Interesting Endgame

In this position, I first check the material. I have a clear advantage: a queen against a rook and one pawn. The function of the pieces also matters.

The queen has a very good function, limiting the white king. The white rook, however, is a strong defensive piece. While it doesn’t seem to have options for strong counterplay, it does possess significant defensive capabilities. It’s positioned next to the white king, making it difficult to separate them, which could make this position much harder to win.

Plan Making:

• Analysis of Winning Possibilities:

There are two paths that could lead to victory:

• Try to win the rook by first separating it from the king and then forking the king and rook with the queen.
• Try to exchange the queen for the rook, ensuring that the rook pawn can safely promote to a new queen.

It’s best to analyze the position using concepts and thoughts first, rather than pure calculation. Humans can more easily follow ideas and concepts than raw calculations. Once a conceptual plan is decided, it should then be supported by calculation.

First Path (Winning the Rook):

• I’m certain that I need my king nearby to pressure the white pieces. I also want to make the opponent's position as passive as possible, limiting the number of squares they can use, which could force the separation of the king and rook.

Second Path (Exchanging the Queen for the Rook):

• It doesn’t seem immediately possible to achieve this exchange. Even if I manage to create opposition (with my king in front of the pawn), it doesn’t guarantee a win because it’s a rook pawn, which typically results in a draw. Having a rook pawn instead of any other type of pawn makes this exchange much harder to execute successfully.
• The only square where it makes sense to exchange the queen for the rook is b3. After the exchange, where the rook takes the queen and the pawn takes the rook, I would either control the promotion square or have the opposition.

For both plans, I need to bring my king closer. The candidate move is 1. ... Kc4. I then assess the opponent’s counterplay opportunities.

Counterplay Opportunities:

• The opponent might try to apply a skewer or otherwise exchange their rook for my queen at a moment that would assure a draw.
• The opponent might try to achieve stalemate. Essentially, if I place the opponent’s king in a position where it has no squares to move to, the opponent could continually check me with the rook, forcing me to capture the rook and ending the game in stalemate.

So, my moves must always be made with two requirements in mind:

• The opponent must not be able to skewer or exchange the rook for the queen at an unfortunate moment.
• The opponent’s king must always have a square to move to.

After my candidate move, 1. ... Kc4, my opponent might play surprising moves like 2. Rc2, Rb3, or Rb4, but none of these lead to stalemate, so I can safely capture the rook. Hence, this is my first move:

1. ... Kc4

2. Rb1

The threat is 3. Rc1, which would result in a stalemate. If 3. ... Qxc1, it would be a stalemate since the white king would have no valid moves, and if I move my king, then 4. Rxc1 Kxc1 results in a draw.

So, I must ensure that the white king always has valid squares to move to after my moves. I would also like my king to make the opponent's position more passive. Ideally, I want my king on c3 or c2, where I can threaten mate in one.

At the moment, I can’t achieve this since my queen is blocking that path. Therefore, it’s natural to reposition the queen to free up space and reduce the chances of stalemate. Thus:

2. ... Qe5.

3. Rc1+ Kd3

4. Ka3

This move attacks our pawn, so I play a move that defends the pawn and threatens mate in one:

4. ... Qb5

5. Ka2

I continue to pressure the white king, forcing the separation of the king and rook.

5. ... Qb3+

6. Ka1

Now, I must be careful of stalemate opportunities since the white king is forced into the corner of the board with no valid moves.

First, I consider 6. ... a3, threatening mate in one. But I realize that after 7. Rc2, I cannot capture the rook with either my king or queen without resulting in stalemate. It’s unclear how to proceed, so I form a new plan.

I want to ensure that the white king has some space to move. I can achieve this by playing Qb4, but I want to do it with tempo, giving my opponent no chances to maneuver. So, first, I give a check:

6. ... Qa3+

7. Kb1 Qb4+

8. Ka1

Now, we have the same position as before my 6th move, but with the queen on b4. Finally, I’m ready to safely play a3:

8. ... a3

9. Rb1

At this point, with a pawn ready on a3, I can continuously threaten mate on b2. The only way for white to prevent this is to keep their rook on the b-file. Additionally, if I limit the valid moves of the white king, the opponent will be forced to move the rook. If I can ensure that my king is safe from stalemate-forcing checks on c2, the rook will eventually have to leave the king due to a lack of moves.

Currently, my queen is attacked, so I must move it to a square that won’t force a stalemate and that will allow me to check the white king when needed. The move is:

9. ... Qd4+

10. Ka2 Kc2

Both goals are achieved. The white king is restricted (if it captures the pawn, I capture the rook), so a rook move for white is necessary while still preventing mate on b2. The white rook must remain on the b-file.

11. Rb7 Qd5+

Check and fork, effectively winning the rook and the game.

If white plays 11. Rb8, for example, I continue checking until a fork is achieved (this is the benefit of my king being on c2—white cannot block with the rook), so 11. ... Qd5+, 12. Ka1 Qe5+ (fork), or 12. Kxa3 Qa5#, but also 12. Kxa3 Qd6+ (fork).