[Retros] the two candidates for x=4 (1+1) SPG, using DR

[Andrew Buchanan]

Folks,

Given the Dead Reckoning arguments earlier today, there are two candidate
positions for the quickest way to reach a (1+1) SPG (x=4).

SPG 17.0?
wKc2, bKg8
wKe1, bKf7

Each extends an SPG to 16.5 by the capture of a rook. But how do the other
proof games reaching this position end? If it's always with the capture of a
minor piece (or in the latter candidate, Kf8xQf7 which would be forced) then
by A1.3 (which is not optional except in fairy chess) we have an SPG. See
P0005394 & P0005405 below.

The computer I am using at the moment isn't very powerful, and I haven't got
Popeye. I think these are both long shots, but certainly they are worth
checking out. I'd be very appreciative. DR should also be borne in mind for
the x=5 quest.

Regards,
Andrew.

Gerd Wilts wrote:


>Francois Labelle wrote:

>

>> (3) BUFFET 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 checked some old documents and I found only 17 (!) such PGs (without

>Article 1.3). All of them can be found on the PDB web site:

>

>P0000245: wKg1, wQc2, bKg7

>P0000370: wKd2, wQc7, bKf7

>P0004246: wKf1, wQb1, bKe8

>P0004247: wKc2, wRa1, bKf7

>P0005389: wKf2, wPa2, bKd8

>P0005394: wKc2, wRg8, bKf8

>P0005395: wKd2, wBa8, bKe8

>P0005396: wKe1, wRg1, bKc8

>P0005397: wKd2, wRg7, bKd8

>P0005398: wKg2, wPf2, bKg7

>P0005399: wKf2, wBb8, bKe7  (dead reckoning!)

>P0005400: wKf1, wBg5, bKf8

>P0005401: wKe2, wNb1, bKc8

>P0005402: wKe1, wRa2, bKd8

>P0005403: wKd2, wRc7, bKf7

>P0005404: wKe1, wRf2, bKd7

>P0005405: wKe1, wRf7, bKe8

>

>The first one was found by Karlheinz Bachmann. The number 19 given in the

>comment to P0005371 is wrong, we (Norbert Geissler and I) had to rule out

>2 of them later because of duals (our program used hash tables so we had

>to check the resulting PGs for duals manually).

>

>Does this list correspond to your list? What is the "missing" PG?

>

>> 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?

>

>x=5 has not yet been done, so there is still hope that a dualfree PG with

>two Kings only exists!