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GNU GENERAL PUBLIC LICENSE
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\documentclass[12pt]{book}
\usepackage{setspace}
\usepackage{xskak}
\raggedbottom
\title{Atomic}
\date{January 2025}
\setlength{\baselineskip}{10pt}
\usepackage[
paperwidth=210mm,
paperheight=297mm,
inner=1in,
outer=0.75in,
top=1in,
bottom=1in
]{geometry}
\newcounter{diagramnum}
\setcounter{diagramnum}{0}
\newcommand{\diagram}[2]{
\begin{center}
\begin{tabular}{c c}
\chessboard[setfen=#1, boardfontsize=20pt] & \chessboard[setfen=#2, boardfontsize=20pt]\\
\addtocounter{diagramnum}{1} \textbf{Diagram \thediagramnum} & \addtocounter{diagramnum}{1} \textbf{Diagram \thediagramnum}
\end{tabular}
\end{center}
}
\newcommand{\db}[1]{
\textbf{(Diagram \number\numexpr\value{diagramidx}-#1\relax)}
}
\newcounter{diagramidx}
\setcounter{diagramidx}{0}
\renewcommand{\d}[0]{\addtocounter{diagramidx}{1}\textbf{(Diagram \thediagramidx) }}
\newcommand{\nline}{\\[\baselineskip]}
\newcounter{example}
\setcounter{example}{0}
\newcommand{\example}{
\addtocounter{example}{1}
\textbf{\underline{Example \theexample:}}
}
\newcommand{\cat}[1]{\subsection*{\underline{#1}}}

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\underline{\Huge{\textbf{Introduction}}}
Chess is played by millions around the world. Due to this, many people have created chess 'variants', games similar to chess
that follow different rules. One of the most popular of these variants is ``Atomic Chess", a variant where when a piece is
captured, the capturing piece is exploded and all non-pawn pieces in a 3x3 area are also exploded, meaning removed from the
board. This means that many beginner games end rather quickly, due to how easy it is to win in the opening, and how many
moves are forced to not immediately get checkmated.
\nline
However once you learn to refute the plethora of opening traps, you find yourself in the middlegame. Here, rooks come into play, and winning positions can easily become drawn or even lost from a deadly rook invasion.
\nline
But once the pieces have been traded, we reach the endgame. And it is here so many people lose points or half-points not knowing the correct technique.
\nline
My hopes are that this book allows many players to improve their endgame skills, allowing more players to rise to grandmaster level.
\newpage
\underline{\Huge{\textbf{Chapter 1: The Basics}}}
Atomic chess has many differences that must first be addressed before mastering the endgame.
\nline
\underline{\large{\textbf{Adjacent Kings}}}
While being up a queen is a trivial win in standard chess, a little more care must be taken in Atomic.
\begin{center}\chessboard[setfen=8/8/4Q3/8/8/2k1K3/8/8]\end{center}
\begin{center}\textbf{Diagram 1}\end{center}
\textbf{(Diagram 1)} Here a common move for white in standard chess would be
\variation{1. Qc6+??}
However in atomic, this is a big blunder!
\variation{1... Kd3!}
What? How is this possible? Well, first understand that kings not being adjacent in standard chess is not an official rule. Rather, it is a 'rule' because since kings being adjacent is check for both sides, it is thus an illegal position. However in atomic, the explosion rule means that kings cannot capture, thus adjacent kings is not check. Thus adjacent kings are possible, and are often an important resource.
\nline
In addition, since capturing one of these kings with another piece would explode the other, kings are immune to checks while adjacent to the opposing king. Because of this, this position is now a draw, as white cannot force the black king to move away from their own king.
However, white was winning in the initial position with
\variation{1. Kf3!}
Now black cannot immediately connect the kings.
\variation{1... Kd3}
Black tries to connect the kings next move.
\variation{2. Kg3!} \textbf{(Diagram 2)}
Now black can no longer follow as the white queen controls the e-file.
\begin{center}\chessboard[setfen=8/8/4Q3/8/8/3k2K1/8/8]\end{center}
%
\begin{center}\textbf{Diagram 2}\end{center}
\underline{\large{\textbf{Checkmating with a Queen}}}
\textbf{(Diagram 2)} Since kings cannot capture, checkmating with a queen is quite easy.
