4pc Antichess - Endgames - 1v1 Basics

This is my second post on 4pc-antichess (first post here), and this time I will focus on endgames.

I will cover only the very basic 2 pieces endgame, when the last two players have a piece each. While some games end up with a clear loser, it is very common that two players finish with very few pieces, and more common in these situations is for the game to reduce to a state of a single piece against a single piece. In order to keep this post short enough, more general endgame discussion, such as setting up capture-chains correctly, is reserved for future posts.

The structure of the post will consist of listing all possible combination of 2 pieces. Before listing the combinations, please note these important things:

1. These endgame techniques can and should be applies also when there are more than two players on the board. Such example is this game with 3 players, where the blue king is far enough not to be relevant for the knight and bishop endgame.

2. I assume that the pieces are far enough from each other, otherwise the player whose turn is can trivially move the piece to be captured.

3. If the endgame is not too chaotic in pieces, you should usually aim for a simplification that leads to a winning simple endgame. This would mean, for example, to capture your opponent pieces on purpose to handicap them. A concrete example: in a king vs. king and knight situation, actively working towards capturing the king, to end up in a king vs. knight winning endgame.

Finally, below is the list of endgame combinations with examples for the most common types. The example may present the technique while not necessarily in a 1v1 endgame, if I did not recall a clean example. See also the "general theory" post regarding the pieces’ general strengths and weaknesses.

Rook vs. X:

1. Rook vs. Rook/Bishop/Queen (example of rooks and a bishop, ignore the pawns): both pieces are long ranged, so the first piece moves in sight of the other, and gets captured. Nothing interesting here, and it rarely happens in a proper-endgame. If it does happen on a board with more pieces, it is a good habit to move the rook against a queen such that the queen attacks it diagonally. This way, you should never worry that you will have to capture the queen if the opponent can waste a tempo on another capture (for bishop this is trivial, and for rook it is impossible not to have both threatening each other).

2. Rook vs. Knight (example: ignore B/Y, assume the pawn-promotion was a rook-move): rook wins. The quickest way to do it is to move the rook to attack the knight. Then the knight moves, and you move the rook to the space previously occupied by the knight. A slower method would be to guard a row in distance 3 from the knight, so it is forced to move the other way, and slowly restricting it to a side of the board. This method should be applied if there are other pieces except for the knight, because then it doesn’t have to move and directly attacking it will result in actually capturing it.

3. Rook vs. King (example): rook wins. The technique is to keep opposition to the king, 2 moves away diagonally. This way, the king is forced to the corner of the board and eventually loses. If the king moves horizontally/vertically, the rook can follow. If it moves diagonally, the rook moves once toward the edge into which you wish to push the king, and then if the king moves into the opposition position, the moves rook 4 squares to "overshoot" the king into another opposition square on the other side of the king.

4. Rook vs. Pawn (example): rook wins. Move the rook to a file near the pawn, and then move to where it can capture the rook. Another way is to wait on a rank until the pawn gets to the previous rank, and then move to be captured. It is usually safest to use the file option, because if there are more pieces on the board, you do not want to lose a tempo by a forced capture just when the pawn can step into the rook’s file. Better safe than sorry.

Bishop vs. X:

1. Bishop vs. Rook: first to move wins, see “Rook vs. Bishop.”

2. Bishop vs. Queen: first to move wins, similar to “Rook vs. Queen.”, both are ranged, move into the queen’s line of sight, preferably horizontally/vertically, so the bishop doesn't threaten the queen (in case other pieces still remain).

3. Bishop vs. Bishop: if both move on the same squares, the first to move to line of sight of the other wins, otherwise it is a dead draw (example). This type of endgame usually happens due to pawn promotion (see the pawn section below), since the original bishops are usually captured in the middle-game.

4. Bishop vs. Knight (example): bishop wins. move the bishop to threaten the knight, when it moves, step into its original square and win. Note that if there are other pieces, a less direct approach should be taken. In the safest (slowest) way, in case the knight has another piece with it, since knights swaps the tile-color every move, once it is on the tiles of the color of the bishop, you can approach. Then when it moves to the other color, move to a square which the knight can capture the bishop.

5. Bishop vs. King (example): draw. The bishop should keep opposition to the king, at least 5 steps away from it. Stay in the middle of the board, so if the king moves toward/away from the bishop, you can move such that opposition is kept. From the king’s perspective, it is possible to move around without getting close to any diagonal of the bishop, and the bishop cannot force it to yield ground.

6. Bishop vs. Pawn (example): usually, the bishop wins. Just move to a diagonal which the pawn will threaten at some point after moving forward, and then move the bishop to be captured. Note that you should threaten this way correctly, such that the pawn’s path is not threatened by the bishop. However, it might be that the bishop can’t do it before the pawn promotes. In this case, if the promotion is on opposite color: promoting to an opposite-color bishop is a draw. This is the best the pawn can have, since any other promotion would lose since the bishop has time to move to a diagonal such that it can move next to the promoted piece right after the promotion. If the promotion square is the same color as the bishop’s, this is a win for the bishop since it can force a capture by any promoted piece.

