15

This is a question concerning online blitz chess.

I'm sure we all have experienced having a completely winning position, but only having a few seconds left on the clock. After one such game I started to wonder: In the ending KQ vs K, is it possible to premove a sequence of moves such that no matter what moves the opponent makes, they will end up check mate?

  • 2
    Do you want to premove the entire sequence of moves leading to mate, or is it just that each time you already need to decide your next move before the opponent moves? The latter should be an easier task, but (as far as my mental calculations reach on a late Friday night) not possible. – Glorfindel Aug 26 '16 at 21:48
  • @Glorfindel Both are interesting, but I really wanted to know if it is theoretically possible to premove the whole sequence. It could be too much to ask for. – Dag Oskar Madsen Aug 26 '16 at 21:54
  • Here I am disregarding how actual servers handle sequences of premoves. I just want to know if a sequence of premoves leading to mate is theoretically possible. – Dag Oskar Madsen Aug 26 '16 at 22:41
  • 6
    Related: you can win at Kriegspiel even with K+R vs. K from most initial positions (not sure if within 50 moves). Not the same problem, though, because you're told about check and can retract moves that prove illegal. See Jim Boyce, A Kriegspiel Endgame, pages 28-36 in The Mathematical Gardner (1981) link.springer.com/chapter/10.1007%2F978-1-4684-6686-7_4#page-1) – Noam D. Elkies Aug 27 '16 at 21:27
9

If the enemy king is cut off at the edge of the board, it is possible to mate him using only premoves. For example:


[StartPly "1"]
[FEN "2k5/Q7/8/8/8/8/8/K7 w - - 0 1"]

      1.Ka2 Kd8 2.Ka3 Kc8 3.Ka4 Kd8 4.Ka5 Kc8 5.Ka6 Kd8 6.Qb7 Ke8 7.Kb6 Kd8 8.Qc7+ Ke8 9.Kc6 Kf8 10.Qd7 Kg8 11.Kd6 Kf8 12.Qe7+ Kg8 13.Ke6 Kh8 14.Kf6 (14.Qf7??=) Kg8 15.Qg7#

Just make sure you don't stalemate your opponent with 14.Qf7. Note that there is of course a much quicker path to mate, the sequence of moves just shows it is possible to exclusively use premoves.

If the enemy king is not cut off at the edge of the board, I doubt if it is possible to premove the entire sequence. In order to mate him, the quadrant in which the enemy king is located has to be narrowed. And that is the problem: whenever the queen is moved, the king might escape the quadrant.

8

I think with the black king on f7 it's also possible. For example, in the following position:


[FEN "8/5k2/3Q4/8/8/3K4/8/8 w - - 0 1"]

this sequence of moves for white checkmates always: Ke4 Kf5 (go to f5 in two moves) Qd7 Kf6 Qh3 Qc8 Qa8 Qh1#

I made this gif to explain why:

enter image description here

In green it is shown where the black king could be (to consider all possibilities). Note that it is important that White's king can reach f5 in two moves (exactly two) because, thanks to the parity, after two moves it is impossible for Black to be in e8 and therefore, Qd7 is safe. Note also that even though 4 is an even number, in 4 moves Black's king could make it, thanks to triangulation.

8

In some special cases you can "premove" to a forced mate even against a King in the center:

8/8/8/8/3k4/7Q/3K4/8 w - - 0 0

1. Qe6! Kc5 2. Kc3! Kb5 3. Qd6! Ka5 4. Qb4+ Ka6 5. Kc4 Ka7 6. Qb5 Ka8
7. Kc5 Ka7 8.Kc6 Ka8 9. Qb7#

(Black's only option is 3...Ka4 when 4 Qb4 is already mate. The alternative 1 Qf5!? Kc4 2 Qe5 Kb4(b3) 3 Qd5(+) or 3 Qc3+ might not be quite good enough.)

5

Just to show it's possible, here is a position, without the opponent king trapped at the edge of the board, where you can premove the entire sequence.

[FEN "8/6k1/4Q3/8/8/8/8/K7 w - - 0 1"]

Move the king to g5, play Qd7(+), and then continue as in Maxwell86's answer.

  • 1
    Very nice example! Would there also be a sequence for the black king on f7? – Maxwell86 Aug 27 '16 at 15:54
  • The black king does not seem to have any moves that do not leave him at the edge where the queen can easily trap him at that edge. – hkBst Sep 9 '16 at 12:37
  • @hkBst Yes, but you don't know in advance which edge the king will move to. – Dag Oskar Madsen Sep 9 '16 at 13:52
  • That is true, but you can move your own king to force one of the edges. – hkBst Sep 9 '16 at 14:09

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