\variation{1. Qe3+ Kc4 2. Qd4+ Kb3 3. Qc3+ Ka2 4. Qa2#}
\nline
\underline{\large{\textbf{Insufficient Material}}}
As the king cannot aid in checkmating, a king and rook, knight, bishop, or 2 knights is insufficient material, and checkmate cannot be forced with 2 bishops or a bishop and knight (though is theoretically possible)
\nline
%
\underline{\large{\textbf{Checkmate with adjacent kings}}}
\begin{center}\chessboard[setfen=8/8/3K4/3pkR2/3P4/8/8/8]\end{center}
\begin{center}\textbf{Diagram 3}\end{center}
\textbf{(Diagram 3)} Sometimes checkmate can still occur with adjacent kings.
\variation{1. Kc7!}
Or \variation{1. Kd7} with the same result.
\variation{1... Kd6}
Despite the kings being adjacent, we have checkmate!
\variation{2. Rxd5#}
Notice that:
a) this was only checkmate as the black king was next to the pawn and the white king wasn't, and
b) regardless of where the king moved \variation{2. Rxd5} was mate regardless.
You are now armed with the necessary information to begin learning atomic endgames.

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\input{header.tex}
\begin{document}
\setlength{\parindent}{0pt}
\setstretch{1.2}
\input{introduction.tex}
% Chapter 2
\newpage
\input{queen.tex}
% Chapter 3
\newpage
\input{pawn.tex}
% Chapter 4
\newpage
\input{rook.tex}
\end{document}

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\begin{center}\underline{\Huge{\textbf{Chapter 3: Pawn Endgames}}}\end{center}
\setcounter{diagramnum}{0}
\setcounter{diagramidx}{0}
\setcounter{example}{0}
Armed with the knowledge of when an extra queen is enough to win, we now move to what came before: pawn endgames.
\example
\diagram{8/8/2k5/2P2p2/5K2/8/8/8}{8/5p2/5P2/4P3/1K6/k7/8/8}
\d Both kings are blocking the pawn, but white is closer to promotion. However, white must take care to avoid a loss!
\nline
\variation{1. Kf3?? f4!} forces white to give way again, when black becomes closer to promotion and will win the race.
\variation{1. Ke5?? f4} (with the goal of connecting the kings) should be an obvious blunder by now: Example 12 from the previous chapter shows the winning technique for black.
\nline
The way to win is \variation{1. Ke3!} (or \variation{1. Kg3!} with the same result). Let's see how this plays out:
\nline
\variation{1. Ke3! f4+ 2. Kf3!} and now black has to move: \variation{2... Kd7 3. c6+ Kc7}. Notice that there is a kind of ``back and forth" game going on: white moves their pawn forward, then black, etc.
\nline
\variation{4. Kg2 f3+ 5. Kf2 Kd8 6. c7+ Kc8 7. Ke1 f2+ 8. Kf1 Kd7 9. c1=Q+ Ke6} and the winning technique is identical to Example 12 from the previous chapter.
\nline
When you are up a pawn, you must take care not to trade all the pawns.
\example
\d Despite being up a pawn, this position is a draw. White has no way to promote without trading pawns.
\variation{1. Kc5 Kb4 2. Kd6 Kc5 3. Ke7} \d \variation{3... Kd4!}
\diagram{8/4Kp2/5P2/2k1P3/8/8/8/8}{8/ppp5/8/PPP5/8/8/8/1Kk5}
Avoiding white's trap: \variation{3... Kd6 4. Kf8+ Ke7 5. e6!} when all of a sudden white is promoting!
\nline
\variation{4. Kg8 Ke4 5. e6}
White can't make any progress, as black can remain on the 4th rank forever.
\nline
\variation{5... fxe6 6. f7 Kf5 7. f8=Q+ Kg6 8. Qg7+ Kf7} with a draw.
\nline
\example
\d This is a famous endgame in regular chess (without connected kings!). However, the result is very different!
\nline
\variation{1. b6 cxb6?}
Indeed, the correct defense is not to take, but rather, \variation{1... c6!} (or \variation{1... a6!}), and white cannot make progress.
\begin{enumerate}
\item Any king move fails to \variation{2... a6}, where since no pawns can be captured, progress is completely impossible.
\item \variation{2. a6} is drawn, as black can keep moving their king forever. If you take, black will simply capture the other pawn, resulting in a draw.
