Page for 1. e3 b6 And on Oct 10 it ended, when I tried a different line in 2. a4 and 5. a5! 1. e3 b6 is a White win ======================================================================== Aug 27-31 (2016): Well, let's try some other lines... I've been searching 1. e3 b6 2. Ba6 Nxa6 3. Qh5 c5 4. Qxh7 Rxh7 5. Ne2!? Rxh2 when after 6. Rxh2 Black has Nh6 or Nc7. The Nh6 line looks pretty good, with 6. Rxh2 Nh6 7. Rxh6 gxh6 8. e4 c4 9. c3! doing well (I tried b3 or d3 first, but both fell off). Black has two moves left, both close to +4 but with some slow-looking endgames to navigate. The alternative 6. Rxh2 Nc7 is around +2, but the lines didn't look so bad when I gave it a first glance. ======================================================================== Aug 28 (2015): The work on 2. a4 continues. The remaining line is: 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Na3 Qh4 5. h3 Qxf2 6. Kxf2 Na6 7. Bxa6 Bxa6 8. d3 Bxd3 9. Qxd3 Rd8 10. Qxh7 Rxh7 The score is approximately +2.7 for 11. Bd2, and 11. c4 is similar. Another idea is 8. Qg4, where Black has Bc4 (+2) and Be2 (+5). I kinda like this line better, as White forces the issue into resolution in an endgame more quickly, rather than shuffle around with a material advantage for awhile. However, the Be2 endgames are already slow, and the ability to use the cluster has been low in the first 2 weeks of September. Oct 11: Everything with 8. Qg4 but Bc4 is solved, but little work has been done there. e3b6.8Qg4reduction.proof.bz2 (175M) ba15e67c5be6c841f1be90f920ae39c1 Oct 26: There are nine remaining moves: Kf8, Ne7, Nh6, Rd8, Ke7, Kd8, Nf6, h6 and c6, for which c6 is at +8 but has some *very* tedious endgames (multiple blocked pawns that need to be unwound). On the positive side, White has a comfortable material edge in all lines I have seen, and for many of these it seems to be only a matter of time. On the negative side, 8 of the remaining scores are not yet very high. Oct 29: Ke7 is solved, though as usual, one is annoyed that the 3 days it took could have been halved if a "promising" White line had been avoided. Oct 31: Nf6 was also not too difficult. Nov 4: Rd8 is now solved. Nov 23: After a lot of work in Ne7 reductions, I turned to h6 and solved it very fast, albeit by transpositions: h6 loses a move on the h-file exchanges and so Ne7 goes into the Be2/Bc4 line, while Rh7 loses another move, and so is the same as Rd8/Ra8, with every other line being easy. As the first line is not in this proof file, it (redundantly) appears again. 8Qg4.work6.proof.bz2 (255M) 306d38e9e0e04f38c72630d6c9d7df97 Dec 10: I have solved the line 9... Nh6 10. Nxc4 Rg8 11. Qxh6 Rxg2 12. Nxb6 cxb6 13. Qxe6 fxe6, and here 13... dxe6 is about +4.5 in log-ratio. There was no obstacle to solving, just slowness due to lots of White choices. Here 11. Qxh7 is another possibility, but I don't think any faster. Dec 11: It turns out that Kd8 had hardly any nontranspositions left. All of Ne7/Ke7/Ke8/h6/Nf6/Rc8 and every part of b5 except for Ke7 is available from other files, but redundantly included in the file below. The main new content is after Kc8. DONE.Kd8.proof.bz2 (120M) 343da80dd23019ec1f200bbae1f2b457 Jan 6: Not much to be said about the completion of Nh6, just hard yakka. Again there are some transpositions into other files. DONE.Nh6.proof.bz2 (202M) 5c30981d688cc5f1fe807db4d70b380a Also, upon clearing the KNOWN directory, I finally decided to finish c6. DONE.c6.proof.bz2 (16M) 57f9bac6176df49bc7a7378877e1528a Jan 17: Ne7 is now done, again rather tedious to convert some advantages. DONE.Ne7.proof.bz2 (278M) 8db951b97cc1d2de4b68ba7c2306786b Early Kf8 news: I'm searching 