Related papers: Let's Play Mahjong!
The tile-based multiplayer game Mahjong is widely played in Asia and has also become increasingly popular worldwide. Face-to-face or online, each player begins with a hand of 13 tiles and players draw and discard tiles in turn until they…
The evaluation function for imperfect information games is always hard to define but owns a significant impact on the playing strength of a program. Deep learning has made great achievements these years, and already exceeded the top human…
Rummikub is a tile-based game in which each player starts with a hand of $14$ tiles. A tile has a value and a suit. The players form sets consisting of tiles with the same suit and consecutive values (runs) or tiles with the same value and…
One of the national treasures, Mahjong, is a strategic card game originating from China, played competitively by constructing and optimizing card hands among four players. In the game, players aim to achieve specific combinations of cards,…
Mahjong is a popular multi-player imperfect-information game developed in China in the late 19th-century, with some very challenging features for AI research. Sanma, being a 3-player variant of the Japanese Riichi Mahjong, possesses unique…
Artificial Intelligence (AI) has achieved great success in many domains, and game AI is widely regarded as its beachhead since the dawn of AI. In recent years, studies on game AI have gradually evolved from relatively simple environments…
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…
Mahjong is a complex game with an intractably large state space with extremely sparse rewards, which poses challenges to develop an agent to play Mahjong. To overcome this, the ShangTing function was adopted as a reward shaping function.…
Consider the following game between a random player R and a deterministic player D. There is a pile of n elements at the beginning. The rules for playing are as follows: In each turn of R, if the pile contains exactly m elements, R removes…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…
The game of memory is played with a deck of n pairs of cards. The cards in each pair are identical. The deck is shuffled and the cards laid face down. A move consists of flipping over first one card then another. The cards are removed from…
Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all…
As one of the worldwide spread traditional game, Official International Mahjong can be played and promoted online through remote devices instead of requiring face-to-face interaction. However, online players have fragmented playtime and…
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
Nim is a well-known combinatorial game in which two players alternately remove stones from distinct piles. A player who removes the last stone wins under the normal play rule, while a player loses under the mis\`ere play rule. In this…
We first prove that solving Mahjong Solitaire boards with peeking is NP-complete, even if one only allows isolated stacks of the forms /aab/ and /abb/. We subsequently show that layouts of isolated stacks of heights one and two can always…
People need to internalize the skills of AI agents to improve their own capabilities. Our paper focuses on Mahjong, a multiplayer game involving imperfect information and requiring effective long-term decision-making amidst randomness and…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an…
Chopsticks is a game played by two players where they start with one finger raised on each hand. On their turn, each player moves by pointing an attacking hand at one of their opponent's hands. The number of fingers on the pointed hand…