[Retros] Re: No (1+1) SPG at x=5

[Andrew]

Francois,
Congratulations on concluding this impressive piece of work. I look forward 
to seeing the detailed results but in the mean time, I just want to say 
congratulations on being the first to find an SPG whose soundness derives 
from A1.3. Also an "at home" position with 3+1 units is incredible. 

As far as the Holy Grail is concerned, the hope is still out there for the 
next generation to explore x=6. For me an apt aspect of your metaphor is 
that one doesn't know if the Holy Grail exists. On the other hand, Everest 
as a metaphor for the overall longest PG would also be appropriate, since 
some PG must surely be the longest. 

Regards for now,
Andrew. 


Francois Labelle writes: 


> The month-long computer analysis of massacre proof games with 5

> non-captures (x=5) that I was running is complete. I found no proof game

> with only two kings on the board, with or without A1.3. 

> 

> The best I get is one diagram with 2 solutions (with or without A1.3). I

> checked the solutions and they're almost identical, so the problem is

> cooked. 

> 

> 

> For PGs with 3 units left on the board I get: 

> 

> - 100 problems without A1.3

> - 13 of these are "disabled" by A1.3

> - 2 new problems are "enabled" by A1.3 (hi Andrew!)

> - for a total of 89 problems with A1.3

> (Recall that for x=4 there were 18 PGs without A1.3, and 17 PGs with

> A1.3.) 

> 

> 

> I verified the two x=5 problems of the Chess Problem Database whose status

> was unknown: 

> 

> P0000284 by Karlheinz Bachmann is C+ by my program

> P1000210 by Thierry Le Gleuher is C+ by my program (also C+ by Popeye

> after 46 min) 

> 

> 

> Here are statistics about the interesting PGs I found along the way: 

> 

> - 26170 at-home

> -   135 stalemate

> -     7 vertical symmetry with KQ-equivalent

> -  1400 horizontal symmetry and color-flip

> -   428 180-degree symmetry and color-flip 

> 

> 

> Some individual SPGs of possible interest: 

> 

> (1+1) in 17.5  (despite being cooked with 2 solutions) 

> 

> (1+2) in 17.0  SPG enabled by A1.3 (428 solutions w/o A1.3)

> (2+1) in 17.0  "                   (6216 solutions w/o A1.3) 

> 

> (7+7) in 11.5  at-home AND mirror symmetric

> (7+7) in 11.5  "

> (5+5) in 13.5  "

> (4+4) in 14.5  "

> (3+3) in 15.5  " 

> 

> (3+1) in 16.5  at-home (most depleted) 

> 

> (7+3) in 13.5  stalemate (least depleted)

> (1+4) in 16.0  stalemate (most depleted) 

> 

> (12+10) in 7.5  vertical symmetry with KQ-equivalent

> (10+10) in 8.5  " (this one has also a variant)

> (6+8)  in 11.5  "

> (6+4)  in 13.5  "

> (4+2)  in 15.0  " (this one is x=4) 

> 

> (2+2) in 16.5  180-degree symmetry and color-flip (most depleted) 

> 

> 

> I didn't backtrack every solution yet. I plan to put the (1+1) problems on

> my website and post the interesting SPGs and their solutions to the

> mailing list in a few days, unless someone contacts me with a more

> glamorous publishing option. Some of the positions are pretty stunning,

> but I haven't found the "holy grail". 

> 

> 	Francois 

> 

> 

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