The Mahjong game has widely been acknowledged to be a difficult problem in the field of imperfect information games. Because of its unique characteristics of asymmetric, serialized and multi-player game information, conventional methods of dealing with perfect information games are difficult to beapplied directly on the Mahjong game. Therefore, AI (artificial intelligence)-based studies to handle the

We present a variant of Sudoku called Sudoku Ripeto. It seems to be the first to admit any combination of repeated symbols, and includes Sudoku as a proper subset. We present other Sudoku Ripeto families, each with a different repetition pattern. We define Sudoku Ripeto squares and puzzles, prove several solving rules that generalize those for Sudoku, and give sufficient conditions to flexibly solve

Since DeepMind's AlphaZero, Zero learning quickly became the state-of-the-art method for many board games. It can be improved using a fully convolutional structure (no fully connected layer). Using such an architecture plus global pooling, we can create bots independent of the board size. The training can be made more robust by keeping track of the best checkpoints during the training and by training

Recent trends in mathematics education emphasize discovery learning over drill. This has proven to be a bad idea in some cases, for the simple reason that practice is required to learn basic arithmetic skills. Drills in arithmetic skills can be made interesting through gamification. This study proposes a family of puzzles that gamify arithmetic practice. The puzzles are designed with an evolutionary

This article is a series of anecdotes about the development of several programs that advanced the state of the art in computer chess. The best known is Cray Blitz, which won the 1983 and 1986 World Computer Chess Championships. However, in terms of overall impact, perhaps Crafty is the most important. As a high-performing open-source program, it has been used by countless number of researchers and

San Jego is a two-player game with perfect information. It is a variation of the games Clobber (2001) and Cannibal Clobber. Given is a rectangular board with black and white pieces on the cells. Multiple pieces which are stacked on each other are called towers. The piece on top of a tower indicatesher owner. A move consists of picking an own tower and placing it completely on top of an adjacent tower

The idea to let machines play games like Chess is quite old, with the Turk11https://en.wikipedia.org/w/index.php?title=The_Turk&oldid=968314029 being one of the first hints. With the invention of computers, this idea got a new boost, and soon the first chess programs were presented. It took about 50 years until it was clear that the machines are superior chess players, far beyond the playing strengths

This contribution reports about an almost forgotten attempt to find themes in chess composition automatically by machine. Based on investigations of the late International Master of Chess Composition Dieter Müller in the 1970s, the writers describe some of his results. They hope to fill a gap in the great history of chess programming.

This article is based on my personal reminiscences about the early days of computer chess tournaments, describing not only how different the technology was, but also that progress was steady and continues today in the broader field of Artificial Intelligence. The author was a participant in the 1stACM computer chess championship (1970) and continued to compete well into the 1980s. Speaking for myself

It is been 46 years since the first computer chess world championship was held in Stockholm in 1974, and there have now been 24 more with over 700 games played. This paper investigates a number of questions that a curious soul might ask regarding the results of these games, especially how they ended. The data provided herein attempts to answer several related questions. In addition, it presents data

BeBe was one of the highest-performing chess programs of the 1980s. This article relates some of the fond computer chess memories from Linda Scherzer, co-author of BeBe.

On August 31, 1970, an experiment began that continues to this day. The first chess tournament for computers was held as part of the Association for Computing Machinery’s (ACM’s) National Conference. The interest generated was tremendous, leading to ACM sponsoring an annual event until 1994. Chesscompetitions continue to this day, allowing for 50 years of data on the growth of artificial intelligence

On July 24–25, 1976, the computer program Chess 4.5 participated in the Paul Masson Chess Classic Tournament. The program achieved an impressive result. This article describes my recollection of this event and its aftermath.

The game of chess involves patterns. In this article we develop a simple description language for chess positions as patterns. It seems useful to catalogue similar positions in a generic form, based on common elements, in order to simplify the search for chess positions. A simple chess pattern language is used here to develop a computer program to find similar chess configurations. The aim is to avoid

2048-like games are a family of single-player stochastic puzzle games, which consist of sliding numbered-tiles that combine to form tiles with larger numbers. Notable examples of games in this family include Threes!, 2048, and 2584. 2048-like games are highly suitable for educational purposes due to their simplicity and popularity. Numerous machine learning methods have been proposed to play 2048-like

TCEC16 was the 16th season of the Top Chess Engine Championship and ran from July 14th to October 13th, 2019. TCEC has become the largest Open Computer Chess Championship. It attracts the best engines in the field and provides an opportunity for a comparative analysis of the Shannon-AB and the new Neural-Network engines’ styles of play. STOCKFISH regained the title of Grand Champion by beating ALLIESTEIN

The 'WCSC 2019' World Chess Software Championship was the ICGA's ninth experimental test of computer chess software in a neutral hardware environment. Held in Macau, this event was won by KOMODO with JONNY and CHIRON scarcely separable in second and third.

