Queen and pawn versus queen endgame

The queen and pawn versus queen endgame is a chess endgame in which both sides have a queen and one side has a pawn, which one tries to promote. It is very complicated and difficult to play. Cross-checks are often used as a device to win the game by forcing the exchange of queens. It is almost always a draw if the defending king is in front of the pawn.
Karsten Müller and Frank Lamprecht say that this endgame occurs quite frequently but Mark Dvoretsky says that it occurs quite seldom. This is the second most common "piece and pawn versus piece" endgame, next to the rook and pawn versus rook endgame.
History.
Before about 1940 all that was known about this endgame was based on some superficial analysis of a few positions from the time of Philidor (1726–95). Analysts gradually started to analyze the endgame. The endgame occurred in a 1944 game between Botvinnik and Ravinsky (below) and much analysis followed. Paul Keres published a large amount of analysis in 1947–49. This analysis was put to the test in the 1954 game between Botvinnik and Minev (below). Minev followed the suggestions of Keres and lost – revealing major flaws in the analysis. In 1955, Shakhmaty v SSSR started a competition for the best analysis of this endgame. Several theorists had contributed useful analysis by the time the competition ended in 1959. Early analysts thought that the ending was almost always drawn with a knight pawn, but Yuri Averbakh questioned that in the 1950s. Averbakh, working with previous analysis, published his extensive analysis in 1962.
A complete analysis was not done until the advent of endgame tablebases, which showed that more positions can be won than was previously thought. Before tablebases, Averbach provided the best coverage, but the 70 pages of analysis in "Comprehensive Chess Endgames" mainly covered only simple positions with the pawn already on the seventh rank. John Nunn wrote three books based on the most important endgames in the five-piece endgame tablebases but omitted this endgame because "... it proved too hard to understand". He also commented "This is the trickiest of all five-man endings, which is unfortunate as it is one of the most common to arise in practice."
General considerations.
According to Reuben Fine and Pal Benko, this ending is a draw unless the pawn is a bishop pawn or a central pawn (i.e. king pawn or queen pawn) and the pawn is in the seventh rank and is supported by its king. If the defending king can get in front of the pawn, the game is a draw; otherwise it is best for the defender to keep his king far away from the pawn. The defender should keep checking until he runs out of check, and then pin the pawn. Based on computer analysis, Müller and Lamprecht give a different description. According to them, normally the defending king needs to be in front of the pawn. A rook pawn or knight pawn is a theoretical draw if the defending king is in front or near the pawn or if the king is in the corner opposite the pawn's promotion square. A knight pawn has more practical winning chances than a rook pawn. A bishop pawn or central pawn is a win if the defending king is not in front of the pawn. A bishop pawn has better winning chances than a central pawn. The position of the defending king is especially important. John Nunn states that analysis since Fine's initial work (published in 1941 in "Basic Chess Endings") has shown that there are many more winning positions than were known at that time (ignoring the fifty-move rule in some cases). Wins by the side with the pawn take up to 59 moves. A cross-check may be necessary to win.
Edmar Mednis gave this breakdown when the defending king is not able to help:
John Nunn gives this summary for the defense:
Naturally, the less advanced the pawn is, the better the defensive chances.
Rook pawn.
In 1985 the chess computer Belle completed the endgame tablebase for this ending. The rook pawn is the most important for actual games since it arises the most frequently, since it is the least likely pawn to have been exchanged. A rook pawn needs to be on at least the sixth rank to have decent winning chances.
Mednis gave the following guidelines, based on his analysis of the tablebase. Assume that White has a pawn on the h-file.
To draw:
To win:
Example of a long theoretical win involving a rook pawn.
Mate can be forced in 235 plies, but under the fifty-move rule the position is a draw.
Knight pawn.
A knight pawn should be on at least the fifth rank to have good winning chances. A knight pawn on the fifth rank has better winning chances than a rook pawn on the sixth rank. There are two reasons for this:
The best place for the defending king is in front of the pawn and the second-best place is in the corner opposite its promotion square.
Bishop pawn.
A bishop pawn offers the best winning chances. One reason is that there is no drawing zone in the opposite corner for the black king if the pawn is on at least the fourth rank. If the pawn is on the fifth rank the defender's chances are small unless the king is in front of the pawn. A pawn on the sixth rank wins unless the defending king is in front of the pawn.
Central pawn.
A central pawn has better chances to win than a rook pawn or knight pawn, but not as good as a bishop pawn. As with the bishop pawn, there is no drawing zone for the defending king in the opposite corner. It is better for the defending king to be on the "short side" of the pawn rather than the "long side".
Example of a long theoretical win involving a central pawn.
Mate can be forced in 247 plies.
Examples from games.
Botvinnik - Ravinsky, Moscow (ch-USSR) 1944.
