1

Are all KQvK positions winnable if the position isn't in itself a stalemate and Black cannot capture on the current move?

  • 2
    Yes; informally, when White gets the move they can always move the queen away far enough that Black has at least one available King move, and then White can run the usual mating algorithm. – Steven Stadnicki Dec 19 '16 at 23:11
3

Yes, all KQvK positions are won under these conditions (no stalemate, no capture). The same holds for KRvK.

The only possibilities for such basic endgames not to be won under your conditions would be:

  1. a piece has too few square available and can be captured by the black king (not immediately but in the next move)
  2. white on the move cannot avoid stalemate (or material loss)

An example for the first case (black to move):

[FEN "7N/8/8/4k3/8/8/6K1/7B b - - 0 1"]

the second case (white to move) looks like this (to avoid stalemate, white's king has to go to the d file when after Kb7, black wins the bishop or knight):

[FEN "kB6/2K5/N7/8/8/8/8/8 w - - 0 1"]

However with the KQvK and KRvK, the queen/rook always have enough space to avoid these problems.

  • Are your positions in EPD format? If so, don't you mean to have w for white-to-move for your second case? Would you please convert them to replayer format? – CodeBricks Dec 20 '16 at 1:14
1

The simple answer to your question is yes. In fact the same is true of a king and rook versus king, the most basic mating material. That's why having an extra pawn in an ending is so valuable, since even if all the other pawns were swapped off, the lone remaining pawn could potentially be promoted to a queen (or even a rook) for a subsequent checkmate.

0

Here are the replayers for user1583209's answer's positions:

[Event "KBNvK Position 1"]
[Site "https://chess.stackexchange.com/a/16130/12032"]
[Date "2016.12.19"]
[Round "?"]
[White "White"]
[Black "Black"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "7N/8/8/4k3/8/8/6K1/7B b - - 0 1"]
[StartFlipped "0"]
[PlyCount "5"]
[SourceDate "2016.12.19"]

1... Kf6 2. Kg3 Kg7 3. Be4 (3. Ng6 Kxg6) 3... Kxh8 1/2-1/2

and

[Event "KBNvK Position 2"]
[Site "https://chess.stackexchange.com/a/16130/12032"]
[Date "2016.12.19"]
[Round "?"]
[White "White"]
[Black "Black"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "kB6/2K5/N7/8/8/8/8/8 w - - 0 1"]
[PlyCount "4"]
[SourceDate "2016.12.19"]

1. Kd7 (1. Kc6) 1... Kb7 2. Nc5+ (2. Bd6 Kxa6) 2... Kxb8 1/2-1/2

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