WSCC 2019 was ICGA's continuation of its investigation of top chess engines playing at Blitz tempo with the consequential loss of accuracy. It was held in Macau in parallel with the 'WCCC' classical tempo and 'WCSC' neutral-hardware events. The ICGA demonstrated that, even so, the engines play at super-GM level. On this occasion, JONNY proved incisive to win while KOMODO sustained two losses.

In the last issue of this volume, the ICGA Journal will go back to its roots by presenting several contributions on computer chess. We start by presenting two scientific articles that explore how to deal with draws in chess. The first article, Are Armageddon chess games implemented fairly? by Vladimir Vargas, describes the chess variant Armageddon chess, where in case of a draw Black is declared the

This is a report of the 'TCEC Cup 4' computational experiment, the 4th TCEC knockout event and the second major part of TCEC’s 16th season. It started on 16th October 2019 and featured the best 32 engines of the ‘TCEC 16’ league event and the games were held at Blitz tempo, The different format called for different optimal settings in the engines, thereby enabling a comparison with performance at slower

The survey was sent to 206 individuals/organizations, including all current ICGA members as well as recent former ICGA members for whom we had an email address. Some of these addresses were invalid, resulting in 194 requests for which we might get a response. In the end, 41 submissions were received via the online survey form, and an additional 4 by email. Of the 45 responses, 75% were from current

WCCC 2019, the 25th World Computer Chess Championship, continued the ICGA's longitudinal computer chess experiment begun in 1974. This event was held in Macau, featured six chess engines and was won by KOMODO which thereby retained its title of World Champion. CHIRON and SHREDDER were respectively second and third.

This is the Chess Engine Rating list of 2019-12 from Svenska schackdatorforeningen, the Swedish Chess Computer Association. SSDF has produced the list for 22 years. Here we supply the 'Selected 50' subset with headline notes on each engine. SSDF's 2019-12 narrative, top 50 and long lists (both with match details) may also be downloaded from here.

In past years, I have paid only cursory attention to DivP, experiencing it as the necessary but pallid taster before the anticipated main course! However, this year’s DivP was extremely entertaining and captivated my attention from beginning to end. The format was slightly odd as – in order to save costs on the hiring of the GPU server – all CPU machines games were played first. The downside was that

A strategy to find fair time controls for Armageddon chess games is presented and exemplified with 2750+ ELO players. The research was divided in two stages. The first one consisted in finding a time control for Stockfish 9 so that it played with an effective strength equal to the average 2750+ ELOplayers of the 2017 World Blitz Chess Championship. Analysis of this stage showed that a fair time control

Stalemating the opponent in chess has given rise to various opinions as to the nature of that result and the reward it should properly receive. Here, following Lasker and Reti, we propose that ‘stalemate’ is a secondary goal, superior to a draw by agreement or rule – but inferior to mate. We report the work of ‘Aloril’ who has created endgame tables holding both ‘DTM’ depth to mate and ‘DTS’ depth

Games can have multiple purposes. They are not only a source of entertainment, but they can also provide an intellectual challenge. At the moment games have an educational or training aspect, they are called serious games. These games are being applied for instance in the health sector, business, or security. There is a link between the AI research applied in serious games and the type of research

This is the Chess Engine Rating list of 2019-07 from Svenska schackdatorforeningen, the Swedish Chess Computer Association. SSDF has produced the list for 22 years. Here we supply the 'Selected 50' subset with headline notes on each engine. SSDF's 2019-07 long list and hw/change logs may also be downloaded from here.

TCEC Season 14 started on November 12 2018 and introduced a number of changes from TCEC 13 (Haworth and Hernandez, 2019b). An enlarged Division 4 featured twelve engines and seven newcomers to accommodate the increasing interest in computer chess and this competition in particular. The other divisions remained eight strong. The five divisions played two or more double round-robins (‘DRR’) each with

In a time when the pace of life is ever increasing and attention spans are ever decreasing, it seems strange that a chess match played between two machines at a long time control should prove so gripping, but the TCEC, LEELA CHESS ZERO and STOCKFISH managed it! The final score of 53.5-46.5, 14 wins to 7, was I think a fair reflection of the relative strength of both engines in a head-to-head contest:

This article defines the challenge of training neural-networks on specific chess endgames and benchmarking their efficacy against the existing sub-8-man endgame tables. The key tasks are to measure how well they play and to infer higher-order rules and guidelines for play from them.

