# KRK

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KRK,

the King and Rook versus King endgame is beside KQR the most elementary endgame with three pieces. If the rook can not be captured immediately - or the losing king isn't stalemated, checkmate can be forced by driving the losing king to the edge or corner of the board, the rook giving mate similar to the back-rank mate, the winning king locking all escape squares, often initiated by a rook tempo move to force the king into opposition.

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KRK Mate in Two

# Heuristics

Simple heuristics of a mop-up evaluation [1], only considering Center Manhattan-distance of the losing king, and Chebyshev distance and/or Manhattan distance between both kings, along with a tiny search, should be sufficient to execute the mate. Further, the rook may receive a bonus to maximize the absolute difference of its rank- and file-distances to the losing king, to confine the king without becoming attacked.

Despite todays engines have no difficulty to win this easily even without tablebases, deviation from optimal tablebase play, in particular in games with short time control, and most compact and efficient code considering symptoms of search pathology remain interesting issues [2].

# Testbed

First implemented by Leonardo Torres y Quevedo in 1912 within his electro-mechanical KRK solver El Ajedrecista, KRK was and still is testbed and subject of research on evaluation and search heuristics and strategies, oracle approaches, mate search, search pathology, search versus knowledge, space-time tradeoff, retrograde analysis and tablebase generation [3], knowledge extraction and compression, feature detection and tuning, learning [4], genetic programming, pattern recognition, decision trees, logic and logic programming [5], inductive and deductive reasoning, rule-based modeling, problem solving and SAT [6]. In 1977, Donald Michie addressed KRK and the infinite board [7].