[Retros] x=5 massacre wrap-up

[Francois Labelle]

The x=5 ply34,35 results are now accessible on my web site.
http://www.cs.berkeley.edu/~flab/chess/problems-massacre.html


2-KING DIAGRAMS

In March I announced a cooked (1+1) SPG with exactly two solutions. The
position is wKd4, bKe8. Below is one of the two solutions, I leave it as a
simple exercise to find the cook.

1. e3 d6 2. Bd3 Be6 3. Bxh7 Bxa2 4. Bxg8 Bxb1 5. Rxa7 Bxc2 6. Qxc2 Rxh2 7.
Qxc7 Rxg2 8. Qxd6 Rxg1+ 9. Rxg1 Rxa7 10. Rxg7 Bxg7 11. Qxb8 Bxb2 12. Qxb7
Bxc1 13. Qxe7+ Rxe7 14. Bxf7+ Rxf7 15. d4 Rxf2 16. Kxf2 Bxe3+ 17. Kxe3
Qxd4+ 18. Kxd4


3-PIECE DIAGRAMS

I traced back the solutions to all 100 3-piece PGs (without A1.3) that I
found at x=5. Interestingly there are really only 75 distinct
middle-games. They slowly branch off starting at ply 29 to finally give
100 PGs at ply 34. There are also often similarities inside the set of 75.

I was hoping to find a proof game with a promotion in the solution but I
found none. Instead among the 75 main branches I found 11 PGs with a
castling in the solution (but no PG with 2 castlings though).

5 white O-O
4 white O-O-O
0 black O-O
2 black O-O-O (including P0000284 by Karlheinz Bachmann)

So castling and massacre seem to go well together (and understandably so,
because a fast moving king reduces the possibilities).

The only thing new I found was 2 twin positions among the 89 problems with
A1.3 (R154 in Problemesis 39).


FUTURE WORK

I think that I can analyze a large part of the case x=6 (6 non-captures).
Looking at the x=5 positions, it seems that the final horizontal position
of a king isn't too important, the vertical position is what matters most.
My plan is to do 4 different searches for a (1+1) SPG in 18.0 moves with
these simple conditions on the final position:

1) white king rank >= 5 and black king rank <= 8
2) white king rank >= 4 and black king rank <= 6
3) white king rank >= 3 and black king rank <= 5
4) white king rank >= 1 and black king rank <= 4

	Francois