10. Qxg8 Kxg8, and can force the line 11. Nxc4 b5 12. axb5 a6 13. bxa6 Rxa6. Here I prefer Nb6, as it forces cxb6, and then b3 requires Black to play either Ra3 or Ra4, immediately giving up the rook. The former is at about +3.5, and the latter at +2.7. Feb 1: Some progress on Kxg8, reducing to Ra4 or Ra3/Kg7 as above. As can be seen, the file size is already getting large. PROG3.Kxg8.proof.bz2 (200M) 730133817087b42bd8ce8b62d1b6726f Feb 15: Solving of the Kxg8/Ra4 line, with again nothing much to say except that the file is again large. PART.Kxg8.Ra4.proof.bz2 (182M) ef5619cc6f79d4d7834fa549c4f65698 Mar 17: I solved some of the Kxg8/Ra3 line a couple of weeks ago, but am only putting it up now. Still some work to do (including Ra8 stalling at +8, while the various king moves were around +4). [Mar 22: now down to Ra8]. [Mar 25: done, and file below represents that]. PART.Kxg8.Ra3.proof.bz2 (121M) 6f26a8380f8b18ed5bf82988b123275a I also switched to the Rxg8 line to convince myself that it is feasible. Although I drove the score up to +2.5, there are still many moves left, and they don't seem to go too fast. This leaves 14 moves: a8d8 +2.454 911706/15631 24121837 0 0 b6b5 +2.564 585841/500096 21379536 0 0 e6e5 +2.690 957210/9769 16787447 0 0 at +5: e4 then Kg8/h6 f8e7 +2.735 1228738/18195 24161595 0 0 f8e8 +2.784 1640117/15110 23634438 0 0 f8g7 +2.934 1107708/26127 22559520 0 0 f8g8 +2.972 1096259/11417 23440585 0 0 f7f6 +2.974 1238822/6360 413787 0 0 h7h5 +3.213 1653979/8694 1409484 0 0 a8e8 +3.474 1305685/9976 22017550 0 0 d7d6 +3.554 1885092/3363 108101 0 0 a7a6 +3.605 2104868/9619 774775 0 0 DONE f7f5 +3.800 1760932/11085 1279617 0 0 DONE h7h6 +4.285 1186792/9898 14112583 0 0 DONE Apr 18: The highest score of the remaining moves was solved. I also spent a couple of weeks while on vacation spinning away at the hardest move (a8d8), and it moved to a bit over +3.1, but didn't look like there was much movement. Apr 20: The second highest score was also easy to complete. PROG2.Rxg8.proof.bz2 (106M) 098ee2f6fe8ca3144e43737391d45e22 Apr 21: So was the third. DONE.a6.Rxg8.proof.bz2 (8.7M) a67e22b64ea084a5f2651d9cbfec5d8d May 7: I looked a lot at 13... h5, and have managed to convince myself that 14. d4?! b5 15. axb5 a5 16. bxa6 Rxa6 17. h4? Ra3! 18. bxa3 e5 19. dxe5 d5 20. exd6 f5 21. e4 fxe4 22. Bb2 e3 is not good as Black reaches an opposite bishop draw. Better seems 14. Ne2, where b5 remains. However, as b5 was a thorn on the previous try, I don't consider this conclusive yet. May 25: Perhaps it unwise to switch horses in mid-stream, but I looked at the alternative 9... Kf8 10. Nxc4, and made some preliminary reductions. From the position after 12. b3 g8e7 +1.657 658772/23970 18712297 0 0 g7f6 +1.657 875474/35102 19205505 0 0 a8d8 +1.720 1178525/8522 15508598 0 0 f7f5 +1.910 2075362/16009 1693372 0 0 a8e8 +2.147 2064871/9806 16328450 0 0 g7g6 +2.277 727623/21984 16666859 0 0 g7h6 +2.723 725233/16036 16227273 0 0 PROG2.Nxc4.proof.bz2 (63M) b0caca21b42f52f18574d93471c658bf ======================================================================== Aug 7: The work on 2. a4 continues. Everything but 2... b5 and 2...e6 PROGRESS.e3b6a4.b5missing.bz2 (26MB) cbccb938c7407ce4d33d2414fd67d7f0 Solution for 1. e3 b6 2. a4 b5 SOLVED.e3b6a4b5.proof.bz2 (188MB) aee1a938d9ff7c6ad7263b52cee85f98 This leaves 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Na3 ... Reduction to 4... Qh4 and 4... b5, and of 4... Qh4 to 5. h3 Qxf2 6. Kxf2 Na6 7. Bxa6 Bxa6 8. d3 Bxd3 9. Qxd3 Rd8 JULY15.proof.bz2 (66MB) c304d2c13a3b8220ebb9a76295333b76 Reduction of 4... b5 to 5. Bxb5 Qg5 6. Bxd7 Qxg2 7. Bxe6 Bxe6 8. h3 Qxh3 9. Rxh3 Bxh3 10. Nxh3 Nd7 11. c4 Nf8 12. c5 Rd8 [ now solved in REDUCTION.8Qxh3.win ] and 5. Bxb5 Qg5 6. Bxd7 Qxg2 7. Bxe6 Bxe6 8. h3 Bxh3 9. Rxh3 Qxf2 10. Kxf2 h5 11. Rxh5 Rxh5 12. Qxh5 Ne7 13. Qxf7 Kxf7 14. d4 Ng8 (15. e4 Nd7 16. Bh6) [ now solved with MORE_REDUCED.win and SOLVED.18Rd8.proof ] WORKING.4b5.win.bz2 (258MB) fb76d0d36d9a41a10b10ec7c296bd6a0 REDUCTION.8Qxh3.win.bz2 (54MB) 3117a5467be29fd734983c1ed881006d Unfortunately, after 15. e4 Nd7 16. Bh6 Nxh6 17. e5 Nxe5 18. dxe5 Rd8 with 19. Ke3 Rd6! 