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 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 master; and grandmaster Keith Arkell has won it 18 times out of 18. In positions that have a forced win, up to 59 moves are required. Tony Kosten has seen the endgame many times in master games, with the stronger side almost always winning. Pal Benko called this the "headache ending".
Being a five-piece endgame, the rook and bishop versus rook endgame has been fully analysed using computers. 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.

History

In 1749 François-André Danican Philidor published a position in which the superior side can force a win. Giambattista Lolli 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, the Szén position was discovered by József Szén, and there is the second- defense. Other winning and drawing positions were studied by Tassilo von Heydebrand und der Lasa, Josef Kling and Kuiper, and André Chéron.
Many of the longest chess games on record involve this endgame since at one time the fifty-move rule under which a draw could be claimed after fifty moves with no was extended to one-hundred moves for this combination of material. For example, the longest tournament game on record is a 269-move game by Ivan Nikolić and International Master Goran Arsović. The last 103 moves had this material and the game ended in a draw.
Anatoly Karpov played a rook vs rook and bishop ending in a 2003 game with 15-year-old Teimour Radjabov, which went 113 moves before an indignant Karpov invoked the 50-move rule with only 14 seconds remaining on the game clock.
In a 2016 game between Fabiano Caruana and Peter Svidler, Caruana succeeded in achieving Philidor's Position on move 102, but failed to take advantage of the situation and the game ended in a draw 16 moves later.

Winning positions

Philidor position

This famous position was studied by and named after François-André Danican Philidor. White wins because his king has reached the sixth and the black king is poorly placed . If this type of position arises, it is usually because of inferior defense. Nevertheless, it is tricky to win.
The winning method is as follows:
Threatening to switch the rook to the other side and checkmate.
This is the best place for the black rook. Alternatives are:
This idle move maintains the necessity of the black rook on the e-file, forcing it to its next best position on e1. White will take advantage of this on move 5.
The winning line only works if the white rook is on b7 or f7.
Or 4...Kc8 5.Ra7 Rb1 6.Rf7 Kb8 7.Rf8+ Ka7 8.Ra8+ Kb6 9.Rb8+.
This is the key idea. It forces the black rook to the inferior third rank while preventing 5...Rd1+. Black is in zugzwang.
If instead 5...Kc8, then 6.Rb4 Kd8 7.Rf4 Re1 8.Ba4 Kc8 9.Bc6 Rd1+ 10.Bd5 Kb8 11.Ra4. Now White completes the following maneuvers, getting the bishop back to d5 with gain of tempo.
If 8...Ke8, then 9.Rg7 and checkmate on g8 next move, else loss of the rook since the bishop covers f3.
If 11...Rd3 12.Ra4 and checkmate or loss of the rook since the bishop covers b3. If 11...Rc2 or 11...Rc1, then 12.Be6+.
Stopping the check on d3 and cutting off the rook entirely.
and checkmate next move,,.
This is an exercise in domination of the black rook. This method works if the kings are on the central four ranks or files. It does not work if the kings are on the rank or file next to the edge – those positions are a theoretical draw, but difficult to defend. If the kings are on a rank or file on the edge of the board the position is a win, but by a different method.

Lolli position

This winning position was discovered by Giambattista Lolli. The position is one rank or file closer to the edge of the board than the Philidor position, so the winning method is slightly different. Switching the attacking rook to the other side of the king is no longer dangerous.
The method:
Or 8...Rb8.

Drawing defenses

Cochrane Defense

The Cochrane Defense is a drawing method discovered by John Cochrane. The Cochrane Defense is the most popular among grandmasters for this endgame. The basic idea is to pin the bishop to its king when there are at least two or between it and the defending king.
Accurate play is required for the defense. The defense is most effective near the center of the board, and does not work on the edge. The Cochrane Defense works when:
The Cochrane defense can also be used with a rook against a rook and knight.

Budnikov versus Novik

The defense is most effective near the center of the board. In this position, if the pieces on the e-file were moved to the f-file, then if 1.Ke5, the response 1...Kg8 puts the black king dangerously close to the corner.
In this position from a 1991 game between Alexandar Budnikov and Maxim Novik, White would like to get his king to d6 and bishop to d5, to win by a method of Philidor ; however, the pin of the bishop to the king prevents it. If White plays 1.Kd5 or 1.Kf5 then Black moves his king in the opposite direction, so if the bishop then moves, the black rook cuts off the white king.
There are some key ideas for the defender to observe:
The game continued:
and the position is back to the basic Cochrane position, rotated 90 degrees, and the fifty-move rule is closer to coming into effect. The Budnikov versus Novik game continued, with the Cochrane position being reached again. Eventually a draw was claimed by the fifty-move rule.

Ljubojević versus Portisch

The Cochrane Defense was also used in this 1982 game between Ljubomir Ljubojević and Lajos Portisch. The Cochrane position occurred again on move 114, rotated 90 degrees. The game was drawn on move 127.
The defending king goes the opposite way as the attacking king.
Cochrane position again, on a different side.

Second-rank defense

The "second-rank defense" is a passive defense with the defending king and rook on a rank or file one over from the edge of the board. The method is reliable but it is possible to go wrong, especially if the defending king is near the corner.

Norri versus Atalik

This 1997 game between Joose Norri and Suat Atalık illustrated the second-rank defense. White cannot reach the Cochrane Defense. Attempting to get the rook behind the black king would get to a lost Philidor Position: 87.Rc8 Rb2+ 88.Kf1 Rf2+ 89.Ke1 Kd3. White uses the second-rank defense. White alternates his rook between c2 and d2 until Black tries to penetrate.
The defending king can be driven to the edge of the board but then the attacker's rook is under attack, so the king cannot approach.
This is another attempt by Black. It seems that White is in zugzwang and any rook move loses, but White has a good move.
Now if 93...Kd3 White has a stalemate defense with 94.Rd2+ so the black king has to back off.
and the game was drawn on move 98.

Carlsen versus Van Wely

The second-rank defense was used by 16-year-old Magnus Carlsen in this 2007 game against Loek van Wely.
It is hard to drive the defending king to the edge. After 65...Rh2+ 66.Kd1 the black rook must move and the white king goes back to e2.
White was in zugzwang and had to temporarily leave the second rank.
Here 66...Kd3 is met by 67.Rd2+.
and the king is back to the second rank. The game continued and the position on move 74 was a reflection of the position on move 66. On move 80 the same defense was set up on the b-file. Black could make no progress and the game was drawn after 109 moves.

Szén position

discovered the Szén position, a defensive drawing position. The kings are opposite in an L-shape and the weaker side's rook defends on the side of his king that has more room. Szén's position is the most important for players. Compared to the [|Philidor Position], the kings are not opposite each other and the defending rook can prevent checkmate. The position is a draw only if there is enough room for the defending king on the side with the rooks.
An example of this defense being used in a game is this 1982 one between József Pintér and Yuri Razuvayev. After 88 moves, the position had a rook and bishop versus a rook. The diagram shows the position after 101. Kd1!, reaching the Szén position. On the 132nd move, White reached a Szén position for the fourth time. The game was drawn on the 138th move.

Second Lolli position

In the second Lolli position, the kings are one row closer to the edge than in the first Lolli position. Unlike the Philidor position and the first Lolli position, this position is a theoretical draw. Several of the moves in the perfect defence are the only move that saves the game.