This is a report of the 'TCEC Cup 3' computational experiment, the 3rd TCEC knockout event and the second major part of TCEC’s 15th season. It featured the best 32 engines of the ‘TCEC 15’ league event and the games were held at Blitz tempo. The different format called for different optimal settings in the engines, thereby enabling a comparison with performance at slower tempi. LEELA CHESS ZERO retained

This report summarises the discussions and conclusions of a recent Dagstuhl research meeting, in which the foundations of the new research field of Digital Archæoludology were established. Starting with the ERC-funded Digital Ludeme Project, research in this field aims to use techniques from the field of Artificial Intelligence (AI), and other computational and data-driven techniques, to study traditional

The Computer Games Workshop (CGW 2018) was held in Stockholm, Sweden, it took place on July 13, 2018, in conjunction with the 27 International Conference on Artificial Intelligence (IJCAI 2018). The Computer and Games Workshop series is an international forum for researchers interested in all aspects of artificial intelligence (AI) and computer game playing. Earlier workshops took place in Montpellier

This is the Chess Engine Rating list of 2019-02 from Svenska schackdatorforeningen, the Swedish Chess Computer Association. SSDF has produced the list for 21 years. Here we supply the 'Selected 50' subset with headline notes on each engine. SSDF's 2019-02 narrative and long list may also be downloaded from here.

This is a report of the 'TCEC Cup 2' computational experiment, the second TCEC knockout event and the second major part of TCEC’s 14th season. It featured the best 32 engines of the ‘TCEC 14’ league event and the games were held at Blitz tempo. The different format called for different optimal settings in the engines, thereby enabling a comparison with performance at slower tempi. This event made history:

This article explores the variety and depth of chess' sub-8-man minor piece endgame. These endgames feature no queens or rooks but at least one bishop or knight, and no more than one per side. Demis Hassabis, now CEO of Deep Mind, has talked of 'the exquisite balance of Bishop and Knight'. The investigation uses the framework of 'Understanding Minor Piece Endgames' by Karsten Mueller and Yakov Konoval

TCEC12 was the 12th season of the Top Chess Engine Championship and ran from 18th April to July 5th, 2018. TCEC has become the largest Open Computer Chess Championship. It attracts the best engines in the field and provides an opportunity for absolute and comparative analysis of the participating engines in a computational experiment. TCEC12 featured the first TCEC appearance of a ‘new architecture’

Since the 1950s, the AI community has been developing techniques in order to outperform humans for a particular game. This has been accomplished in many board games such as Chess, Checkers, and Go. Recently, new challenges have been proposed such as real-time strategy (RTS) games. Here the agents have to make decisions in real-time environments that have imperfect information, nondeterminism, and a

This is a report of the 'TCEC Cup 1' computational experiment, the first TCEC knockout event and the second major part of TCEC’s 13th season. It featured the best 32 engines of ‘TCEC 13’ and the games were held at Blitz tempo, The different format called for different optimal settings in the engines, thereby enabling a comparison with performance at slower tempi. This event notably featured the first

This special issue on Computer Aided Game and Puzzle Design marks a broadening of scope for the ICGA Journal, to reflect the increasingly diverse submissions over recent years covering wider ranges of games and aspects beyond move planning and game analysis. But our focus is still on computer implementations of physical and mathematical games rather than video games, for which computer aided content

Romero’s FINALGEN of 2012 creates designer endgame tables for specific chess positions that feature no more than one non-pawn piece per side. Larger hard discs and faster solid-state discs have extended the reach of this software and encouraged its greater use. Some new discoveries illustrate here what is now feasible and how FINALGEN may be combined with other tools to reach definitive and likely

There were two Hex tournaments at the 2018 Computer Olympiad in New Taipei City: 11×11 — proposed by Piet Hein in 1942 — and 13×13. Visa problems unfortunately prevented Chinese teams from competing, leaving two contestants for each tourament: DEEPEZO from Japan, by Kei Takada, supervised by Masahito Yamamoto; and MOHEX-3HNN from Canada, by Chao Gao, supervised by Ryan Hayward and Martin Müller and

Five divisions, each of eight engines, played two or more ‘DRR’ double round robin phases each, with promotions and relegations following. Classic tempi gradually lengthened and the Premier division’s top two engines played a 100-game match to determine the Grand Champion. The strategy for the selection of mandated openings was finessed from division to division. The revised TCEC engine lineup is illustrated

In this paper we investigate the game of Cram, which is the impartial version of Domineering. We have built Cram endgame databases for all board sizes < 30 squares. We developed a program that fills the databases with their Combinatorial Game Theory (CGT) values. Since Cram is an impartial game, all CGT values for Cram positions are so-called nimbers, indicated by ∗n . The nimber value of a position

