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MatPlus.Net Forum Retro/Math Last-Move PGs

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### Last-Move PGs

This is a spin-off from the related thread by Alex Levit. Below is a very simple example of a "last-move PG", a collaboration with Mark Kirtley:

9...Qd8 (16+15) C? { PG in 9.0, with last-move of ...Qd8 }
Solution hidden below:
1.Sf3 e5 2.Sd4 Bb4 3.f3 Bc3 4.dxc3 Qf6 5.Bg5 Qb6 6.Be7 Sc6 7.Bf8 Sce7 8.Kf2 c6 9.Kg3 Qd8
Since the bQ (moving last) must've entered via the a5-d8 diagonal, it has to use the triangle rundlauf path because ...Sce7 can occur no earlier than black's 7th. Given that, there'd be no time for ...c6 ...Q~ ...Qd8 at the end. So any 1...e6 tempo ideas will fail.

Hope to find some better examples to post here.

EDIT: Corrected the length to 9.0 moves, sorry!

In my opinion the move 8... Qd8 doesn't determine all previous moves exactly.
1.Nf3 c6 2.Ng1 Qa5 3.Nf3 Qd8 4.Nf3 Qa5 5.Ng1 Qd8 6.Nf3 Qa5 7.Ng1 Qc7 8.Nf3 Qd8
Or doesn't I understand your intention?

As I understand, Dan wants to reach the position on the diagram (as in standard proof games), with the additional constraint that the last move has to be 8... Qd8.

A hint for solvers - white pieces can not reach their position in 8 moves, try 9 moves.

Nikola: Oops! I corrected the original post.

Frank: Bojan has it right. The stipulation 9...Qd8 means "proofgame ending with 9...Qd8". That is, after 9...Qd8, the diagrammed position must be reached.

OK, it's clear now. A "conditional proof game".

Seconding Nicola's message, I think there is a misprint in the stipulation. Reads: 8...Qd8 (16+15) C? { PG in 8.0, with last-move of ...Qd8 }
Should probably be 9...Qd8 (16+15) C? { PG in 9.0, with last-move of ...Qd8 }. White makes 9 moves and, as can be seen from Dan's hidden solution, it ends by 9. - Qd8.

@Frank: Exactly. :-)
@Bojan: See my previous "oops". :-)

You can, of course, computer-test such a proofgame, by grepping the output of Natch (all solutions to PG9.0) for the last move (in this case: "9.* Qd8").

Without having solved your problem (time constrained...), I must admit I'm curious why you would stipulate a final move (rather than simply stipulate a sound PG8.5).
Would you mind clarifying what value this serves?

There is a relevant article, by Frolkin & Prentos, which well covers a number of interesting ideas for adding to the proofgame stipulation.
I would highly recommend it, for anyone yet to read it (perhaps somebody can reference it; if not, I'll try to dig it up).

Just for clarity... a stipulated move surrenders any thematic advantage -- for example, this return, by itself, would not constitute a "circuit" of the bQueen.
I once encountered a claim of "Valladao Task," by somebody who had stipulated h-00-n (help castle); but, this can not be considered legitimate, when the only castling move (which is a full third of the theme) is entirely motivated by the stipulation.

I'm not saying this is your purpose here... I'm simply curious to learn why you would want to mandate a move within a proofgame.
Hey, if it gets me a Queen Schnoebelen, I'm all for it. :-)

To be precise, indicating Qd8 is not fully indicating the last move, but only its target. Saying otherwise, the indication here is not the last move, but only the fact that the last move is a Queen move (necessarily black as the game is in 9.0, and necessarily going to d8, as shown in the diagram position).

>"To be precise, indicating Qd8 is not fully indicating the last move, but only its target."

Interesting observation, Nicolas.
You can not say the same about Peter RÃ¶sler's "6.gxf8=N#" -- although, he does not fully indicate what is to be captured on f8.
But, the beauty of Peter's word problem lies in the minimal information provided -- just a single move (nothing to be extracted from an accompanying final diagram, nor an extraneous PGn.5 stipulation).
Ideally, a word problem stipulates the minimal information, to achieve a maximal, unique experience.

>"Saying otherwise, the indication here is not the last move, but only the fact that the last move is a Queen move (necessarily black as the game is in 9.0, and necessarily going to d8, as shown in the diagram position)."

