7

A fun thing to do is to try to achieve specific "achievements" (like these) in real games.

One such achievement is to checkmate with a king move. As the king itself obviously can't deliver checks, it would have to be through a discovery (or castling, but one seldom has castling rights preserved in the endgame).

When can this be forced? It seems to require more fire power than a regular checkmate

A queen and a heavy piece is enough to force this through the standard knight-opposition manoeuvre to drive the king to a corner and then setting up the checkmate

[title "Queen + heavy piece"]
[fen "8/1K6/5k2/8/8/8/8/R2Q4 w - - 0 1"]

1. Qd5 Kg7 2.Qe6 Kh8 3.Qe7 Kg8 4.Kb8 Kh8 5.Ra8 Kg8 6.Kb7#

Queen and bishop doesn't seem to be enough, at least with the same setup. While the king can cover the g8 prison square while simultaneously uncovering the bishop, the enemy king unfortunately escapes down the h file:

[title "Queen + bishop"]
[fen "7k/4Q2/5K2/8/8/8/8/B7 w - - 0 1"]

1. Kf7+ Kh7

Queen + bishop + light piece to cover h7 would be enough.

Some basic checkmates like KQvK, KRvK and KBNvK are obviously not possible since their required setups have no room for a discovery

What other material combinations can force a king move checkmate?

1
  • 2
    In your KQB vs. K position: try 1. Qd7 Kg8 2. Qf7+ Kh8 3. Kg6#. Sep 15, 2022 at 19:10

2 Answers 2

4

I also looked a bit into "king discovered mates that can be forced from any nonspecial position", and the following material suffices:

  • RR (obvious)
  • RXY where X and Y are light officers (Ka5 Ra1 Nd7 Nd8, Ka8 is easily forced, Kb6#; replacing a knight with a bishop is analogous)
  • XYZ also suffices except for 3 N (Kc6 Bh1 Nd7 Nb4, Ka8 is easily forced, Kb6#; Nd7 may be replaced with Bh2)

On the other hand...

  • QX does not force (neither B or N can cover b8 and c8 together), thus RX neither

Since P can promote and black material must be captured before mate, this should cover all cases (e.g. QXY can be "reduced" to XYZ).

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  • 2
    QB does work with a B-battery, as Ravi Fernando noted in a comment on the original question. (This can be done near a corner of either color; e.g. Ke6,Qg5,Bb3 / Kh7: 1 Ba2 Kh8 2 Qh6+ Kg8 3 K-any #) Sep 15, 2022 at 20:34
  • Note that BBN even works in the unlikely case of B's of the same color: Kc6 Bc4 Be6 Na6 / Ka7 is "easily forced", and then 1 Bed5 Ka8 2 Kb6#. Sep 15, 2022 at 20:38
  • @NoamD.Elkies: Oh, a B mate. Clever. Overlooked that one. Sep 15, 2022 at 21:04
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As you noted, no "K + single piece" can achieve this. Here is an overview to the "K + two x" cases, of which only three cases don't work. Note that these base cases allow for any further pieces, so there are only 8 exceptions that can't achieve this.

Queen+x works in all cases

1. KQPvK

[fen "7k/5P2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

2. KQBvK

[fen "7k/5B2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

3. KQNvK

[fen "7k/4N3/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

4. KQRvK

[fen "RK5k/3Q4/8/8/8/8/8/8 w - - 1 0"]

1. Kb7

5. KQQvK

[fen "7k/5Q2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

Bishop+x works in all cases

6. KBPvK

[fen "7k/5P2/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

7. KBNvK

[fen "7k/4N3/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

8. KBBvK

[fen "7k/5B2/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

9. KBRvK

[fen "R3K2k/8/6B1/8/8/8/8/8 w - - 1 0"]

1. Kf7

Rook+xworks in all cases

10. KRPvK

[fen "R3K2k/8/6P1/8/8/8/8/8 w - - 1 0"]

1. Kf7

11. KRNvK

[fen "R3K2k/8/5N2/8/8/8/8/8 w - - 1 0"]

1. Kf7

12. KRRvK

[fen "RK5k/2R5/8/8/8/8/8/8 w - - 1 0"]

1. Kb7

KRBvK, KRQvK see above.

The 8 exceptions

KPvK, KNvK, KBvK, KRvK, KQvK,

KNNvK, KNPvK, KPPvK

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  • 1
    I'm not convinced by the KQBvK position shown. The black king must have moved into the corner from g8 in the previous move, because of a bishop check. But then: couldn't it have moved to f8 instead? Doesn't look forced, the same way that a (regular) KNNvK checkmate position exists but isn't forced. Sep 14, 2022 at 15:46
  • Same for the KQNvK and KBNvK cases. The discovered checkmate isn't forced. Sep 14, 2022 at 15:48
  • 3
    Some retrograde analysis on some of these positions yields some unforced positions. For example, in the mate with two bishops, nothing is stopping Black from playing Kh6 instead of Kh8 on the previous move. Sep 14, 2022 at 18:04
  • 1
    Also, this answers "mate in some special position". I'd like to see "long mate from random position". For example, RR is easy. I look into that myself :-) Sep 15, 2022 at 8:44

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