[Retros] Re: Happy New Year!

[Andrew]

Francois,

Two thoughts: 

(1) There are existing search engines which will determine the legitimate 
proof games to reach a given diagram. At what point might it become more 
efficient for an engine not to begin with the initial game array, but with 
e.g. a database of 12 ply positions, filtering out those which clearly (due 
to captures and pawns moves) cannot lead to the goal position? 

(2) The most surprising part of your email:

> The lowest n without a diagram for ply <= 8 is n=3413.

I think there is a moral not just for composers of chess problems but also 
for engineers. One can spend a lot of time to build a structure with certain 
properties, but there is a price to be paid for comprehensibility. Often we 
need to pay that price, because that's the only route we have to get to a 
solution. But here's an example where using a general program, we can build 
all the solutions, "Nature's solutions", and not just the ones which would 
occur to a human designer. The constrast between Noam's highly ingenious 
2004 and "Nature's" effortless retort is remarkable. I find it quite moving. 

Regards,
Andrew. 


Francois Labelle writes: 


> 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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