\item \variation{2. bxa7} and black can do whatever, as long as they remember to play \variation{3. a6 bxa6!}, with a draw.
\end{enumerate}
However, if black immediately plays \variation{1... cxb6?}, the proximity of white's king allows a simple win.
\nline
\variation{2. a6! bxa6}
Or \variation{2... b5 3. c6 b4 4. c7 b3 5. c8=Q b2} and we win with the same method as Example 10 from the previous chapter.
\nline
\variation{3. c6 a5 4. c7 a4 5. c8=Q a3 6. Ka2+ Kb2 7. Qc3 Kb1 8. Kb3 Kc2 9. Ka4+!}
Not \variation{9. Kc4?! Kd3} where no progress has been made.
\nline
\variation{9... Kb3 10. Ka5+ Kb4 11. Qxa3#}
\nline
\textbf{\large{\underline{Pawn Structures}}}
\example
\diagram{8/2k3p1/2P4p/8/8/1p4P1/1K5P/8}{8/2k5/2P5/6pp/6PP/1p6/1K6/8}
\d Whoever is forced to move their king first, loses. White must take care to avoid a \textbf{mirror}. Only one move wins!
\begin{enumerate}
\item \variation{1. h3? g6!} creates a mirror: the pawn structures are identical when reflected. This is now lost, e.g. \variation{2. h4 h5 3. g4 hxg4 4. h5 gxh5} and white must move.
\item \variation{1. h4? g5!} also loses, e.g. \variation{2. h5 g4}, or \variation{2. g4 h5} \d creates a mirror, or \variation{2. g4 hxg5 3. g5 hxg5} also wins for black.
\end{enumerate}
The winning move is \variation{1. g4!}, where white can create a mirror next move.
\begin{enumerate}
\item If \variation{1... h5}, we have \variation{2. gxh5 g5 3. h3!}, or \variation{2... g6 3. h4!}
\item If \variation{1... g5}, \variation{2. h3!} creates a mirror.
\end{enumerate}
In a sense, a pawn mirror is the atomic equivalent of opposition. Once all the pawns are traded, the position simplifies to Example 1.

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\underline{\Huge{\textbf{Chapter 2: Queen Endgames}}}
% Intro
\nline
This chapter is all about how to win with a queen, including with connected kings. Being able to checkmate a disconnected king (i.e. disconnected from the opposing king) with a queen is assumed knowledge for this chapter.
\nline
% Example 1
\addtocounter{example}{1}
\noindent{\textbf{\underline{Example 1: Checkmate with 2 Queens}}}
\diagram{8/8/8/5Q2/2Q5/8/6k1/7K}{8/8/8/8/8/8/7Q/5QkK}
\d With an extra queen, we can win despite the connected kings by getting into the position shown in Diagram 3 with black to move.
\variation{1. Qh3 Kh2}
Our queen cannot get to the right square (h2), so we make a waiting move (meaning a move that makes minimal difference to the position)
\variation{2. Qh4! Kg1 3. Qh2}
One queen down, one to go.
\variation{3... Kg2 4. Qf1 Kg1} \d \variation{5. Qe1!}
Making another waiting move, forcing black to give way.
\variation{5... Kg2 6. Qeg1!} \d
\diagram{8/8/8/8/8/8/6kQ/6QK b}{8/8/8/2p5/2P3K1/6k1/2Q5/8}
The black king is forced to move away.
\variation{6... Kf3 7. Qgg2+}
Preventing the black king from reattaching to the white king.
\variation{7... Ke3 8. Qe4#}
\noindent{\textbf{\large{\underline{Opposing Pawns}}}}
\nline
% Example 2
\example
\d Despite only having a queen, the opposing pawns tip the balance to a win.
We must first get our queen two squares to the side of the opposing pawn (i.e. a5 or e5).
\variation{1. Qf5 Kf3 2. Qe5} \d
\diagram{8/8/8/2p1Q3/2P3K1/6k1/8/8 b}{8/8/8/2pKQ3/2P5/4k3/8/8 b}
Creating a "gate" between the queen and the pawn. Now we bring our king through the gate.
\variation{2... Kg3 3. Kf4 Kf3 4. Ke4 Ke3 5. Kd5+!} \d
Now we bring our king diagonally left behind the pawn.
