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Endspiel,
a Windows chess program and explanation tool dedicated for simple Endgames, written by Wilhelm Barth.
Endspiel combines rule-based knowledge with a modified alpha-beta search to generate explanations.
The rules cover a large part of the positions of an endgame. For each such position they define a score interval guaranteed to contain the true value.
Multiple rules may be applied, resulting in the intersection and narrowing of intervals.
Further, an alpha-beta search finds the values for all positions not covered and removes uncertainties
left by too wide intervals in rule-scored positions. Thus, the method yields a correct evaluation for every position and.
furthermore, the rules governing the position of its successors provide some tutorial insight to the user about the reasons behind the evaluations.
Moreover, automatic validation assures that mistakes in the rules will be discovered and then can be eliminated in dialogue
[1].
Rules
For a specific endgame, e.g. KPK, KQKQ, KQKP, or KPKP, a system of rules is developed, which decides for the positions whether they are won, drawn or lost. The remainder of the positions may be left undecided. The rules may be arranged by decision trees [2] [3], or they may be examined sequentially until applicable to the position involved [4]. The rules consist of conditions to match and associated score intervals which may express some uncertainty. A winning position obtains the value of (maxval - k), where maxval is a huge positive integer, i.e. minus mate score, and k the minimum of
- number of plies on the shortest path to mate, and
- minimal number of plies ending with an irreversible move on the winning path
For instance in KPK (BTM), the case of opposition on the same file, white king on the stop square, the interval is defined by value[maxval-8, maxval-4].
KPKP
In his 1995 ICCA Journal article on KPKP with passed pawns [5], Wilhelm Barth elaborates on following six rules applied in his Endspiel program, along with several examples.
# | Description | Conditions | Assessment |
---|---|---|---|
1 | wP can promote without support of its king and bP is blocked |
♚∉□ ∧ ♔∈⤋ | White wins |
2 | wK stops bP definitely | ♔∈■ ∧ (D (♔,♟) < D (♚,♟) ∨ D (♔,🛑) < D (♚,🛑)) | White achieves at least a draw |
3 | wp reaches promotion before bP does | 𝒘 ::= D (♙,♕) - D (♟,♛) 𝒘 >= 3 usually wins, but 8/3K4/4P3/5p2/8/8/8/5k2 w - - |
White wins or achieves a draw depending on 𝒘 and some other conditions |
4 | wk stops bP definitely after wP has attracted the bK |
(𝒘 > 0 ∨ (𝒘 == 0 ∧ ♟♛!+)) ∧ ♚∈□ ⇒ rule 2 | White achieves at least a draw |
5 | with support of its King, wP promotes before bP does |
conditions similar to rule 3 | White wins or achieves a draw depending on 𝒘 and some other conditions |
6 | bP is unstoppable and bK stops wP and wK cannot parry both threats |
addresses Réti Endgame Study | Black wins |
Symbols:
- ∧ - and
- ∨ - or
- ∈ / ∉ - Element of / Not Element of
- ■, □ - Square of The White, Black Pawn
- ⤋ - Black Pawn's Front Span
- D - Chebyshev Distance
- 🛑 - Black Pawn's Tele Stop
- ♕ / ♛ - White / Black Pawn's Promotion Square
- !+ - No Check after Queening
See also
Selected Publications
- Wilhelm Barth, Stephan Barth (1991). Programme für korrekte Schachendspiele und deren Validierung. Institutsbericht, Nr. 34. Institut für Computergraphik, TU Wien (German)
- Wilhelm Barth, Stephan Barth (1992). Validating a Range of Endgame Programs. ICCA Journal, Vol. 15, No. 3 [6]
- Wilhelm Barth (1994). 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 (German)
- Wilhelm Barth (1995). Combining Knowledge and Search to Yield Infallible Endgame Programs A study of passed Pawns in the KPKP endgame. ICCA Journal, Vol. 18, No. 3
- Steven Edwards (1995). Comments on Barth’s Article “Combining Knowledge and Search to Yield Infallible Endgame Programs.” ICCA Journal, Vol. 18, No. 4
- Heinz Herbeck, Wilhelm Barth (1996). An Explanation Tool for Chess Endgames Based on the Rule Method. ICCA Journal, Vol. 19, No. 2
External Links
- Neues Schachprogramm für Spezialprobleme, October 28, 1996 (German)
- Computer Chess site (Barth, Herbeck) (Wayback Machine)
References
- ↑ Wilhelm Barth (1995). Combining Knowledge and Search to Yield Infallible Endgame Programs A study of passed Pawns in the KPKP endgame. ICCA Journal, Vol. 18, No. 3
- ↑ Ross Quinlan (1983). Learning Efficient Classification Procedures and Their Application to Chess End Games. Machine Learning: An Artificial Intelligence Approach
- ↑ Gerhard Mehlsam, Hermann Kaindl, Wilhelm Barth (1991). Feature Construction during Tree Learning. GWAI 1991
- ↑ Jaap van den Herik (1983). Representation of Experts' Knowledge in a Subdomain of Chess Intelligence. IJCAI 1983
- ↑ Wilhelm Barth (1995). Combining Knowledge and Search to Yield Infallible Endgame Programs A study of passed Pawns in the KPKP endgame. ICCA Journal, Vol. 18, No. 3
- ↑ Ulrich Thiemonds (1999). Ein regelbasiertes Spielprogramm für Schachendspiele. University of Bonn, Diplom thesis (German)