[Retros] Hit Team theme progress

François Labelle flab at wismuth.com
Fri Aug 25 14:48:54 EDT 2017

Hi Andrew,

I recently computed every checkmate proof game up to 6.5 moves, so I 
searched my files for PGs satisfying your conditions.

First, I want to introduce some terminology. It looks like we can 
classify pure mates into 3 categories:

(1) pure ordinary mate (the Wikipedia definition without the "unless..." 
(2) pure pin-mate (when we need the "unless..." clause),
(3) pure double-check mate (not covered by the Wikipedia definition it 

For (2) and (3) I'm using Noam's nomenclature as found at 
http://www.math.harvard.edu/~elkies/FS23j.05/glossary_chess.html , but 
not necessarily his definitions. For (3), Noam's page says "double 
checks are allowed if both checking units are needed for checkmate", but 
this seems too broad to me and not in the spirit of definition (1). 
Andrew's definition is "each check could be countered if the other unit 
was not present". I'm not sure if it's the same as Noam's or what I have 
in mind, it depends on Andrew's meaning of "countered". For me the test 
where we remove one attacking piece or the other is really about whether 
the attacks on the king's current square can be countered or not, so I 
would exclude moving the checked king as a way to counter the check 
during the test, and only leave capturing and interposing as the allowed 

In any case the precise definition of (3) doesn't matter for now because 
I've only programmed the detection of pure ordinary mates (1).

Returning to Andrew's task, 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.

Here are the 4 examples of minimal length:

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?

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#

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

I found no examples of size 4 or larger in 6.5 moves or less. Keep in 
mind that I only searched for pure mates of type (1).


On 22/08/17 10:29 AM, andrew buchanan wrote:
> Summary of progress
> Theme: proof game showing a pure mate, where except for the "hit team" 
> of White pieces actually involved in the mate, all pieces including bK 
> are in apparent starting position (homebase).
> Details: Wikipedia tells us a pure mate is a checkmating position in 
> chess in which the mated king and all vacant squares in its field are 
> attacked only once, and squares in the king's field occupied by 
> friendly units are not also attacked by the mating side (unless such a 
> unit is necessarily pinned to the king to avoid it interposing to 
> block the check or capturing of mating unit).
> (1) What we have. The original two:
> www.janko.at/Retros/d.php?ff=rnbqkbn1/ppp1pPp1/4P3/8/8/8/1PP1PP1P/RN2KBNR 
> SPG in 8.5 Yaakov Mintz
> www.janko.at/Retros/d.php?ff=rnbqkb2/ppppp1p1/6Q1/8/8/8/PPPP1PPP/RNB1KBNR 
> SPG in 5.5 C+ me
> and 4 more new ones by me:
> www.janko.at/Retros/d.php?ff=1nbqkbn1/p1ppppp1/8/8/8/8/PP1PPP1P/RNr1K1NR 
> SPG in 7.0 C+
> www.janko.at/Retros/d.php?ff=1nbqkb1r/1ppppp1p/8/8/8/8/P1PPPP1P/RN2K1r1 
> SPG in 9.0 C+
> www.janko.at/Retros/d.php?ff=rnQ1k1nr/p1pppp2/8/8/8/8/P2PPPPP/1NB1KBNR 
> SPG in 8.5 C+
> www.janko.at/Retros/d.php?ff=rnb1kbnr/ppp1pp2/8/8/8/8/PP1PPP1P/RNB1K1q1 
> SPG in 7.0 C+
> (2) If Yaakov Mintz is reading this, I would be grateful if he can 
> give me a list of his "hit team" compositions. Or if he is not 
> subscribed, perhaps some friend can forward him this please?
> (3) Noam's multiple 6. ... Nf3# problems, my 6. ... Nxf3#. And after 
> so many months, I can't remember mine! Did anyone find any of these? 
> One try is:
> www.janko.at/Retros/d.php?ff=rnbqk2r/pppp1ppp/8/8/8/2b2n2/PPP1PPPP/R1BQKB1R 
> SPG in 6.0 C+
> But this is not pure, because d2 is attacked by N&Q. N&Q both deliver 
> check on e1 at the same time, but that's not an issue as each check 
> could be countered if the other unit was not present.
> (4) I am no longer pursuing the "total home circuit" challenge, to get 
> a problem where all remaining pieces are on their original squares, 
> and the result is mate. I am informed that a top composer gave up on 
> this, and I am of the same inclination.
> (5) Thanks to Bernd Gräfrath for the link to Quartz 37 article on 
> Proof Game checkmates. It's curious that ending a proof game with 
> check may be a minor defect, while to end it with mate is a positive 
> feature. Making a position mate is not really difficult though. Here 
> the additional requirements that the mate be pure and the 
> "homebaseness" of all non-mating units seem to dominate the design.
> All the best,
> Andrew
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