou at the 77th ply, as shown in Fig. 1b, resulting in a substantial point gain.

Game 2: SimCat vs. MeowCaTS vs. Asura vs. Golem

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Fig. 1.

Golem won game 62 in match 2.

WIND S W 1 0

Score −2500 −2500 7500 −2500

SQRWALL 333 441 243 292 171 310 370 172 242 413 470 440 341 473 331 290 260 180 283 382 340 363 192 392 241 272 151 251 173 431 361 442 461 162 291 311 422 360 421 143 140 373 463 142 183 433 170 232 160 263 423 471 381 193 371 281 252 342 313 443 240 113 352 411 460 120 391 141 112 450 362 430 213 182 390 210 420 452 383 221 181 332 211 393 432 410 191 123 322 253 372 262 220 280 380 282 161 190 132 230 321 350 223 353 330 212 351 130 323 250 462 122 163 121 312 293 343 231 152 133 271 222 131 261 153 472 270 233 273 150 451 110 412 453 320 111

1. W HD 413 2. N M 120 3. N HD 442 4. W P 442 440 441 5. W HD 370 6. N EL 382 370 392 7. N HD 461 8. E M 391 9. E HD 463 10. S M 141 11. S HD 263 12. W M 112 13. W MD 112 14. N M 450 15. N MD 450 16. E M 362 17. E HD 433 18. S M 430 19. S HD 423 20. E P 423 421 422 21. E HD 311 22. S M 213 23. S HD 471 24. W P 471 473 470 25. W HD 310 26. N M 182 27. N HD 431 28. E M 390 29. E HD 291 30. W P 291 290 292 31. W HD 333 32. N M 210 33. N MD 210 34. E M 420 35. E UG 420 36. E M 111 37. E MD 111 38. S M 452 39. S HD 381 40. W M 383 41. W MD 383 42. N M 221 43. N HD 120 44. E M 181 45. E HD 232 46. S M 332 [S E] 47. S HD 193 48. W M 211 49. W MD 211 50. N M 393 51. N MD 393 52. E P 393 390 391 53. E HD 373 54. S M 432 55. S HD 371 56. W M 410 57. W MD 410 58. N M 191 59. N HD 151 60. E M 123 [E E] 61. E MD 123 62. S M 322 63. S HD 281 64. W M 253 65. W HD 243 66. N M 372 67. N MD 372 68. E M 262 69. E MD 262 70. S M 220 [S E] 71. S HD 252 72. W M 280 [W E] 73. W MD 280 74. N M 380 75. N HD 340 76. E M 282 77. E MD 282 78. S M 161 79. S HD 342 80. W M 190 81. W MD 190 82. N P 190 191 192 83. N HD 251 84. E M 132 85. E MD 132 86. S M 230 87. S HD 313 88. W M 321 89. W SM 171 172 242 253 260 331 341 321 Self-Drawn, 3 MeowCaTS won

At the 31st ply, as shown in Fig. 2a, MeowCaTS made the decision to discard 3-sou. This move broke the pair of 33s and reduced the number of pairs, making it insufficient to accomplish All Triplet. However, it significantly increased the winning chance of this hand. If MeowCaTS could obtain 7-wan, 4-tong, or 5-tong, it would be able to wait for 2-sou or 5-sou, which amounted to a maximum of 8 possible waiting tiles. In contrast, if MeowCaTS had chosen to accomplish All Triplet, the maximum number of tiles to wait for would have been 4, making it more challenging to win. In practice, MeowCaTS gave up accomplishing All Triplet and made the hand easier to win, which demonstrated a distinct playing style compared to Golem. Finally, MeowCaTS won this game by picking 2-sou at the 89th ply and gained 7,500 points. Based on our observations, accomplishing All Triplet was very difficult in this game.

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Fig. 2.

MeowCaTS won game 119 in match 4.