In 1944 Botvinnik played a perfect endgame against Grigory Ravinsky. The starting position, after 86...b1=Q, is winning.
87.Qa7+! [The only move that wins!] 87...Kf6 88.Qf7+ Ke5 89.Kh6 Qh1+ 90.Kg7 Kd4 91.Qf6+ Kc5 92.Kg8 Kb5 93.g7 Ka4 94.Kf7 Qh5+ 95.Ke7 Qc5+ 96.Qd6 Qg5+ 97.Kf8 Qf5+ 98.Ke8 Qh5+ 99.Kf8 Qf5+ 100.Ke7 Qg5+ 101.Qf6 Qc5+ 102.Kd7 Qd5+ 103.Kc7 Qa5+ 104.Kb7 Qb5+ 105.Qb6 Qd7+ 106.Qc7! Qb5+ 107.Ka7 Qd5 108.Kb8 Qg8+ 109.Ka7 Qd5 110.Qf4+ Ka5 111.Qf6 Qc5+ 112.Kb7 Qb5+ 113.Kc7 Qc5+ 114.Kd7 Qd5+ 115.Ke7 Qc5+ 116.Kf7 Qc4+ 117.Ke7 Qc5+ 118.Ke6 Qc8+ 119.Ke5 Qc3+ 120.Kf5 Qd3+ 121.Kg5 Qe3+ 122.Kg6 Qe8+ 123.Kh6 Qg8 124.Qe5+ Ka4 125.Kg6 Qc8 126.Qf4+ 1–0
A possible continuation, by endgame tablebases, could have been:
126...Kb3 127.Qf7+ Ka4 128.g8=Q Qg4+ 129.Kh6 Qh4+ 130.Kg7 Qg3+ 131.Kf8 Qd6+ 132.Qe7 Qh6+ 133.Qgg7 Qf4+ 134.Qgf7 Qb8+ 135.Qfe8++-[Exchanging queens.]
Botvinnik - Minev, Amsterdam (ol) 1954.
Ten years later, analyzing his adjourned game against Nikolay Minev, Botvinnik improved the winning method. But even then he erred two times (at 61 and 77). The position after 55...a1=Q is drawn. The game continued:
56.Qg4+ Ka5 57.Qxe6 Qh8+ 58.Kg6 Qc3 59.g4 Qd2 60.g5 Qd4? [60...Ka4=] 61.Qf5+? [61.Kh7!+-] 61...Ka4= 62.Kh5 Qh8+ 63.Kg4 Qh1? [63...Ka3=] 64.Qf4++- Ka5 65.Qe5+ Ka4 66.g6 Qd1+ 67.Kg5 Qd8+ 68.Kf5 Qc8+ 69.Kf4 Qc1+ 70.Qe3 Qc7+ 71.Qe5 Qc1+ 72.Kf5 Qc8+ 73.Kg5 Qd8+ 74.Qf6 Qd5+ 75.Qf5! Qd8+ 76.Kh5 Qe8 77.Qf4+? [77.Kg4+-] 77...Ka5? [77...Ka3!=] 78.Qd2++- Ka4 79.Qd4+ Ka5 80.Kg5 Qe7+ 81.Kf5 Qf8+ 82.Ke4 Qh6 83.Qe5+ Ka4 84.g7 Qh1+ 85.Kd4 Qd1+ 86.Kc5 Qc1+ 87.Kd6 Qd2+ 88.Ke6 Qa2+ 89.Qd5 Qe2+ 90.Kd6 Qh2+ 91.Kc5 1–0
Now either a cross-check will force the exchange of queens, or else the pawn will promote.
Queen and two pawns versus a queen.
This is usually a win for the two pawns, but victory can be difficult to achieve even in winning positions, as even the slightest inaccuracy may lead to perpetual check. Positions in which one of the pawns is vulnerable to attack may be drawn, but they are unusual.
There are a number of other drawing exceptions, most notably with connected rook and knight pawns (a- &amp; b-pawns, or g- &amp; h-pawns) in which the defending king is ahead of the pawns.
An example is Smbat Lputian vs. Gevorg Harutjunyan, 2001. The position after 86.h6 (the last pawn move of the game) is a draw. Play continued until move 142, with inaccuracies on both sides swinging the position from a draw to a forced win, and back again. Interestingly, Black could have claimed a draw by the fifty-move rule for the last several moves, including the final position in which he resigned, but he did not.
Queen and two pawns versus a queen and pawn.
Normally this is a win for the two pawns, but a surprising result of seven-piece Lomonosov tablebases is that the longest possible win require 594 plies. However, in Kasparov versus the World, Kasparov was the side with a single pawn, but won because his pawn was far more advanced than the world team's pawns, which also hindered perpetual checks by them.
References.
Bibliography