Status for 1. e3 e6 UPDATE (Aug 13th): 1. e3 e6 is (tenatively) solved. All that remains is to expand to the full proof tree and verify. UPDATE (Jul 22nd): My attempts in the lines below have failed. Some lines were never close, and the better ones were KRNP vs K with additionally facing a4/a5 pawns. HOWEVER, thus I went back and tried other lines (such as Nd2 or Nc3 at move 9). And it seems that 7. Bxb6 Qxb6 8. Qxf7! (rather than Qxh7) is going to work out, it is currently above 5 in log-ratio, and some eminently winnable endgames seem the only obstacle. The proof number perhaps about 80000, though of course this includes transpositions and also cases where an inoptimal ratio-move has a lower pn. Jul 26th: Currently at about +6.3 in log-ratio and 45000 in proof number. The line has been reduced to: 1. e3 e6 2. b4 Bxb4 3. Qg4 Bxd2 4. Qxg7 Bxe3 5. Bxe3 c5 6. Bxc5 b6 7. Bxb6 Qxb6 8. Qxf7 Kxf7 9. Nh3 Qxf2 10. Kxf2 Ba6 11. Bxa6 Nxa6 12. a4 Nc7 13. a5 Ne7 14. Ke3 Rhd8 15. Ra3 Nc8 16. a6 Nxa6 17. Rxa6 Rb8 18. Rxe6 Rxb1 19. Rxb1 Kxe6 20. Kf4 Kf7 21. Rf1 And now Black has Rf8 or a5, the mainlines of which converge after c4. (At move 14, Black can play Kf6, then 15. Rc1 Kf7 16. Ra3 Rhd8 17. Rh1 Nc8 18. a6 Nxa6 19. Rxa6 Rb8 20. Rxe6 Rxb1 21 Rxb1 Kxe6 22. Kf4 Kf7 23. Rf1 is a rather complicated transposition, all forced for Black). Progress is in try.Qxf7.bz2 (51MB) 5246923032ae111b3afc39de400d3d2e For those with the Aug 5 rebuild of WinningGUI, the file below can be used: tryZ.Qxf7.bz2 (51MB) b96efee05e8621f06d1358987c133909 Various lines after this have been solved, what remains seems to be lots of things like KRNPPP vs K that don't have the any foreseeable resolution, but "must" be won. I repeat what I said above, that I see nothing where I think Black might escape, though of course I have not peered down every line. The two lines left are: 21. Rf1/c4/c5 vs a5/a4/Rf8, then White plays 24. Nf2 a3 25. Rb1 Na7/Nb6/Rh8 21. Rf1/c4/c5 vs a5/Na7/Rf8 and forced is 24. Rh1 Ra8 25. Kf5 Nc8 26. Rf1 Kf6 27. Kxf6 Ne7 28. Kxe7 Ra6 29. Kxd7 Rf6 30. Rxf6 h6 31. Rxh6 a4 NOTE: After reviewing the situation, I think the most reasonable plan is to generate KRNPPP vs K tablebases, with the assumption that pawns promote to rooks. This seems to cover almost all the remaining lines. To generate these should not be a RAM problem, as the worst case is KRRRRN vs K, which is 2^42/4!/8 or 21.3 gigapositions (the pawns can be fixed individually, using the DTZ metric). But this takes a lot of code-writing and testing, especially if SMP is introduced. It is also of course possible that some of the desired 7-unit endgames are not won, though the situation has some flexibility. It seems that a bit over 700 gigapositions need to be considered in all (this is a significant overcount, as not all pawn positions are relevant), which would be comparable to about 20% of the total standard 6-piece EGTB, and those take a week or two to build. As I say, code-writing looks to be the bottleneck! Update: In fact, Ronald de Man was able to solve the above position at move 21 using his solver and 6-piece TBs (in search). It seems that most of the 7-piece endgames that I was worried about are actually quite easily convertible into 6-piece wins. I am currently building some relevant 6-piece tablebases, and will then look to replicate this result. ======================================================================== ======================================================================== Apr 12: Added "non-main" lines, reduces the situation to solving 1. e3 e6 2. b4 Bxb4 3. Qg4 Bxd2 4. Qxg7 Bxe3 5. Bxe3 c5 6. Bxc5 b6 7. Qxh7 Rxh7 8. Bxb6 Qxb6 9. Na3 Qxf2 10. Kxf2 Rxh2 11. Rxh2 Nh6 12. Rxh6 Ba6 13. Bxa6 Nxa6 14. Rxe6 fxe6 moves e2e3 e7e6 b2b4 f8b4 d1g4 b4d2 g4g7 d2e3 c1e3 c7c5 e3c5 b7b6 moves g7h7 h8h7 c5b6 d8b6 b1a3 b6f2 e1f2 h7h2 h1h2 g8h6 moves h2h6 c8a6 f1a6 b8a6 h6e6 f7e6 Where I think 15. c4 is the move to make (and then Black should play d5) [The idea with 9. Na3 vs others, is to setup c4, and Na3-c2 is useful too]. e3e6.nonmain.new.bz2 (35MB) a8726cfc515c487ff664f399862259fc Aor 19: Three moves after 15. c4 are unsolved (Kf7, Ke7, d5). The "hard" moves included here are d6, e5, Kd8, Nc5, Nc7, Kf8, Rd8, compared to Nb4, Nb8, Rb8, and Rc8 which are quite easy. The Rd8 proof originally had a lot of loops from transpositions, and I had to rewrite wintree to make it work. May 2nd: Kf7 is solved. I first went down a hard path on move 16 (trying Ke3 and g4), but Kf3 seems quickest. Black cannot give up the rook (say on h2) as easily, for White is one tempo closer than after Ke3. The line after Kf3/d5 looked hard, but then I realised I had already solved it in International Rules (transposed from the d5 line). Here White mainly follows the "plan" of Na1-b1-d2, and a g-pawn push, with Ra1-h1 or Ra1-f1 and Ng1-h3-f2 also useful. [It should be noted: the automatic methods do NOT find this "plan" very readily, and I originally hit upon it myself, particularly pushing the g-pawn]. The proof expander managed to cause a loop (this is still possible, though not too likely), but this was remedied with a bit of manual work. The previous options at move 15 took 20 million nodes (as did the non-main lines), while Kf7 took 42 million. This leaves Ke7 and d5, hopefully much of the work from International Rules will transfer for the latter (though I still haven't it solved it there). move15.left2.bz2 (108MB) 80636bab835c5cc615fb8a78cdc29cc8 May 6th: I am off to Europe for a month. Little (if any) work will be done then. The hard line for Ke7 seems to be 15. c4 Ke7 16. Ke3 Nc7 17. Nb5 Nxb5 18. cxb5 Rh8 19. Kf3 a6 20. bxa6 e5 21. Kg3 Rh2 22. Kxh2 d5 The point is that White will find it hard to stop the d+e pawns effectively, and promoting the a-pawn or g-pawn doesn't do that much to help. A similar line appeared for Kf7 (with various of the sidelines eventually being solved). Trying to transpose to the previous method of solving Kf7 does not seem to work too well. For instance 15. c4 Ke7 16. Kf3 d5 17. cxd5 exd5 18. Nh3 Nc5, and White doesn't gets arranged fast enough, while 16. Nh3 runs into Kf6, when White has to play c5 and Black again has the two central pawns to make life difficult. The idea of 16. Nc2 does not seem sufficiently effective against Nc7 for me to pursue it too deeply. 16. Nc2 Nc7 17. Ne3 Rd8 18. Nh3 d5 19. Nxd5 Rxd5 20. cxd5 exd5, and what exactly does White have with the extra rook?