[Retros] At Home SPGs, and more

[Francois Labelle]

(1) ANDREW'S 3 SPG CHALLENGES

I reached ply 10 for at-home PGs, and did mirror-symmetric and checkmate
PGs up to ply 9. Here are some handy anchor links.

http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html#at-home
http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html#mirror
http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html#checkmate

Andrew Buchanan wrote:


> > Any guesses as to how many dual-free deletion

> > SPGs there are at ply 9 and 10?

>

> I imagine there may be hundreds.


The numbers are 41 and 114. Good guess!


> There are some other SPG challenges which I would also be interested in

> cataloguing:

>

> (1) checkmates.

> The shortest is 1.e4 f5 2.exf5 g5 3.Qh5#.


I get 3 diagrams at ply 5, and 51 diagrams at ply 6. After that it just
explodes. I'm afraid the lists are boring, most checkmates are just
variations on the same ideas, but for the computer they're all distinct.
Are you going to pick one representative diagram for each distinct idea?

There's a funny problem I runned into: "checkmate" is a property of
position, not diagram. Is it possible to come up with a diagram which is
either checkmate or not checkmate depending on whether some specific en
passant capture is possible or not? Now imagine that the checkmate is
uniquely realizable, but the diagram is not! I don't think it happened in
my search, but theoretically the diagrams that I'm counting may require
the text "checkmate".


> (2) mirror-symmetric positions in an *odd* number of plys (i.e. no

> shorter SPG in an even number of plys exists). Here are four

> "originals", all SPG 3.5. (Well I *think* Jonathan's is original.)

> [...]

> There is no attempt to be exhaustive here.


Well, it turns out that your list *was* exhaustive for 3.5, apart from a
simple variation to one of the diagrams.

I get 51 mirror-symmetric SPG 4.5.


(2) REPLIES TO JOOST

Joost de Heer wrote:


> Only one acceptable double-solution proofgame in both 8 and 9 halfmoves:

>

> rnbqkbnr/pp1ppppp/8/8/8/8/PPP1PPPP/RN1QKBNR

> SPG 4.0 (2 solutions)

>

> 1. d4 Nc6 2. Bf4 Nd4 3. Bc7 Nc6 4. Bb8 Nb8

> 1. d4 c5 2. Bh6 cd4 3. Qd4 Nh6 4. Qd1 Ng8


Thank you for your verification! By the way, this particular "acceptable
double-solution proofgame" is a rediscovery, Cornel Pacurar composed it
before me.


> > [...] using the fact that every sub-proof-game of a

> > dual-free proof game must be dual-free.

>

> Actually, this isn't true: A proofgame can have a unique solution, but

> intermediate positions aren't necessarily unique. The uniqueness comes

> from preserving castling rights or the need for a double-step as last

> move to allow an ep-capture.


Sorry, I guess I meant "any intermediate position encountered in the
solution of a uniquely realizable position is a uniquely realizable
position (where by 'position' I mean diagram + castling info + e.p.
info)". Then to test a diagram one would simply try all the possible
castling/e.p. possibilities.


> Is there, besides #5 in the second article, another 3-solution proofgame

> (so not 3-variations, i.e. three different begin moves)? Perhaps your

> research can give us an answer to this.


Different begin moves? Would you be happy if 2 solutions were exactly the
same, except that White's first 2 moves are transposed? I think not. If on
the other hand I ask that no single move may match another move even if
the timing is different, then I'm sure I can miss some excellent problems.
I get the feeling that solution independence is not a yes/no concept like
"being cooked", but that it's continuous and subjective. And I doubt that
you could describe mathematically what you're looking for without a good 5
rounds of trial and error, but you can try!


(3) BUFFET SPGs

I don't know what's the right name for this, I'm talking about those SPGs
where every move is a capture except x moves, for x = 3,4,...

I was able to do x=3 and x=4 with my program, but apparently this stuff is
already known.

For x=3, I get 3 SPG 15.5 with 4 pieces left on the board.

On the Chess Problem Database Server, the comment attached to P0005406
lists the same 3 problems and mentions that they're the only 3 such SPGs.

For x=4, I get many SPG 16.5 with 3 pieces left on the board:

18 SPGs without Article 1.3 of the Laws
17 SPGs with Article 1.3 (Dead Reckoning!)

A comment in German attached to P0005371 talks about 19 such SPGs. So
there's a slight discrepancy here.

I'm not sure yet if I can do x=5, it's really on the cutting edge of what
I can tackle. The comment in German seems to imply that no one has done it
before. Is it true?


(4) ARTICLE 1.3 OF THE LAWS

I've come to wonder if there's *any* efficient way at all to test a chess
position for article 1.3. I'm talking about a step-by-step procedure that
would work for every position (no "high-level" thinking).

Article 1.3 is:

"If the position is such that neither player can possibly checkmate, the
game is drawn."

Here's my poor attempt at a concrete example:

 _________________

|                 |

| . . . . . . . . |

| . . . . . . . . |

| . . . Q . . . . |

| . . Q . . . . . |

| r R . . . . . . |

| k n . . . . . . |

| . . b . B . . . |  drawn by Article 1.3

| K . . . . . . . |

|_________________|



This is drawn by Article 1.3 because the next 6 plies are forced:

1. Rxb3+ Kxb3+ 2. Qa3+ Rxa3+ 3. Qxa3+ Kxa3

and then we fall into a situation with two bishops on the same color
squares.

And this isn't "drawn" like in a chess problem where you're supposed to
evaluate the position, a player is *legally obliged* to stop playing right
there, with the 9 pieces still on the board. Novice players are already
having problems not putting themselves into check, how can they be
expected to spot this drawn position?!

I'm sure people here could come up with some plausible looking
configurations with long or complicated branchings leading to stalemates,
KKN, KK + same-color-square-bishops, or some other form of dead position.
This would show the Chess Federation just how hard it can be to apply
Article 1.3, both for humans and for computers.

I'm sorry if this has already been hashed to death.


	Francois