\variation{5... Kd4 6. Kc6+ Kd5 7. Kb7+!} \d
\diagram{8/1K6/8/2pkQ3/2P5/8/8/8 b}{8/8/8/p7/P4K2/5kQ1/8/8}
This is the same situation we had in Chapter 1, Diagram 3, but with a queen instead of a rook.
\variation{7... Kc6 8. Qxc5#}
\nline
% Example 3
\example
\d With a rook pawn the process is very similar.
\variation{1. Qg5 Ke4 2. Qc5 Kf3 3. Ke4 Ke3 4. Kd4 Kd3 5. Kc4 Kc3 6. Kb5+ Kc4 7. Ka6+} \d
\diagram{8/8/K7/p1Q5/P1k5/8/8/8 b}{2k5/2K1Q3/8/8/3p4/3P4/8/8}
Similar to Example 2, but we can't keep going left! Luckily going straight up works just as well.
\variation{7... Kb5 8. Ka7+ Kb6 9. Qxa5#}
\nline
% Example 4
\example
\d \variation{1. Qb4 Kd7}
For white to win, the white king must go through the gate from white's side of the board.
Observe \variation{2. Kc6 Kc7 3. Kc5 Kc6 4. Kc4 Kc5 5. Kb3+} (\variation{5. Kc3+ Kc4 6. Kd2+} would work if it was legal! Unfortunately the black pawn controls c3) \variation{5... Kc4 6.Kc2 Kb3! 7. Kd2 Kc2!} and black isn't forced to go next to the pawn without the white king also adjacent.
\variation{2. Kd6 Ke6 3. Ke5 Kf5 4. Kf4 Kg5 5. Kf3 Kf4 6. Ke2 Kf3} \d
\diagram{8/8/8/8/1Q1p4/3P1k2/4K3/8}{8/2p5/2P5/6k1/4QK2/8/8/8}
Note how \variation{6... Ke3 7. Qxd4#} is mate immediately! Now thw white king is on the correct side of the pawns and is ready to go through the gate.
\variation{7. Kd2 Ke2 8. Kc2 Kd2 9. Kb3+ Kc3 10. Kc4 Kb3 11. Kd5+ Kc4 12. Ke6+ Kd5 13. Qxd4#}
\nline
% Example 5
\example
\d A similar strategy can be used for an unadvanced black pawn.
\variation{1. Qe7 Kf5 2. Ke5 Ke6 3. Kd6 Kd7}
Blocking our path, so we wait by stepping to the side.
\variation{4. Ke6! Kd6 5. Kd7 Ke6} \d
\diagram{8/2pKQ3/2P1k3/8/8/8/8/8}{2K5/2pkQ3/2P5/8/8/8/8/8}
\variation{6. Kc8+ Kd7} \d
Since white can't go to b9, white must go left and take an extra move to exit the blast radius.
\variation{7. Kb8+ Kc8 8. Ka8 Kb7 9. Qxc7#}
\nline
% Example 6
\example
\d With opposing knight pawns a different technique must be used.
\diagram{8/1p6/1P1kK3/8/8/5Q2/8/8}{8/1pKQ4/1Pk5/8/8/8/8/8}
\variation{1. Qf7 Kd7}
Blocking our queen from getting into position, so we use this move to stop any more of this blocking business.
\variation{2. Qe7!}
Forcing the black king to move away.
\variation{2... Kd6 3. Qd7 Ke5 4. Kd6 Kd5 5. Kc7+ Kc6} \d \variation{6. Kc8+!}
The easiest way to win. With no way to get out of the blast radius if we go left, we need to get into a different position.
\variation{6... Kc7 7. Kd8!} \d
\diagram{3K4/1pkQ4/1P6/8/8/8/8/8 b}{8/8/8/2p1Q3/2P1Kk2/8/8/8 b}
Putting black in zugzwang, as the d8 square is no longer available. Black must move their king to another square next to the pawn, allowing checkmate.
\variation{7... Kc8 8. Qxb7#}
\nline
% Example 7
\example
\d Here's a trick the defender can use, and how to break the defense.
\variation{1... Kf5!?}
Preparing to meet \variation{2. Kd5?!} with \variation{2... Ke6!} and no progress has been made. However there is an easy way to win.
