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WALTZ: A Strong Tzaar-Playing Program

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Computer Games (CGW 2013)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 408))

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Abstract

Tzaar is an abstract strategy two-player game, which has recently gained popularity in the gaming community and has won several awards. There are some properties, most notably the high branching factor, that make Tzaar hard for computers. We developed Waltz, a strong Tzaar-playing program, using enhanced variants of Alpha-beta and Proof-number Search based algorithms. After many tests with computer opponents and a year of deployment on a popular board-gaming portal, we conclude that Waltz can defeat all available computer programs and even strong human players. In this paper we describe Waltz, its performance and an enhancement of Proof-number Search developed for Waltz that can be also used in other domains than Tzaar.

Tomáš Valla—This work was supported by the Centre of Excellence—Inst. for Theor. Comp. Sci. (project P202/12/G061 of GA ČR).

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Notes

  1. 1.

    The name stands for the recursive acronym Waltz ALgorithmic TZaar.

  2. 2.

    There are also some more programs available, but due to their design it is not possible to run automatic play-outs between them and Waltz.

  3. 3.

    299 players have played Tzaar in the last six month till May 10, 2013 and 24 842 Tzaar games were finished on BAJ from October 31, 2008 to May 10, 2013.

  4. 4.

    For a win a player obtains some ELO points according to his and opponent’s ELO and his opponent loses the same number of points. New player receives ELO \(1\,500\).

  5. 5.

    Some of these games were played for testing purposes.

  6. 6.

    ELOs of players and other data in this section were up to the date March 4, 2013.

  7. 7.

    Some of these games were against other Waltz versions—this was done to increase robot’s ELO, otherwise strong players would not want to play against an opponent with a low ELO.

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Author information

Authors and Affiliations

  1. Faculty of Information Technology, Czech Technical University in Prague, Praha 6, Czech Republic

    Tomáš Valla

  2. Faculty of Mathematics and Physics, Charles University in Prague, Praha 1, Czech Republic

    Pavel Veselý

Authors
  1. Tomáš Valla
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  2. Pavel Veselý
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Correspondence to Pavel Veselý .

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Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Tristan Cazenave

  2. Universiteit Maastricht, Maastricht, The Netherlands

    Mark H.M. Winands

  3. School of Information Science, JAIST, Nomi, Japan

    Hiroyuki Iida

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Valla, T., Veselý, P. (2014). WALTZ: A Strong Tzaar-Playing Program. In: Cazenave, T., Winands, M., Iida, H. (eds) Computer Games. CGW 2013. Communications in Computer and Information Science, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-319-05428-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-05428-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05427-8

  • Online ISBN: 978-3-319-05428-5

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