20. exd6 cxd6 etc., White may be +4.5 or so but the endgame does not seem to progress (two knights versus one is not a big advantage, and the Black g-pawn is annoying). An alternative plan is 19. c4, which I've managed to creep up past +5 with no obvious signs of stalling, but at best looks to be a very formidable task. Oh well, no easy solution... Aug 19: Reduction to 15. e4 Nd7 16. Bh6 Nxh6 17. e5 Nxe5 18. dxe5 Rd8 MORE_REDUCED.win.bz2 (55MB) 96f2b29b15f2153ad27a4047e2153e46 Aug 27: now in TBs for this line. This took less effort than I had guessed (only about 6-7 million nodes in the upper tree), but more time due to sharing the usage of the cluster. SOLVED.18Rd8.proof.bz2 (122MB) 1d517c862455ee3477f91397db5f78b9 I have also spliced together the above 4 files, as a solution to 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Na3 b5. It is just under 300 million nodes. BIG.4b5.proof.bz2 (483MB) 1dc400748ee5b793299c774316dc9821 ======================================================================== May 7-14 I have switched to 2. a4, as the 2. Ba6 lines are not moving much (if at all). Everything except e6 has been shown to lose (proofs below). The 2...b5 line is 145 million nodes, the rest about 15 million. I am looking at 3. Ra3, which after Bxa3 4. Nxa3 Qe7 have some tricky queen races, which after much searching (starting from negative scores in some cases) are resolved to be White wins it seems. However, Black also has b5 on move 4, and this has been bouncing up and down (+2.5 was the highest). The only other try at move 4 is Qh4 (at +3 currently). About 5-10 million searches have been done with b5/Qh4, and the situation is fairly stable in the +2 to +3 range. Furthermore, most of the resulting endgames look winnable to me (unlike many of the sidelines I solved, where there were some opposite bishop configurations that were +11 and looked quite drawish). Note: when moving to a new e3b6 directory, it seems that I copied over the FLAT information (for 4-piece TBs) for International rules rather than for FICS rules, so the first proofs here were faulty. Thanks to Klaas Steenhuis for pointing this out. 4... Qh4 seems much more difficult now, as 5. h3 Qxa4 6. Qf3 Qxa3 7. Qxa8 Qxb2 8. Qxb8 Qxc2 9. Qxc7 Qxd2 used to instantly be solved as a White win, but under FICS rules seems at best to get to a RRN vs KKK endgame.... Jul 9: Good news, 10. Qxc8 Qxe1 11. Qxe8 Qxe3 12. Qxf7 Qxh3 13. Rxh3 Nh6 14. Bxh6 gxh6 15. Qxh7 Rxh7 16. Rxh6 Rxh6 17. Bc4 b5 18. Bxe6 Rxe6 19. f4! wins, and so (as before) only Qxf2 is left at move 5. The mainline for 4... Qh4 is 5. h3 Qxf2 6. Kxf2 Na6 7. Bxa6 Bxa6 8. d3 Bxd3 9. Qxd3 Rd8, when after Qxh7 White will end up with a favourable endgame that I think should be won, but it looks slow. The mainline is 10. Qxh7 Rxh7 11. c4 Rxh3 12. Rxh3 Ne7 (Nh6/b5) 13. Bd2 Kf8 14. Ke2 b5 15. axb5 a6 (Nc8) 16. bxa6 Kg8 17. Rh6 gxh6 18. c5 Working proof file for 2. a4 e6 JULY15.proof.bz2 (66MB) c304d2c13a3b8220ebb9a76295333b76 One mainline for 4... b5 is 5. Bxb5 Qg5 (all others proven) 6. Bxd7 Qxg2 7. Bxe6 Bxe6 8. h3 Qxh3 9. Rxh3 Bxh3 10. Nxh3 Nd7 11. c4 Nf8 12. c5 Rd8 (others are in TBs), when Qg4 or f4 might