\variation{2. Kd3+! Ke4} \d \variation{3. Kd4!}
This square was not able to be used before, as the black pawn defended this square. Now the black king is adjacent to d4, thus this square is now available for use.
\diagram{8/8/8/2p1Q3/2P1k3/3K4/8/8}{8/p7/P7/3kQ3/3K4/8/8/8}
\variation{3... Kd5}
Any other king move allows \variation{4. Kd5} when the standard technique can be used.
\variation{4. Kc3!}
Now any move allows \variation{5. Qxc5#}.
\nline
% Example 8
\example
\d With a rook pawn white can use a similar strategy to 2 queens.
\variation{1. Kc5 Kc6 2. Kb6 Kb7 3. Kc7 Kb8 4. Kb7 Ka8 5. Kb8 Kb7 6. Ka8 Kb8 7. Qe8 Kb7 8. Qb8} \d
\diagram{KQ6/pk6/P7/8/8/8/8/8 b}{8/8/8/8/8/3p1Q2/3P1K2/5k2}
Forcing the kings to disconnect. Notice how this is just like the position with 2 queens, but with the black pawn as the second queen.
\variation{8... Kc6 9. Qb7+ Kd6 10. Qc6+ Ke5 11. Qd5+ Kf6 12. Qe6+ Kg7 13. Qf7+ Kh6 14. Qg6#}
\nline
% Example 9
\example
\d White uses the usual technique and plays:
\variation{1. Ke3+}
However black sets a trap!
\variation{1... Ke1!?} \d \variation{2. Qg3+!}
\diagram{8/8/8/8/8/3pKQ2/3P4/4k3}{6Q1/6k1/5K2/8/8/3p4/8/8}
The simplest way to win. White needs to avoid \variation{2. Kd4??} which is stalemate!
\variation{2... Kf2 3. Kd4 Ke3 4. Kc5 Kd4 6. Qxd3#}
\textbf{\large{\underline{Queen vs Pawn}}}
\nline
% Example 10
\example
\d To win this, we must first block the pawn. However, many obvious moves fail.
\variation{1. Qa2?? d2!}
\variation{1. Qb3?? d2 2. Qd1 Kf7!} draws for reasons you will see in the next example.
The safest way to win is to block with the king.
\variation{1. Ke5+! Kf6 2. Kd4! Ke5}
Or \variation{2... d2} \d \variation{3. Kc3!} where \variation{3... d1=Q 4. Qe6+} is mate in 3, and \variation{3... Ke5} falls into \variation{4. Kb2 Kd4 5. Qd5+! Kc3 6. Qxd2#}. The move that holds on the longest is underpromoting to a knight with check, however this only delays the inevitable by 1 move.
\diagram{6Q1/8/5k2/8/3K4/8/3p4/8}{6Q1/8/8/8/8/2kp4/3K4/8}
\variation{3. Kc3 Kd4}
If black tries \variation{3... d2} then \variation{4. Kb2!} reaches the same position as above, but with a different move order.
\variation{4. Kd2! Kc3} \d
The pawn is now blockaded, but how do we win? First, get your queen behind the pawn.
\variation{5. Qd5 Kc2 6. Qd4}
If \variation{6... Kc3} or \variation{6... Kc1} then \variation{7. Ke3 Kd2 8. Kf4 Ke3 9. Qxd3#} wins easily enough (this also works with the king on c2).
\variation{6... Kd1!?} \d
\diagram{8/8/8/8/3Q4/3p4/3K4/3k4}{8/6k1/5K2/8/8/8/3p4/3Q4 b}
Now \variation{6. Ke3 Ke2 7. Kf4 Kf3} doesn't work. Black has opposition, so we make a waiting move.
\variation{8. Qc4!}
This move does nothing. And that's what we want. Now black has to choose a side.
\variation{8... Ke2 9. Kc3! Kd2 10. Kb4! Kc3 11. Qxd3#}
\nline
% Example 11
\example
\textbf{(Diagram 24)} Here an obvious move would be:
\variation{1. Qb3?}
Preparing to block the pawn. However black can draw!
\variation{1... d2! 2. Qd1} \d \variation{2... Kf7!}
Now black can always stay one square above the white king. There is no square where the white king is not next to the pawn and the square above is. If the queen moves, black promotes.
