Is that position always a draw? I've tried to play it few times and I always end with lone bishop or a stalemate

8/3k3/p7/2Pb4/PP6/2KP4/8/8 w KQkq - 0 1
  • Whose move, and who are you hoping wins? Jan 24 '20 at 10:54

You cannot get a definitive answer, but in all likelihood, 99.99% it is a draw no matter who is to move (I am the type of person, who never says I am positive unless there is 100% proof, and that is impossible here, however likely).

The overwhelming factor in this position is that the black bishop does not control the a1 square, so even if white had no pawns, it would be a draw. It is clear that white can also never break the blockade either if black just plants his king on c6. It would remind me of an opposite color bishop blockade, but white has no bishop. Just Kc6, and Bd5-h1 with an easy draw.

The only reasonable exception would be if somehow white played a5, and later was zugzwanged into having to play b5 (like eventual stalemating the king on a1, forcing b5. That said, just avoid a5 (white can actually play b5 right now if on the move to avoid that issue).

It seems like a pretty easy draw either way to this long-time Master.

P.S. My Stockfish at a depth of 48 still reads 0.00

  • I am not sure about the name but isn't there a list of endgame sitations where e.g. all possible sitations with 3 pieces has been analysed and the best move calculated. This has been done for 4,5,6 and now also for 7 pieces. So for 7 pieces, we do know the best move. So if we would look at that, we would know if its 99.99% or 100% ;) (maybe I am wrong) Jan 26 '20 at 21:59
  • @FinnEggers Those are called "tablebases", and they are done for up to 7 total pieces, but there are 8 here, so they still cannot give a definitive answer. Again, I am virtually positive, but my nature stops me from saying 100%. Jan 26 '20 at 22:01
  • Yeah alright. I mean they must have been calculated aswell so you are probably right. Jan 26 '20 at 22:05
  • By the way, I have a significant subset, but not all, of the 7-piece tablebases on my computer, so my engine used them as I was answering the question. Jan 26 '20 at 22:08
  • 1
    I just realised this position has 8 pieces instead of 7. Jan 26 '20 at 22:14

Yes this should be drawn because:

  • White has pawns only on one side of the board, and thus cannot overload the bishop (which can sometimes be achieved if you have pawns on both flanks).
  • Black king is well positioned to blockade the pawn advance, and in particular preventing the white king to get to c5 and cover the two connected passers.
  • b5 will always we met with a5 fixing the weak pawn on a4 which can be targeted by the bishop as soon as the king start chasing the bishop. And of course blacks keeps the pawn by playing a5, i.e., white cannot simply ignore the queenside and roam around the board chasing the bishop.

Concretely, here are a few ways the game can proceed, in all of which black holds comfortably:

 [title "Trying some possible continuations"]
 [fen "8/3k3/p7/2Pb4/PP6/2KP4/8/8 w - - 0 1"]

 1. b5 a5 2. c6+ (2. Kd4 Bb3 3. Kc3 (3. c6+ Kd6 {again not allowing Kc5}) Bxa4 4. Kc4 Bd1 {and black holds trivially as white king cannot leave the a-pawn running.}) Kc7 3. Kd4 Kd6 (3...Bb3 {cannot allow Kc5 after c6 has been played, else white will be able to advance the connected pair of b-c pawns and win} 4. Kc5 Bxa4 5. b6+ {white wins}) 4. c7 (4. Kc3 Be6 {and black simply sits, white cannot make progress without losing pawns.}) Bb7 {and the c pawn is lost next.}
  • even 1 b5 axb5?! 2 axb5 is a tablebase draw. Jan 25 '20 at 20:01
  • 2
    @NoamD.Elkies good to know! I just assessed the position by rote and applied Occam's razor to settle on a5 :)
    – Ellie
    Jan 25 '20 at 21:34

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