work out, the capture sequences with the queen can be hard to resolve, and the endgames don't always win. The other mainline for 4... b5 is with Bxh3 or Qxf2 on move 8. ======================================================================== This is my mainline (though White has various other possibilities): 1. e3 b6 2. Ba6 Nxa6 3. Qh5 c5 4. Qxh7 Rxh7 5. Kd1 Rxh2 6. Rxh2 e6 7. b4 cxb4 8. Rh6 gxh6 9. d3 b3 10. cxb3 Ba3 11. Bxa3 Nb4 12. Bxb4 a5 13. Bxa5 Rxa5 moves e2e3 b7b6 f1a6 b8a6 d1h5 c7c5 h5h7 h8h7 e1d1 h7h2 h1h2 e7e6 b2b4 c5b4 moves h2h6 g7h6 d2d3 b4b3 c2b3 f8a3 c1a3 a6b4 a3b4 a7a5 b4a5 a8a5 All other Black options in this line are losing. My principal considerations for White here are 14. a3 and 14. Kc2, with the former leading to 14. a3 Rxa3 15. Rxa3 Ba6 16. Rxa6 Qc8/Qb5/b5/Ke7, with White having an extra Knight in a resulting endgame. However, this does not seem easy to win. The other line is 14. Kc2 Rxa2 15. Rxa2 Ba6 16. Rxa6, when Black has Qg5, Qe7, or b5. UPDATE: As I had expected, I think Black does OK with Qg5 in these lines. Another main possibility is 5. Kf1, where my notes from a year ago say that Rb8 and Nc7 (on move 6) are the best options for Black. I think I've chased down Rb8 into a convoluted endgame (something like KNNPPP vs KK and a blocked pawn pair), and while Nc7 looked difficult, it did show some promise, the principal lines being ones where White is some material down but Black is very limited in mobility. ======================================================================== Status for 5. Kf1 (Sep 5) [Feb 20] Every Black move except Nc7 and Rb8 is solved. WORKING.b6.Kf1.bz2 (124M) 5f4be74b49ac7e89cc146618ae23a0fd I am not that optimistic about Nc7. Here are mainlines for it and Rb8. 1. e3 b6 2. Ba6 Nxa6 3. Qh5 c5 4. Qxh7 Rxh7 5. Kf1 Rxh2 6. Rxh2 Nc7 I am currently looking at 7. Ke2 here. (March 2015) Then Rb8 is lost by transposition, Na6 transposes to the Rb8/Ra8 line below, and c4 and a5 are left. The former is where I spent a lot of time recently, and just as I was getting unhopeful, the score (Nilatac ratio) started looking a bit more positive. 7. Ke2 c4 8. Rh6 gxh6 9. d3 cxd3 10. cxd3 b5 (Rb8/Nb5/f5) 11. Nd2 e6 [Rb8/b4/Ne6] 12. b3 Bb4 (Ba3) 13. Ba3 Bxd2 14. Kxd2 Qe7 (Ne7/Ke7/b4/d6/Rb8) I have not looked much at 7. Ke2 a5, the notes say: 7. Ke2 a5 8. b4 axb4 9. Na3 Rxa3 10. Bxa3 bxa3 11. Kd1 Ba6 12. c3/Rh6 coming down (say) into KRN+5 vs KNN+6, few open files, probably stodgy. And for Rb8: 1. e3 b6 2. Ba6 Nxa6 3. Qh5 c5 4. Qxh7 Rxh7 5. Kf1 Rxh2 6. Rxh2 Rb8 7. Ke2 Ra8 8. Ke1 Nh6 9. Rxh6 gxh6 10. b4 cxb4 11. d3 Qc7 12. c3 bxc3 13. Nxc3 Qxc3 14. Bd2 Qxd2 15. Kxd2 and Black has Nb8/b5/Kd8/Nc7/e5/f6/Rb8 ranging from +2 to +5. This position is a bit different than most I have solved, in that *Black* is two bishops (and a pawn) ahead in material, but then again, bishops are not that useful of pieces, and White has much better structure and mobility. I also don't claim to understand the king-rook tempo bit on move 7. Another idea (which is my current favourite) is 10. Ke2 c4 11. b3 cxb3 12. cxb3 Nb4 (Nc7) 13. Ba3 Nxa2 14. Rxa2 Rb8 (Ba6) 15. Bxe7 Bxe7 (Qxe7) 16. Rxa7 Qc7 (Ba3) 17. Rxc7 Ba3 18. Rxd7 Bxd7 19. Nxa3 Bb5 (Bh3/Ba4) 20. Nxb5 Almost everything after 12...Nb4 ends up in a similar KNN+5 vs KR+3, and I think White should win, though quite slowly. The mainline after 12. cxb3 Nc7 13. d3 f5 14. Nh3 f4 15. Nxf4 is e6, with 16. Nxe6 dxe6 17. b4 Qxd3 18. Kxd3 Bxb4 19. Bd2 Bxd2 20. Nxd2. The other option at move 15 is Nd5 when after 16. Nxd5 Qc7 17. Nxb6 Qxb6 18. Nd2 Qxb3 19. Nxb3 White ends up most lines a rook (or more) up. But all these lines look *far* away from being solved.