Losing Chess : 1 a3 e6 is a win for Black (reporting work by Klaas Steenhuis, October 2015)

Klaas Steenhuis has announced a proof that in Losing Chess the White opening move 1 a3 loses, Black having a forced win starting 1...e6. The proof took more than nine months of search, again using Mark Watkins's solver program for Losing Chess, and the proof file had about 195 million nodes. It can be found on Mark's web site http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/ (scroll down to "White moves that lose").

Klass remarks that the most important Black replies appeared to be 1...e6 and 1...Na6, but it soon turned out that after 1...Na6 White had a strong defence in 2 c3. So he concentrated on 1...e6, where the difficult reply turned out to be 2 c4. This soon had a score indicating it was solvable, but progress was very difficult. This applied in particular to the line

1 a3 e6 2 c4 Bxa3 3 Nxa3 c5 4 d4 cxd4 5 Qxd4 b6 6 Qxd7 Kxd7 7 c5 bxc5 8 Bg5 Qxg5 9 Nc2 Qxg2 10 Rxa7 Rxa7 11 Bxg2 Ra3 12 bxa3 Kc6 13 Bxc6 Nxc6



where Black's only way of maintaining an advantage was by sacrificing his king. This line also shows that the size of a subtree in a proof is not necessarily a good indication of its difficulty. The subtree after 13...Nxc6 contains only about 16 per cent of the nodes of the proof, but more than half the total search time was spent on it.

Some very difficult manoeuvring followed these moves. In most lines, White eventually had to give up more and more material, including his rook, leaving an endgame where he had only a king, often as a result of promotion of the a-pawn, against two or three Black pieces (these not including the king) plus a couple of pawns. These endgames were generally too difficult to solve with Klaas's usual tools, but with Mark's help he generated some crucial 6-man tablebases under the simplifying restriction that the side trying to win could promote only to rook. This is by far the best option in almost all positions of this kind, and restricting to it saves an enormous amount both of generation time and of storage capacity. The most important tablebases he built for this purpose were RBPPP v K, RNPPP v K, and RBNPP v K. With these he could solve a lot of positions that at first had seemed too difficult.

There still remained one position that Klaas could not solve, so he again asked Mark for help. Mark was able to solve this last position using a tablebase for RPPPP v K, which Klaas had not generated but which Mark had.

Klaas also made use of Stan Goldovski's "Giveaway Wizard" to help identify lines on which to concentrate. Stan had died, tragically young, in 1999, and it cannot be often, in a field as dynamic as this, that an exploratory computer program is still contributing to leading-edge research more than sixteen years after the death of its author.