1,007 research outputs found
New Results for Domineering from Combinatorial Game Theory Endgame Databases
We have constructed endgame databases for all single-component positions up
to 15 squares for Domineering, filled with exact Combinatorial Game Theory
(CGT) values in canonical form. The most important findings are as follows.
First, as an extension of Conway's [8] famous Bridge Splitting Theorem for
Domineering, we state and prove another theorem, dubbed the Bridge Destroying
Theorem for Domineering. Together these two theorems prove very powerful in
determining the CGT values of large positions as the sum of the values of
smaller fragments, but also to compose larger positions with specified values
from smaller fragments. Using the theorems, we then prove that for any dyadic
rational number there exist Domineering positions with that value.
Second, we investigate Domineering positions with infinitesimal CGT values,
in particular ups and downs, tinies and minies, and nimbers. In the databases
we find many positions with single or double up and down values, but no ups and
downs with higher multitudes. However, we prove that such single-component ups
and downs easily can be constructed. Further, we find Domineering positions
with 11 different tinies and minies values. For each we give an example. Next,
for nimbers we find many Domineering positions with values up to *3. This is
surprising, since Drummond-Cole [10] suspected that no *2 and *3 positions in
standard Domineering would exist. We show and characterize many *2 and *3
positions. Finally, we give some Domineering positions with values interesting
for other reasons.
Third, we have investigated the temperature of all positions in our
databases. There appears to be exactly one position with temperature 2 (as
already found before) and no positions with temperature larger than 2. This
supports Berlekamp's conjecture that 2 is the highest possible temperature in
Domineering
Recommended from our members
Can Deep Blue™ make us happy? Reflections on human and artificial expertise
Sadly, progress in AI has confirmed earlier conclusions, reached using formal domains, about the strict limits of human information processing and has also shown that these limits are only partly remedied by intuition. More positively, AI offers mankind a unique avenue to circumvent its cognitive limits: (1) by acting as a prosthesis extending processing capacity and size of the knowledge base; (2) by offering tools for studying our own cognition; and (3) as a consequence of the previous item, by developing tools that increase the quality and quantity of our own thinking. These ideas are illustrated with chess expertise
Chess Endgames and Neural Networks
The existence of endgame databases challenges us to extract higher-grade information and knowledge from their basic data content. Chess players, for example, would like simple and usable endgame theories if such holy grail exists: endgame experts would like to provide such insights and be inspired by computers to do so. Here, we investigate the use of artificial neural networks (NNs) to mine these databases and we report on a first use of NNs on KPK. The results encourage us to suggest further work on chess applications of neural networks and other data-mining techniques
Secrets of Pawnless Endings
It is now 32 years since Ströhlein’s pioneering computation of KRKN and ten years since the publication of Nunn’s Secrets of Rook Endings. This book defined a new genre under his authorship and editorship (Nunn, 1992, 1994, 1995; Müller and Lamprecht, 1999, 2001) and has merited a second edition. Now comes the second edition of Secrets of Pawnless Endings
KQQKQQ and the Kasparov-World Game
The 1999 Kasparov-World game for the first time enabled anyone to join a team playing against a World Chess Champion via the web. It included a surprise in the opening, complex middle-game strategy and a deep ending. As the game headed for its mysterious finale, the World Team re-quested a KQQKQQ endgame table and was provided with two by the authors. This paper
describes their work, compares the methods used, examines the issues raised and summarises the concepts involved for the benefit of future workers in the endgame field. It also notes the contribution of this endgame to chess itself
Comparing Typical Opening Move Choices Made by Humans and Chess Engines
The opening book is an important component of a chess engine, and thus
computer chess programmers have been developing automated methods to improve
the quality of their books. For chess, which has a very rich opening theory,
large databases of high-quality games can be used as the basis of an opening
book, from which statistics relating to move choices from given positions can
be collected. In order to find out whether the opening books used by modern
chess engines in machine versus machine competitions are ``comparable'' to
those used by chess players in human versus human competitions, we carried out
analysis on 26 test positions using statistics from two opening books one
compiled from humans' games and the other from machines' games. Our analysis
using several nonparametric measures, shows that, overall, there is a strong
association between humans' and machines' choices of opening moves when using a
book to guide their choices.Comment: 12 pages, 1 figure, 6 table
Strategies for Constrained Optimisation
The latest 6-man chess endgame results confirm that there are many deep forced mates beyond the 50-move rule. Players with potential wins near this limit naturally want to avoid a claim for a draw: optimal play to current metrics does not guarantee feasible wins or maximise the chances of winning against fallible opposition. A new metric and further strategies are defined which support players’ aspirations and improve their prospects of securing wins in the context of a k-move rule
Library discovery through augmented reality: a game plan for academics
In order to create innovative pathways to services and resources, the authors propose placing a “game-layer” on top of the library, luring new patrons with the potential of playing an Alternate/Augmented Reality Game (ARG). Using both physical and virtual library space a variety of “nodes” are created, drawing players to various library locales even regular patrons may be unfamiliar with and presenting them with story fragments and puzzles. Each node requires players to use library resources like databases and books, or engage library staff at known service points in order to move forward. Players contribute to the game itself in the form of puzzle solutions. Far more illustrative than a guided tour or required course/class, this library ARG encourages players to discover and utilize resources within the context of the game, generating fluency in library systems, places and platforms. But more importantly, the ARG invites a process of “meta-level reflection” invaluable throughout a patron’s academic career
- …