Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments

JWHM Uiterwijk; Janis Griebel

doi:10.1007/978-3-319-67468-1_6

Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments

JWHM Uiterwijk^*, Janis Griebel

^*Corresponding author for this work

Networks and Strategic Optimization

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

Combinatorial games are a special category of games sharing
the property that the winner is by denition the last player able to move.
To solve such games two main methods are being applied. The rst is a
general alpha-beta search with many possible enhancements. This technique is
applicable to every game, mainly limited by the size of the game due to
the exponential explosion of the solution tree. The second way is to use
techniques from Combinatorial Game Theory (CGT), with very precise
CGT values for (subgames of) combinatorial games. This method is only
applicable to relatively small (sub)games. In this paper1 we show that the
methods can be combined in a fruitful way by incorporating an endgame
database filled with CGT values into an alpha-beta solver.

We apply this technique to the game of Clobber, a well-known all-small
combinatorial game. Our test suite consists of 20 boards with sizes up
to 18 squares. An endgame database was created for all subgames of
size 8 and less. The CGT values were calculated using the CGSUITE
package. Experiments reveal reductions of at least 75% in number of
nodes investigated.

Original language	English
Title of host publication	BNAIC 2016: Artificial Intelligence
Subtitle of host publication	28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers
Publisher	Springer Verlag
Pages	78-92
Number of pages	15
Volume	765
ISBN (Print)	9783319674674
DOIs	https://doi.org/10.1007/978-3-319-67468-1_6
Publication status	Published - 2017
Event	28th Annual Benelux Conference on Artificial Intelligence (BNAIC) - Amsterdam, Netherlands Duration: 10 Nov 2016 → 11 Nov 2016 https://bnaic2016.cs.vu.nl/

Publication series

Series	Communications in Computer and Information Science
Volume	765
ISSN	1865-0929

Conference

Conference	28th Annual Benelux Conference on Artificial Intelligence (BNAIC)
Country/Territory	Netherlands
City	Amsterdam
Period	10/11/16 → 11/11/16
Internet address	https://bnaic2016.cs.vu.nl/

Keywords

SEARCH

Access to Document

10.1007/978-3-319-67468-1_6

Cite this

Uiterwijk, JWHM., & Griebel, J. (2017). Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments. In BNAIC 2016: Artificial Intelligence: 28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers (Vol. 765, pp. 78-92). Springer Verlag. https://doi.org/10.1007/978-3-319-67468-1_6

Uiterwijk, JWHM ; Griebel, Janis. / Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments. BNAIC 2016: Artificial Intelligence: 28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers . Vol. 765 Springer Verlag, 2017. pp. 78-92 (Communications in Computer and Information Science, Vol. 765).

@inproceedings{41911fa97f044875b73d687aa72a164d,

title = "Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments",

abstract = "Combinatorial games are a special category of games sharingthe property that the winner is by denition the last player able to move.To solve such games two main methods are being applied. The rst is ageneral alpha-beta search with many possible enhancements. This technique isapplicable to every game, mainly limited by the size of the game due tothe exponential explosion of the solution tree. The second way is to usetechniques from Combinatorial Game Theory (CGT), with very preciseCGT values for (subgames of) combinatorial games. This method is onlyapplicable to relatively small (sub)games. In this paper1 we show that themethods can be combined in a fruitful way by incorporating an endgamedatabase filled with CGT values into an alpha-beta solver.We apply this technique to the game of Clobber, a well-known all-smallcombinatorial game. Our test suite consists of 20 boards with sizes upto 18 squares. An endgame database was created for all subgames ofsize 8 and less. The CGT values were calculated using the CGSUITEpackage. Experiments reveal reductions of at least 75% in number ofnodes investigated.",

keywords = "SEARCH",

author = "JWHM Uiterwijk and Janis Griebel",

year = "2017",

doi = "10.1007/978-3-319-67468-1_6",

language = "English",

isbn = "9783319674674",

volume = "765",

series = "Communications in Computer and Information Science",

publisher = "Springer Verlag",

pages = "78--92",

booktitle = "BNAIC 2016: Artificial Intelligence",

address = "Germany",

note = "28th Annual Benelux Conference on Artificial Intelligence (BNAIC) ; Conference date: 10-11-2016 Through 11-11-2016",

