[Retros] Happy New Year!
Francois Labelle
flab at EECS.Berkeley.EDU
Mon Jan 19 14:31:32 EST 2004
On Fri, 16 Jan 2004, Andrew Buchanan wrote:
> It's usual practice in SPGs not to have any text e.g. "both sides can
> still castle".
I'm sorry about that. I'm a computer scientist, not an SPG composer!
But I think you noticed that it's not just any random text, it's what's
missing from the graphic to fully specify the position.
I have files containing every distinct position and the number of games
leading to it for ply 0-8. The position takes into account castling and en
passant, not by choice but by *necessity*, so that I can use the file for
ply n to generate ply n+1. I simply searched those files for "2004" and
realized later that I had to add the text.
> So what's the quickest *diagram* which can be generated by exactly 2004
> proof games? (i.e. no restriction on castling (or e.p.!)) Is there one
> in ply =< 8?
"Diagram", that's a beautiful word to explain precisely what the SPG
community wants! So I went ahead and collapsed my lists of "positions"
into lists of "diagrams".
You're going to laugh, a minor modification does the trick:
_________________
| |
| r n b q k b n r | Francois Labelle & computer
| p p p p . p p p | January 19, 2004
| . . . . p . . . |
| . . . . . . . . |
| . . . . . . . . |
| . . . . P . . P |
| P P P P . P P . | PG-3.5
| R N B Q K B N R | 2004 solutions
|_________________|
There are 4 such diagrams at ply 7 (those e-pawn can be put on e4 and e5).
There are 1664 PGs with 2004 solutions at ply 8 (871 non-shortest PGs and
793 SPGs).
The lowest n without a diagram for ply <= 8 is n=3413.
The largest n with a diagram for ply <= 8 is n=16327.
The most unsound proof game in 4.0 moves is:
_________________
| |
| r n b q k b n r | Francois Labelle & computer
| p p p . . p p p | January 19, 2004
| . . . . . . . . |
| . . . p p . . . |
| . . . P P . . . |
| . . . . . . . . |
| P P P . . P P P | PG-4.0
| R N B Q K B N R | 16327 solutions
|_________________|
Francois Labelle
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