King vs. X:

1. King vs. Rook: loses, see “Rook vs. King”.

2. King vs. Bishop: draw, see “Bishop vs. King”.

3. King vs. Queen: I don’t recall ever seeing such a clean endgame, usually there are more pieces on the board, which the queen is forced to take, and the king has free tempi to move into its line of sight and win. As a pure endgame, the queen wins by keeping opposition to the king at a distance of 2-knight-moves. The king must go back, and the queen pursues, until the king end in the end of the board and loses. But again, usually a queen in the endgame is occupied with captures, so it is better not to have a queen in the endgame (see a bad example here, with even more pieces).

4. King vs. King (example): a draw. No king would approach the other, so they can keep opposition with 2 squares between them. That being said, with 3 players involved, two may cooperate to push the third into the corner and then capturing both of them like this example. If this happens to you, you should try to capture one opponent before the other gets too close, if that is possible, in order to end in a shared 3rd-4th place rather than 4th.

5. King vs. Knight (example): king wins. The king keeps opposition to the knight, aiming for distance 5. At that position, the knight can move only backwards. If the knight moves 2-back-1-side, then the king can keep opposition. If the knight moves 1-back-2-side, the king follows. It is hard to explain in words how to chase the knight, but in general step toward it, while not allowing it to move near the king. Sometimes the opposition would become 3 diagonal moves, which is also fine. If that is the king’s move, move diagonally to triangulate. The best way to understand the technique is the example in the link. It may seem like the knight is faster than the king, but the board is too small for it to go around in circles (which would be possible if the board was larger).

6. King vs. Pawn (example): usually, the king wins. If the king is close enough to reach the pawn before promotion, it wins. One way to assure winning with the king is to approach a pawn from the side, so it captures the king. Another way, sometimes happens when chasing a pawn, is the keep close until it promotes, and then if the king is close, no matter what piece it is – it can move to be captured. When the king is too far, for example behind the pawn or on the other side of the board, the pawn can win if it is able to promote to a rook. Because of that, the king should get as fast as possible to a row/file where the pawn would promote. If it manages to get there in time (at the latest by the move following the promotion), then the pawn cannot promote to a rook, and will likely promote to a king or a bishop, which is a draw (see the relevant cases).

Knight vs. X:

1. Knight vs. Rook: loses, see “Rook vs. Knight”.

2. Knight vs. Bishop: loses, see “Bishop vs. Knight”.

3. Knight vs. King: loses, see “King vs. Knight”.

4. Knight vs. Queen: loses. I have never seen this endgame, but theoretically the queen can function either like a rook or a bishop: it moves to threaten the knight from afar, the knight moves away not into another line of sight of the queen, and then the queen moves to where it was, and wins.

5. Knight vs. Knight (example): consider the state when both are on the same color of tile, then the first to move from this position wins. This is because the first player can move to be captured by the second player, but not the other way around. The way to force it is to move the first knight as close as possible to the other knight, by sticking next to it. The second knight can move away from the first knight into a 2-diagonal distance, but eventually it ends on the end of the board, and then it must move to where it can capture the first knight (see the example for concrete details).

6. Knight vs. Pawn (example1, example2): depends, but in favor of the pawn. If the pawn and knight are on the same color of tiles, and it is the knight’s move, then the pawn wins. This is because both of them change color each move, and the knight can never make itself be captured by the pawn. Eventually, the pawn promotes to a bishop, and at that position the knight must leave the color of the bishop, so the bishop can’t capture it, and we get into a winning bishop-vs-knight endgame. In example1: ignore R/B and focus on the situation of Y/G.
On the other hand, if the knight and pawn are on the same color and it is the pawn’s turn, then the knight can be captured, assuming it is close enough to reach before the pawn promotes safely. Safely means that the knight can’t get near the pawn before the promotion. If the pawn can promote, choosing a knight guarantees a win since the two knights are on opposite color such that it is the un-promoted knight’s turn. Note that if your pawn is at its starting square, you can assure the colors are correct (first scenario). If not, then you should hope the colors are correct, or that the opponent’s knight is far enough from your pawn’s path. In example2 I miscounted the tempi, and lost because of that (moving once with the k-pawn was a win, but I moved two squares).

Pawn vs. X:

1. Pawn vs. Queen: rare endgame. Unless the queen is forced to capture other pieces, it can apply either the rook’s method or the bishop’s method to win.

2. For any other piece, see “X vs. Pawn”.

Queen vs. X:

1. See “X vs. Queen”.

In conclusion, as a general rule of thumb pawns and knights are the weakest to end up with, bishops are rare in an endgame, rooks and queens are unlikely to end up in a simple endgame because usually they will be forced into a capture-sequence, and the most "popular" endgame piece would be the king, providing freedom of movement and relative safety against capture-sequences due to its short range (a plus in this case). However, pawns promotions to a rook are preferable if they can be done safely, and sometimes a bishop promotion is the way to win or draw rather than lose.

That is all for this post.