\variation{3. Ke5 Ke6 4. Kd4 Kd5 5. Kc3 Kc4 6. Kc2 Kc3 7. Kb1 Kb2 8. Kc1 Kc2 9. Kb2 Kb3 10. Kc3 Kc4 11. Kd4 Kd5 12. Kc5 Kc6 13. Kd6 Kd7 14. Kc7 Kc8 15. Kd8 Kd7! 16. Ke8 Ke7! 17. Kf8 Kf7! 18. Ke7 Ke8!}
If white tries to shake the black king by going to the 8th rank, black can go directly below, where once white leaves the back rank black again goes above. The game is a draw.
\nline
% Example 12
\example
\diagram{4Q3/8/4p3/8/8/8/8/Kk6}{8/8/8/4p3/4Q3/3kK3/8/8}
\d With the pawn further away from promotion the winning technique is much simpler.
\variation{1. Qc6 e5 2. Qe4}
The easiest way to win. We don't need to immediately block with the king here, as the pawn doesn't immediately promote.
\variation{2... Ka2 3. Kb2 Kb3 4. Kc3 Kc4 5. Kd3 Kc3 6. Ke3 Kd3} \d \variation{7. Qd5 Kd2 8. Ke4+ Ke3}
Now our king blockades the pawn, and the same process can be applied as last example.
\variation{9. Qe6 Kf4 10. Kd5 Ke4 11. Ke6 Kd5 12. Qxe5#}
\nline
% Example 13
\example
\diagram{8/1Q6/8/8/7p/4kK2/8/8}{8/8/8/8/8/5Q1p/6kK/8}
\d Here we can immediately block with the king.
\variation{1. Kg2 h3+ 2. Kh2 Kf2}
Now we make the gate like we did with opposing pawns.
\variation{3. Qf3+ Kg2} \d
We would like the king to be either below or above the king. \variation{3... Kg1} transposes into the main line a move earlier, and if \variation{3... Kg3} then \variation{4. Kh1+ Kg2 5. Qxh3#} is mate in 2.
\variation{4. Qe3!}
Making a waiting move. Black has to move either above or below the white king, where white will extract their king in the opposite direction.
\variation{4... Kh1 5. Kg3 Kg2}
Or \variation{5... h2 6. Kg4 Kg2 7. Kg5!} and the kings are disconnected.
\variation{6. Kg4 Kg3}
Again, \variation{6... h2 7. Kg5!}
\variation{7. Kh5+}
Not \variation{7. Kg5+?? Kf4! 8. Kh5+ Kg5! 9. Qg1 h2!} when all of a sudden it's a draw!
\variation{7... Kg4 8. Qxh3#}
\nline
% Example 14
\example
\diagram{6Q1/8/8/8/8/2k4p/8/3K4}{8/8/8/8/8/8/5Q1p/6kK}
\d Here we need to block the pawn with our king, but \variation{1. Qa8? h2 2. Qh1 Kd2} is a dead draw (see Example 11). Plus we don't have time to get the king in front. The only way to block with the king is to block with the queen on h2, giving the king an extra square.
\variation{1. Qg3+! Kd2 2. Qh2!}
Now we have all the time in the world to get our king to h1 and block the pawn with our king.
\variation{2... Ke1 3. Ke2 Kf1 4. Kf2 Kg1 5. Kg2 Kf2 6. Kh1+ Kg1 7. Qf2 h2} \d
Now the pawn is blocked with our king. What now? We use the same idea as Example 8!
\variation{8. Qf1 Kg2 9. Qg1 Kf3 10. Qg2+}
and wins.
\nline
% Example 15
\example
\diagram{3Q4/6p1/8/8/Kk6/8/8/8}{8/4QKp1/4k3/8/8/8/8/8}
\d Here we force the pawn to push using the same method as with opposing pawns, where black either has to get mated the same way or push the pawn, where the usual technique can be applied.
\variation{1. Qe7}
Setting up the gate.
\variation{1... Ka5 2. Kb4 Kb5 3. Kc4 Kc5 4. Kd4 Kd5 5. Ke5 Ke6 6. Kf5 Ke5 7. Kg6+ Kf6 8. Kf7 Ke6} \d \variation{9. Kf8+! Kf7 10. Ke8!}
Now any king move allows \variation{11. Qxg7#}, so the pawn is forced to push.
