# Endspiel

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Endspiel,
a Windows chess program and explanation tool dedicated for simple Endgames, written by Wilhelm Barth in the 90s. 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 - -
𝒘 == 2 usually wins, but rook and bishop pawn cases
𝒘 == 1 often wins, but more exceptions with other pawn files
𝒘 == 0 normally draw, but some skewer cases that win
𝒘 == -1 despite exceptional drawn positions,
left without evaluation

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

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