[Retros] Hit team response

andrew buchanan andrew at anselan.com
Fri Sep 1 00:02:08 EDT 2017

Dear chess friends,

Responses to emails from Noam Elkies, Nicolas Dupont & Francois Labelle.
(1) Noam wrote:
>Andrew -- does this accomplish the task you had in mind?

No - this is still the "armchair team" theme, which has been explored before, where *all* remaining members of the winning side are on their starting squares. I'm not really interested in this right now, because it's been worked already, while this hit team problem is new. This is not the subject of this thread.

(2) Noam wrote:
> Is the last of these the correct position?  As it stands it's not mate
(9 . . . Bh3).

Oops. And why do my notes say that this one was published? Can find it in email anywhere. Let's scratch this one.

(3) Nicolas wrote:
>What do you mean by "mating units"? The plural seems to allow 
>discovered checkmate, but it looks a misprint as in that case there 
>are quite easy solutions such as:
>1. Cg1-f3  Cb8-c6    2. Cf3-e5  Cc6-d4    3. Ce5xd7  Cd4xe2
>4. Dd1xe2  Pb7-b5    5. De2xb5  Cg8-f6    6. Cd7xf6#

In your example PG, Nicolas, the double check on e8 is fine because each can be interrupted separately (block wQ or capture wN) but d7 is doubly attacked, and so the mate is definitely not pure.

I'm not trying to invent a new concept here, just trying to adapt something which already exists, but as usual it's hard to find a proper definition online. So here is my best effort to fill in the gaps.

Start with Noam's definition (referenced by Francois at http://www.math.harvard.edu/~elkies/FS23j.05/glossary_chess.html):
Pure mate (n.): a checkmate in which each of the squares in the field of the checkmated King is controlled exactly once. Double checks are allowed if both checking units are needed for checkmate; a square blocked by a friendly piece may not be attacked unless the attack is a pin necessary for the checkmate (which is then a ``pure pin-mate''). For example, the position White Kg6,Ra8,Bd6 vs. Black Kf8 is a pure double-check mate; and adding a Black Bishop on e7 makes it a pure pin-mate, but with a Black Pawn instead of the Bishop the mate would be neither pure nor a pin-mate. A pure mate is a ``model mate'' if it uses all the attacker's men except possibly the King and pawn(s); it is an ``ideal mate'' if every unit on the board is required for the checkmate. Each of the pure mates above is ideal (and thus a fortiori a model mate). 

But I don't think this is complete:
- We are looking at the final position not the move leading up to it, so a piece which simply discovers mate is not "involved" in it.
- If a piece blocks a potential defensive move, is it "necessary" for the checkmate? (e.g. White Kg6,Ra8,Rd6 vs. Black Kf8,Pe7,Be5). I suppose yes.
- If a piece pins a potential defender when that defender is *not* adjacent then I suppose the piece is necessary. (e.g. White Kf6,Ra8,Bc5 vs. Black Kf8,Bd6). I suppose yes.
- If a piece blocks what would otherwise be check of mating side king. (e.g. White Kg6,Rb8,Rd6 vs. Black Kf8,Pe7,Ra6). I suppose no.
- Now double mate. This can only be pure if each separate check could be countered separately by capture or block, if the other were absent. Note that king flight is not sufficient to counter a single check for these purposes, because we need to know that the attack on the king's square itself is not too powerful. But if any other flight square is doubly covered, then this means that the mate cannot be pure and therefore cannot be model.

If someone wants to tidy this up, please do.

(4) Nicolas wrote:
>Here is a non-ambiguous solution (with a single mating unit):
>1. Pd2-d4  Pc7-c5    2. Fc1-h6  Pc5xd4    3. Dd1xd4  Dd8-c7
>4. Dd4xa7  Dc7xh2    5. Da7-e3  Dh2xh6    6. De3-c1  Dh6xc1#

No this is definitely not a pure mate, because f1 is both occupied by wB and attacked by bQ.

(5) Francois wrote:
> pure ordinary mate only for now
> I found 4, 26, 41 and 298 examples in 5.0, 5.5, 6.0 and 6.5 moves (respectively), so asking for any proof game satisfying the conditions doesn't seem to be restrictive enough and Andrew should probably be asking for examples that optimize various things.

>1. f4 e5 2. fxe5 Nf6 3. exf6 Qxf6 4. h4 Qxh4+ 5. g3 Qxg3#
>1. c4 d5 2. cxd5 Qxd5 3. f3 Qxf3 4. h3 Qxh3 5. g3 Qxg3#
>1. Nc3 d5 2. Nxd5 Qxd5 3. f3 Qxf3 4. h3 Qxh3 5. g3 Qxg3#
>1. h4 g5 2. hxg5 Nh6 3. gxh6 Bxh6 4. f4 Bxf4 5. g3 Bxg3#
>In each example the hit team has size 1. Maybe we can ask for a shortest example for each possible size of the hit team?

I think finding the shortest example for each mating matrix is interesting, rather than just size of hit team. And then looking for more complex matrices. Whimsical situations (e.g. wQ at home still participates) are cool too. Then conventional criteria such as minimizing the number of captured units.

>For size 2, I found 11 examples in 5.5 moves. Here's an example using a queen at home as one of the hit pieces:
>1. d4 c5 2. Bd2 cxd4 3. Bc3 dxc3 4. Nxc3 d5 5. Nxd5 Qc7 6. Nxc7#

Whimsical indeed

>For size 3, I found 28 examples in 6.5 moves. Here are two examples:
>1. d4 d6 2. Bf4 Bg4 3. Bxd6 Bxe2 4. Bxc7 Qxd4 5. Qxd4 Bb5 6. Bxb5+ Nd7 7. Bxd7#

Reminiscent of Anderssen-Dufresne, 1852 - see wikipedia pure mate page.

>1. e4 d5 2. exd5 Qxd5 3. Qg4 Qxa2 4. Bc4 Qb3 5. Ra6 Qd3 6. Rf6 Qd8 7. Bxf7#

Nice bQ journey :-)

It would be really great to have the composer's perspective from Yaakov Mintz. And Noam's Nf3# compositions too! :-)

All the best,
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