Depth, balancing, and limits of the Elo model

-Much work has been devoted to the computational complexity of games. However, they are not necessarily relevant for estimating the complexity in human terms. Therefore, human-centered measures have been proposed, e.g. the depth. This paper discusses the depth of various games, extends it to a continuous measure. We provide new depth results and present tool (given-first-move, pie rule, size extension) for increasing it. We also use these measures for analyzing games and opening moves in Y, NoGo, Killall Go, and the effect of pie rules

Regular Boardgames

We propose a new General Game Playing (GGP) language called Regular Boardgames (RBG), which is based on the theory of regular languages. The objective of RBG is to join key properties as expressiveness, efficiency, and naturalness of the description in one GGP formalism, compensating certain drawbacks of the existing languages. This often makes RBG more suitable for various research and practical developments in GGP. While dedicated mostly for describing board games, RBG is universal for the class of all finite deterministic turn-based games with perfect information. We establish foundations of RBG, and analyze it theoretically and experimentally, focusing on the efficiency of reasoning. Regular Boardgames is the first GGP language that allows efficient encoding and playing games with complex rules and with large branching factor (e.g.\ amazons, arimaa, large chess variants, go, international checkers, paper soccer).Comment: AAAI 201

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

What is Mathematics and What Should it Be

This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.Comment: 10 page

Scaffolding Human Champions: AI as a More Competent Other

Artifcial intelligence (AI) has surpassed humans in a number of specialised intellectual activities—chess and Go being two of many examples. Amongst the many potential consequences of such a development, I focus on how we can utilise cutting edge AI to promote human learning. The purpose of this article is to explore how a specialised AI can be utilised in a manner that promotes human growth by acting as a tutor to our champions. A framework for using AI as a tutor of human champions based on Vygotsky’s theory of human learning is here presented. It is based on a philosophical analysis of AI capabilities, key aspects of Vygotsky’s theory of human learning, and existing research on intelligent tutoring systems. The main method employed is the theoretical development of a generalised framework for AI powered expert learning systems, using chess and Go as examples. In addition to this, data from public interviews with top professionals in the games of chess and Go are used to examine the feasibility and realism of using AI in such a manner. Basing the analysis on Vygotsky’s socio-cultural theory of development, I explain how AI operates in the zone of proximal development of our champions and how even non-educational AI systems can perform certain scafolding functions. I then argue that AI combined with basic modules from intelligent tutoring systems could perform even more scafolding functions, but that the most interesting constellation right now is scafolding by a group consisting of AI in combination with human peers and instructors.publishedVersio