Searching for solutions in games and artificial intelligence

Allis, L.V.

doi:10.26481/dis.19940923la

Cited by 103 publications

(43 citation statements)

References 32 publications

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“…From the results shown, it can be determined the complexity is roughly between that of connect four [20] and 8x8 domineering [16]. As both connect four and domineering are considered solved games, the conclusion can be drawn that Brandubh is tractable for both weak and strong solving.…”

Section: Discussionmentioning

confidence: 99%

An Upper Bound on the State-Space Complexity of Brandubh

Compy

Evey

McCullough

et al. 2020

2020 IEEE Conference on Games (CoG)

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Before chess came to Northern Europe there was Tafl, a family of asymmetric strategy board games associated strongly with the Vikings. The purpose of this paper is to study the combinatorial state-space complexity of an Irish variation of Tafl called Brandubh. Brandubh was chosen because of its asymmetric goals for the two players, but also its overall complexity well below that of chess, which should make it tractable for strong solving. Brandubh's rules and characteristics are used to gain an understanding of the overall state-space complexity of the game. State-spaces will consider valid piece positions, a generalized rule set, and accepted final state conditions. From these states the upper bound for the complexity of strongly solving Brandubh is derived. Great effort has been placed on thoroughly accounting for all potential states and excluding invalid ones for the game. Overall, the upper bound complexity for solving the game is around 10 14 states, between that of connect four and draughts (checkers).

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Section: Discussionmentioning

confidence: 99%

An Upper Bound on the State-Space Complexity of Brandubh

Compy

Evey

McCullough

et al. 2020

2020 IEEE Conference on Games (CoG)

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“…Ti-Rong Wu 1 , I-Chen Wu 1 , Senior Member, IEEE, Guan-Wun Chen 1 , Ting-han Wei 1 , Tung-Yi Lai 1 , Hung-Chun Wu 1 , Li-Cheng Lan 1 G (Submitted to IEEE TCIAIG on May 30, 2017. ) precious computing resources that are available.…”

Section: Multi-labelled Value Network For Computer Gomentioning

confidence: 99%

“…Although the rules of Go are simple, its game tree complexity is extremely high, estimated to be 10 360 in [1] [40]. It is common for players with different strengths to play ℎ-stone handicap games, where the weaker player, usually designated to play as black, is allowed to place ℎ stones 2 first with a komi of 0.5 before white makes the first move.…”

Section: Introductionmentioning

confidence: 99%

Multilabeled Value Networks for Computer Go

Chen

et al. 2018

IEEE Trans. Games

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This paper proposes a new approach to a novel value network architecture for the game Go, called a multi-labelled (ML) value network. In the ML value network, different values (win rates) are trained simultaneously for different settings of komi, a compensation given to balance the initiative of playing first. The ML value network has three advantages, (a) it outputs values for different komi, (b) it supports dynamic komi, and (c) it lowers the mean squared error (MSE). This paper also proposes a new dynamic komi method to improve game-playing strength.This paper also performs experiments to demonstrate the merits of the architecture. First, the MSE of the ML value network is generally lower than the value network alone. Second, the program based on the ML value network wins by a rate of 67.6% against the program based on the value network alone. Third, the program with the proposed dynamic komi method significantly improves the playing strength over the baseline that does not use dynamic komi, especially for handicap games. To our knowledge, up to date, no handicap games have been played openly by programs using value networks. This paper provides these programs with a useful approach to playing handicap games.Although the rules of Go are simple, its game tree complexity is extremely high, estimated to be 10 360 in [1] [40]. It is common for players with different strengths to play ℎ-stone handicap games, where the weaker player, usually designated to play as black, is allowed to place ℎ stones 2 first with a komi of 0.5 before white makes the first move. If the strength difference (rank difference) between both players is large, more handicap stones are usually given to the weaker player.In the past, computer Go was listed as one of the AI grand challenges [16][28]. By 2006, the strengths of computer Go programs were generally below 6 kyu [5][8][14], far away from amateur dan players. In 2006, Monte Carlo tree search (MCTS) [6][11][15][23][37] was invented and computer Go programs started making significant progress [4][10][13], roughly up to 6 dan in 2015. In 2016, this grand challenge was achieved by the program AlphaGo [34] when it defeated (4:1) Lee Sedol, a 9 dan grandmaster who had won the most world Go champion titles in the past decade. Many thought at the time there would be a decade or more away from surpassing this milestone. Up to date, DeepMind, the team behind AlphaGo, had published the techniques and methods of AlphaGo in Nature [34]. AlphaGo was able to surpass experts' expectations by proposing a new method that uses three deep convolutional neural networks (DCNNs) [24][25]: a supervised learning (SL) policy network [7][9][18][26][38] learning to predict experts' moves from human expert game records, a reinforcement learning (RL) policy network [27] improving the SL policy network via self-play, and a value network that performs state evaluation based on self-play game simulations. AlphaGo then combined the DCNNs with MCTS for move generation during game play. In MCTS, a fast rollout policy was...

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“…Due to this scarce documentation, Tafl games have never been subject to proper analysis, and therefore we don't know their complexity, nor their solution to any degree. 1 The purpose of this work is to provide an initial estimate of the complexity of Tablut, with the hope to lay the grounds for deeper studies.…”

Section: Introductionmentioning

confidence: 99%

An Upper Bound on the Complexity of Tablut

Galassi¹

2021

Preprint

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Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper bound to its complexity is found eventually by dividing the state-space of the game into subspaces according to specific conditions. This upper bound is comparable to the one found for Draughts, therefore, it would seem that the open challenge of solving this game requires a considerable computational effort.

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Searching for solutions in games and artificial intelligence

Cited by 103 publications

References 32 publications

An Upper Bound on the State-Space Complexity of Brandubh

An Upper Bound on the State-Space Complexity of Brandubh

Multilabeled Value Networks for Computer Go

An Upper Bound on the Complexity of Tablut

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