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Computer Chess

(Barth, Herbeck)

This program uses the strict rules-search method (Barth and Barth, 1991, 1992). It is essential that part of the positions of the endgame considered have to be treated by rules, without it being necessary, however, to find rules for all positions; indeed, some positions may be left undecided. Thus, the finding of simple rules not overburdened by exceptions is facilitated.

For every position covered by the rules, they define an interval guaranteed to contain the true value. For example: "If White is to move and can capture the black Pawn the value is in [draw,win]." Note that many positions of the endgame may be ignored by the system of rules; for others an uncertainty may be left (as in the example just given). All deficiencies are supplemented and all uncertainties are removed by an appropriate alpha-beta-search. Herbeck (1995) uses the B* Algorithm.

Thus, granted an appropriate amount of time, the program will find the best possible result and a corresponding move for any position of the endgame under consideration. Failing enough time, it will produce an interval showing the knowledge found before curtailment. Yet, the interval is guaranteed to contain the true value of the position. An automatic validation component guarantees the rules to be free of errors (e.g. if some strange board configuration has been overlooked by the programmer). So far, almost all four-piece endgames have been implemented.

The fact that the rules seem quite natural to the average chess player makes interaction with the program much more interesting. In particular, the user may ask for an explanation to be displayed, and will be able to understand the plain text answer. This allows a "computer-aided teaching" approach.

Example: Reti's endgame problem

If moving 1.Kg8 or 1.Kh7, the program quickly finds that after 1....Kb6 Black has the possibility to both lead its pawn to promotion and hold the white pawn, i.e. Black wins. However, within a few seconds it also states that White will be able to reach a draw by moving 1.Kg7.

The solution and arbitrary variants can interactively be followed and evaluated, and often the program will comment a position and explain what it leads to.

Related Publications

W. Barth: Combining Knowledge and Search to Yield Infallible Endgame Programs

A study of passed Pawns in the KPKP endgame.
In: ICCA Journal, Vol. 18 (1995), No. 3, pp. 148-159.

W. Barth: Computerschach

- Ein korrektes Programm für das Endspiel König und Bauer gegen König und Bauer
- Unterteilung von Endspielen in Klassen
- Behandlung der Stellungswiederholung bei der Intervallbewertung
Institutsbericht Nr. 36, Institut für Computergraphik, TU Wien, Februar 1994.

W. Barth, S. Barth: Validating a Range of Endgame Programs

ICCA Journal, Vol. 15 (1992), pp. 132-139.

H. Herbeck: Eine Erklärungskomponente für Endspiele im Computerschach unter Verwendung der Regelmethode

Dissertation, TU Wien, Technisch-Naturwissenschaftliche Fakultät, 1995.

H. Herbeck: Solving Chess Endgames using the B* Algorithm and the Rule Method

Abstract, CSGP Workshop, Chinese University Hongkong, May 1995.

H. Herbeck, W. Barth: An Explanation Tool for Chess Endgames Based on the Rule Method

ICCA Journal 19, 2, pp. 75-82, 1996.

Software

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