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Material Symmetry to Partition Endgame Tables

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chineseDarkChess.pdf (256.6Kb)
Date
2014
Dewey
Recherche opérationnelle
Sujet
material symmetry
Conference name
8th International Conference on Computers and Games, CG 2013
Conference date
08-2013
Conference city
Yokohama
Conference country
Japan
Book title
Computers and Games 8th International Conference, CG 2013, Yokohama, Japan, August 13-15, 2013, Revised Selected Papers
Author
Van den Herik, H.Jaap
Publisher
Springer
Publisher city
Berlin Heidelberg
Year
2014
ISBN
978-3-319-09164-8
URI
https://basepub.dauphine.fr/handle/123456789/13878
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  • LAMSADE : Publications
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Author
Buron, Cédric
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Cazenave, Tristan
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Jouandeau, Nicolas
104738 Laboratoire d'Informatique Avancée de Saint-Denis [LIASD]
Saffidine, Abdallah
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Communication / Conférence
Item number of pages
257
Abstract (EN)
Many games display some kind of material symmetry. That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards.Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple relatively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess, dominoes, and skat.In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables.

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