url = "https://bnaic2016.cs.vu.nl/",

}

Uiterwijk, JWHM & Griebel, J 2017, Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments. in BNAIC 2016: Artificial Intelligence: 28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers . vol. 765, Springer Verlag, Communications in Computer and Information Science, vol. 765, pp. 78-92, 28th Annual Benelux Conference on Artificial Intelligence (BNAIC), Amsterdam, Netherlands, 10/11/16. https://doi.org/10.1007/978-3-319-67468-1_6

Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments. / Uiterwijk, JWHM; Griebel, Janis.
BNAIC 2016: Artificial Intelligence: 28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers . Vol. 765 Springer Verlag, 2017. p. 78-92 (Communications in Computer and Information Science, Vol. 765).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments

AU - Uiterwijk, JWHM

AU - Griebel, Janis

PY - 2017

Y1 - 2017

N2 - Combinatorial games are a special category of games sharingthe property that the winner is by denition the last player able to move.To solve such games two main methods are being applied. The rst is ageneral alpha-beta search with many possible enhancements. This technique isapplicable to every game, mainly limited by the size of the game due tothe exponential explosion of the solution tree. The second way is to usetechniques from Combinatorial Game Theory (CGT), with very preciseCGT values for (subgames of) combinatorial games. This method is onlyapplicable to relatively small (sub)games. In this paper1 we show that themethods can be combined in a fruitful way by incorporating an endgamedatabase filled with CGT values into an alpha-beta solver.We apply this technique to the game of Clobber, a well-known all-smallcombinatorial game. Our test suite consists of 20 boards with sizes upto 18 squares. An endgame database was created for all subgames ofsize 8 and less. The CGT values were calculated using the CGSUITEpackage. Experiments reveal reductions of at least 75% in number ofnodes investigated.

AB - Combinatorial games are a special category of games sharingthe property that the winner is by denition the last player able to move.To solve such games two main methods are being applied. The rst is ageneral alpha-beta search with many possible enhancements. This technique isapplicable to every game, mainly limited by the size of the game due tothe exponential explosion of the solution tree. The second way is to usetechniques from Combinatorial Game Theory (CGT), with very preciseCGT values for (subgames of) combinatorial games. This method is onlyapplicable to relatively small (sub)games. In this paper1 we show that themethods can be combined in a fruitful way by incorporating an endgamedatabase filled with CGT values into an alpha-beta solver.We apply this technique to the game of Clobber, a well-known all-smallcombinatorial game. Our test suite consists of 20 boards with sizes upto 18 squares. An endgame database was created for all subgames ofsize 8 and less. The CGT values were calculated using the CGSUITEpackage. Experiments reveal reductions of at least 75% in number ofnodes investigated.

KW - SEARCH

U2 - 10.1007/978-3-319-67468-1_6

DO - 10.1007/978-3-319-67468-1_6

M3 - Conference article in proceeding

SN - 9783319674674

VL - 765

T3 - Communications in Computer and Information Science

SP - 78

EP - 92

BT - BNAIC 2016: Artificial Intelligence

PB - Springer Verlag

T2 - 28th Annual Benelux Conference on Artificial Intelligence (BNAIC)

Y2 - 10 November 2016 through 11 November 2016

ER -

Uiterwijk JWHM, Griebel J. Combining Combinatorial Game Theory with an Alpha-Beta Solver for Clobber: Theory and experiments. In BNAIC 2016: Artificial Intelligence: 28th Benelux Conference on Artiﬁcial Intelligence, Amsterdam, The Netherlands, November 10–11, 2016, Revised Selected Papers . Vol. 765. Springer Verlag. 2017. p. 78-92. (Communications in Computer and Information Science, Vol. 765). doi: 10.1007/978-3-319-67468-1_6