\variation{10... g5 11. Qe3 g4 12. Qg3 Ke7 13. Kd7 Kd6 14. Ke6 Ke5 15. Kd5 Kd4 16. Ke4 Ke3 17. Kf3 Kf2 18. Kg2 Kg1} \d
Now we use the normal strategy, however when we extract our king right we have to go up due to the edge of the board.
\diagram{8/8/8/8/6p1/6Q1/6K1/6k1}{8/8/8/8/8/2pQ4/3pKk1/8}
\variation{19. Qf4 g3 20. Qg4 Kf2 21. Kh3 Kg2 22. Kh4 Kh3 23. Kh5+ Kh4 24. Qxg3#}
\nline
% Example 16
\example
\d This position is completely drawn.
\variation{1. Kd1 c2+! 2. Ke2 c1=Q 3. Kf3 Qb2 4. Qxd2}
With a simple draw.
\nline
% Example 17
\example
\diagram{8/8/5p2/2p1pP2/2P1P3/8/1Q2k3/4K3}{8/8/5p2/QKp1pP2/1kP1P3/8/8/8}
\d With multiple opposing pawns the winning strategy is the same as with just 1 set of opposing pawns.
\variation{1. Qa3 Kd2 2. Qa5 Ke2 3. Kd2 Kd3 4. Kc3 Kc2 5. Kb3 Kb2 6. Ka4 Ka3 7. Kb5 Kb4} \d \variation{8. Kc6+ Kb5 9. Kd7+ Kc6 10. Qc5#}
\nline
% Example 18
\example
\diagram{8/8/8/p1p1p1p1/P1P1P1P1/8/K2Q4/1k6 w - - 0 1}{8/8/8/p1p1p1p1/PpPpPpPp/1P1P1P1P/8/KkQ5}
\d While is it possible to win without losing the queen, the alternative (albeit longer) method is much simpler (and less risky!).
\variation{1. Qd5 Kb2 2. Qxc5}
With a simple win.
\nline
% Example 19
\example
\textbf{(Diagram 41)} The game can still be won without a queen sacrifice, and the solution is quite elegant: use the black king to allow us to pass through to the other side, where the win is trivial.
\nline
\variation{1. Qc2! Ka1 2. Kb2 Kb1 3. Kc3+ Kb2 4. Kd3+! Kc3 5. Kd4!}
Gates don't always have to be with the opposing pawn! This gate setup is useful in a variety of ways to force the enemy king to a certain square.
\nline
\variation{5... Kd3 6. Kd5+ Kd4}
We have many ways to win here. One way is to utilise the fact the opposing king must move away next move with \variation{7. Qb2 Ke3 8. Qd4+!}.
\nline
\variation{7. Ke6+ Kd5 8. Qf2 Kd6 9. Qxc5#}
But this way is much more elegant (and faster!).
\nline
% Example 20
\example
\d Here we sacrifice the queen for a pawn break.
\variation{1. Qe1 Ka2 2. Qxb4! Kb1 3. b4! axb4 4. a5 Ka2 5. a6 Kb1 6. a7 Ka2 7. a8=Q Kb1 8. Qa5 Ka2 9. Kb2 Kb3 10. Ka3 Ka4 11. Kb4 Ka4 12. Kb5 Kb4 13. Kc6+ Kb5 14. Kd7+ Kc6 15. Qxc6#}
\nline
% Example 21
\example
\diagram{8/8/8/5Q2/pp6/1P6/P5Kk/8}{8/8/8/8/P7/8/1p4Kk/1Q6}
\d If all the pawns are traded off, this position becomes a dead draw. However this is winning!
\variation{1. bxa4! b3 2. a4! b2 3. Qb1!} \d
Without the a-pawn this would be drawn (Example 11), but as white has an extra pawn, they win.
\variation{3... Kg3 4. a5 Kh2 5. a6 Kg3 6. a7 Kh2 7. a8=Q Kg3}
How do we win though? With a horizontal gate!
\variation{8. Qb7 Kh2 9. Qb4!} \d
\diagram{8/8/8/8/1Q6/8/1p4Kk/1Q6 b}{8/8/8/8/1Qk5/1K6/1p6/1Q6}
Now we bring our king through the gate.