In games with a large number of legal yet complicated moves like Shogi, the number of candidate moves that can be performed are considerably large especially for beginners; therefore, often, beginners encounter situations where they cannot select the next move to play. The hint function in the existing Shogi programs provides support by directly showing candidate moves. However, such direct hints may

We describe a means of mixed logical and probabilistic reasoning with knowledge in the popular game Clue. Using pseudo-Boolean constraints we call at-least constraints, we more efficiently represent cardinality constraints on Clue card deal knowledge, perform more general constraint satisfaction in order to determine places where cards provably are or are not, and then employ a WalkSAT-based solution

A major achievement in 2018 has been the production of 7-man Syzygy ‘EGT’ endgame tables to a metric given the label DTZ50" here. This resulted from a fine collaboration between Bojun Guo and Ronald de Man, evolving the latter’s code to manage the issues of meeting the larger 7-man challenge.

This is the Chess Engine Rating list of 2018-10 from Svenska schackdatorforeningen, the Swedish Chess Computer Association. SSDF has produced the list for 21 years. Here we supply the 'Selected 50' subset with headline notes on each engine. The full details of the 2018-10 may also be downloaded from here.

One approach to game design is to start with existing ideas and to modify them in interesting new ways. This process of "creative plagiarism" is applied to the Japanese logic puzzle Sudoku to create a new variant called Ludoku, which simplifies some aspects of the original puzzle while adding new strategies without adding undue complexity. This paper describes the design process from initial conception

Computer analysis was very much to the fore in this, Carlsen’s most highly contested World Champion¬ship Match. It could be found on the web and in support of the various live commentaries on offer. Here, we focus on game six of the classic phase and game one of the rapid-tempo tie-break. More extensive analysis can be found in the e-repository version of this note.

After the successes of TCEC Season 10 (Haworth and Hernandez, 2018a), the Top Chess Engine Championship moved straight on to Season 11, starting January 3 2018 but with a new structure. Five divisions, each of eight engines, played one or more ‘DRR’ double round robin phases each, with promotions and relegations following. Classic tempi gradually lengthened and the Premier division’s top two engines

Computer chess has stimulated human imagination over some two hundred and fifty years. In 1769 Baron Wolfgang von Kempelen promised Empress Maria Theresia in public: “I will invent a machine for a more compelling spectacle [than the magnetism tricks by Pelletier] within half a year.” The idea of an intelligent chess machine was born. In 1770 the first demonstration was given.The real development of

The 'WCSC 2018' World Chess Software Championship was the ICGA's eighth experimental test of computer chess software in a neutral hardware environment. Held in Stockholm, this event was won by KOMODO after a play-off against BOOOT.

Abstract. The game of Hex can be played on multiple boardsizes. Transferring neural net knowledge learned on one boardsize to other boardsizes is of interest, since deep neural nets usually require large size of high quality data to train, whereas expert games can be unavailable or difficult to generate. In this paper we investigate neural transfer learning in Hex. We show that when only boardsize

TCEC is the Top Chess Engine Championship (TCEC, 2018). Better known by my TCEC nickname of Cato the Younger, I was the person in charge of the opening positions for TCEC Season 10 (Haworth and Hernandez, 2018). I have been doing this since Season 5, first for this tournament’s founder Martin Thoresen, and more recently for Anton Mihailov, our tournament director and the owner of chess website Chessdom

I’ve only attended a few WCCCs in the past, e.g. in Paderborn, Maastricht and Leiden. From my point of view, Stockholm was overall one of the best tournaments! I really liked the venue in the Stockholmsmässan and the combination with the AI conferences. Playing in the entrance hall, we had quite a lot of visitors watching the games and asking questions, and one could even meet some well known ‘computer

When solving k-in-a-Row games, the Hales–Jewett pairing strategy [Trans. Amer. Math. Soc. 106 (1963 ), 222–229] is a well-known strategy to prove that specific positions are (at most) a draw for the first player. For non-overlapping possible winning lines (groups) it requires two empty squares per group to be marked, i.e., with a coverage ratio of 2.0. In this paper we present a new strategy, called

WSCC 2018 was ICGA's continuation of its investigation of top chess engines playing at Blitz tempo with the consequential loss of accuracy. They demonstrated that, even so, the engines play at super-GM level. On this occasion, KOMODO demolished the field and so won all three ICGA titles in Stockholm.

WCCC 2018, the 24th World Computer Chess Championship, continued the ICGA's longitudinal computer chess experiment begun in 1974. This event was held in Stockholm, featured eight chess engines and was won by KOMODO after a play-off against GRIDGINKGO.