I'm not exactly sure where you are going with this...
It seems a slightly tortured attempt to minimize the information contained within the stipulation, when you consider that the accompanying stipulation & final diagram provides us with the queen's color, the final destination square, and we know it did not capture (we know everything except for which of 3 squares it came).
I agree that your wording is to be preferred (it is minimal), but it hardly conceals that the stipulation here is essentially: "bQ-d8."
Which makes me wonder, all the more: what is the intended purpose (perceived benefit)?

In fact, I don't think the "word problem" genre is best characterized as a "move" which determines the game.
For example, one of my favorite word problems is: http://www.softdecc.com/pdb/search.pdb?expression=probid=%27P1017611%27
[I must concede having some reason for bias here.]

"Find the shortest game (I don't believe the author actually stipulated the number of moves -- it seems to be provided here as a favor for solvers), in Circe Parrain, to achieve quadruple-check, and mate."
In other words, "Shortest Circe Parrain game to ++++#".

The solution (which lasts 7.5 moves!) appears to be completely unique, without stipulating a unit, or a destination square, or even which side makes the final move (and, certainly, no final diagram).
And, even if you understand the trick (to achieve quadruple check, it is necessary to rebirth 2 unit simultaneously, which can only be achieved after capturing a reborn unit while simultaneously capturing a pawn en passant), the problem still presents an extremely difficult solving challenge.

That this can be done in Circe Parrain (where it would be a major understatement to say that a unique game is more difficult to achieve) still boggles my mind.

OK, I took a look... simple solve (I assumed it would be more difficult)...
Now it really appears that stipulating the last move spoils entirely the paradoxical effect (and nullifies any thematic intent).

This can be achieved, in as many moves, without aid from an additional constraint.
For comparison, see: http://www.softdecc.com/pdb/search.pdb?expression=probid=%27P1180338%27

KB: "I'm simply curious to learn why you would want to mandate a move within a proofgame."

Any experienced PG composer (myself included) has faced the dilemma of an idea being (seemingly) impossible with normal PG constraints. The "last-move" stipulation can, in some cases, make the 'impossible' possible. Or, perhaps, make the whimsical easier to achieve.

The example is a first-attempt of the latter persuasion, for demonstrating the stipulation, nothing more. I hope to find some better examples to post in due course.

Dan,

Understood... I do like how you continue exploring new frontiers.
Sorry if I was prematurely critical of your first sketch.

@Kev -- No worries! The "last-move" stipulation should be employed judiciously, just as one would treat NWK, K-in-check, promoted force, etc. Just another tool in the kit.

Here is another interpretation of Dan's suggestion:

Kostas Prentos
PG 8.5: Black was just selfmated (14+13)

Solution: 1.e3 g5 2.Bd3 g4 3.Bxh7 g3 4.Bg6 Rxh2 5.Qg4 Rh5 6.Kd1 Ra5 7.Rh7 gxf2 8.Rxf7 f1=Q+ 9.Rxf1# (Queen Schnoebelen)

Waiting for a possible comment from the initiator Dan, just informing that, if we had the possibility to vote by 'thumbs up/down' I would vote 'thumb definitively up'! Queen Schnoebelen in an orthodox proofgame has been considered to be impossible. Now we have it here! Do we now have to give a thought to the question, is selfmate an orthodox stipulation? Does adding the selfmate element into the proofgame stipulation make this an unorthodox/fairy problem? In my opinion no. - Congratulations and thanks to Kostas for giving us something new!

(18) Posted by Kevin Begley [Thursday, Mar 8, 2012 05:51]; edited by Kevin Begley [12-03-08]

Beautiful interpretation, Kostas!!

Now, I wonder how many ply can a Schnoeblen Queen survive (prior to capture)?

KP: Well done! I might have stipulated simply "9.RxQf1#", but your way works too.

PO: I have an idea for a "conditional PG" that looks promising, but needs another pair of eyes. Interested?

KB: Perhaps there could be a Q promotion, then several intervening moves, then a battery-check forcing the capture of the Q. Sky's the limit. :-)

Yes, Dan, interested! You probably have my e-mail; also can be used the Notes of this MatPlus (a service that we members use little / are not aware of).