Rook and bishop versus rook endgame

The rook and bishop versus rook endgame is a chess endgame where one player has just a rook, bishop and king, and the other player has only a rook and king. It has been studied many times through the years. This combination of material is one of the most common pawnless chess endgames. It is generally a theoretical draw, but the rook and bishop have good winning chances in practice because the defense is difficult. Ulf Andersson won the position twice within a year, once against a grandmaster and once against a candidate grandmaster; and grandmaster Keith Arkell has won it 18 times out of 18 (Hawkins 2012:193). In positions that have a forced win, up to 59 moves are required (Speelman, Tisdall & Wade 1993:382). Tony Kosten has seen the endgame many times in master games, with the stronger side almost always winning (Kosten 1987:11). Pal Benko called this the "headache ending" (Benko 2007:154).

Computer endgame tablebases show that 40.1% of the legal positions with this material are theoretical wins, but that includes many unnatural positions that are unlikely to occur in games. Edmar Mednis estimated that less than 4% of starting positions that occur in games are theoretical wins (Mednis 1996:80).

In 1749 François-André Danican Philidor (1726–1795) published a position in which the superior side can force a win. Giambattista Lolli (1698–1769) studied a similar position with a forced win. On the other hand, there are several drawing techniques possible if a winning position such as the Philidor position has not been reached. The Cochrane Defense was discovered by John Cochrane (1798–1878), the Szén position was discovered by József Szén (1805–1857), and there is the second-rank defense. Other winning and drawing positions were studied by Tassilo von Heydebrand und der Lasa, Josef Kling and Kuiper, and André Chéron (Nunn 2002:178–86).

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