\variation{9... Kg3 10. Kf3 Kf4 11. Ke3 Kf3 12. Kd3 Ke3 13. Kc3 Kd3 14. Kb3 Kc4} \d \variation{15. Ka3+ Kb3 16. Ka4 Ka3 17. Q1xb2#}

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\begin{center}\underline{\Huge{\textbf{Chapter 4: Rook Endgames}}}\end{center}
\setcounter{diagramnum}{0}
\setcounter{diagramidx}{0}
\setcounter{example}{0}
Rook endgames share some similarities with queen endgames, but with one key difference: A rook and king cannot checkmate a lone king.
\nline
The following example showcases the key differences.
\nline
\example
\diagram{8/8/4p3/2k1P3/1K6/8/7R/8}{8/8/4pKR1/4P1k1/8/8/8/8}
\d Like normal, we first make a gate.
\nline
\variation{1. Rg2 Kb5 2. Rg6 Kc4 3. Kc3 Kd3 4. Kd4 Ke4 5. Ke3 Kf4 6. Kf3 Ke4 7. Kg4 Kf4 8. Kg5 Kg4 9. Kf6+ Kg5} \d
All well and good for now, but...
\nline
\variation{10. Ke7+ Kf4!}
\nline
Utilising the fact that the rook cannot checkmate on its own, black avoids the swift loss after \variation{10... Kf6?! 11. Kd8+!} when \variation{12. Rxd6#} is unstoppable. So while the same technique as with a queen could be applied to separate the kings, this alone isn't enough to checkmate.
\nline
However, white is still winning! As our pawn is on the fifth rank, we can sacrifice the rook when the kings are on opposite corners of the board. This allows us to promote and stop the kings from connecting in time.
\nline
But which corner should we go to? Consider the following line:
\nline
\variation{11. Rg4+ Kf3 12. Kf8}
We cannot force the king closer to the corner this move, so we use our move to get to the opposite corner.
\nline
\variation{12... Ke3 13. Rf4 Ke2 14. Rf3 Ke1 15. Rf2 Kd1 16. Re2 Kc1 17. Rd2 Kb1 18. Rc2 Ka1 19. Kg8 Kb1 20. Kh8 Ka1} \d
\diagram{7K/8/4p3/4P3/8/8/2R5/k7}{7K/5Qk1/8/8/8/8/8/8}
And now trying \variation{21. Rc6 Kb2! 22. Rxe6 Kc3 23. e6 Kd4 24. e7 Ke5 25. e8=Q+ Kf6 26. Qf7+ Kg7} \d is a draw.
\nline
So what went wrong? Is it just a draw? Not quite. Notice how if our rook was on b3 instead of c2, then \variation{21. Rb6 Ka2 22. Rxe6 Kb3 23. e6 Kc4 24. e7 Kd5 25. e8=Q} is easily winning. Black wasn't able to approach before we took the pawn.
\nline
The easiest way to win is to force their king to a8 (or h8), where we can take the e6 pawn from either angle.
\nline
From \db{2} we can instead play
\nline
\variation{11. Ke8}
Our king is in a difficult spot, but we need to move it back to avoid the kings reconnecting.
\nline
\variation{11... Ke4 12. Rg4+ Kd5 13. Rd4+ Kc6 14. Kf8!}
Ensuring the kings don't reconnect.
\nline
\variation{14... Kc7 15. Rd6 Kc8 16. Rd7 Kb8 17. Rc7 Ka8 18. Kg7 Kb8 19. Kh6 Ka8 20. Kh5 Kb8 21. Kh4 Ka8 22. Kh3 Kb8 23. Kh2 Ka8 24. Kh1 Kb8} \d
\diagram{1k6/2R5/4p3/4P3/8/8/8/7K}{4Q3/8/8/4k3/8/8/8/7K}
Unlike before, we can now attack the pawn without the king approaching.
\nline
\textbf{Note: }Remember kings can move diagonally! When ``distance" is defined as the least possible moves to get from one king to the other, a horizontal movement along the 8th rank doesn't decrease this distance.
\nline
\variation{25. Re7 Kc8 26. Rxe6! Kd7 27. e6+ Kd6 28. e7 Ke5 29. e8=Q+} \d \variation{29... Kf4 30. Qe3+!} and wins.
\cat{Opposing Pawns}
\d shows the squares that the white pawn can be on such that white is winning in a King and Rook vs King with Opposing Pawns endgame.
\diagram{, pgfstyle = color, color = red, opacity = 0.5, markfield={d5}}{}