2

Can white win this Q and P endgame?

From this position, put black Queen on the best defensive square, then it's white to move.

[fen "8/1PQ3pk/6pp/8/8/8/8/3K4 w - - 0 1"]

Maybe like this:

[fen "8/1PQ3pk/6pp/8/q7/8/8/3K4 w - - 0 1"]

My computer gives +6 for white, but doesn't seem to be able to find a winning strategy.

  • 1
    What do you mean by put black Q on the best defensive square? If I put the black queen on b1, b3, f3 or h1 I could capture the pawn on b7 in the next move... Also there will be squares where black can capture the pawn in the second move (after another check. – user1583209 Feb 21 '17 at 10:14
  • Indeed. Let me correct the mistake – jf328 Feb 21 '17 at 10:19
3

Black seems to be able to get away with a draw by perpetual check. The usual way for White to escape that, is to advance the pawn, or interpose his/her own queen while giving check (thereby forcing the exchange of queens). The latter is impossible because black's king is well protected. The former is impossible as well, as long as black remembers to give check from the a-file if the white king is on a8.

Your computer probably doesn't see a threefold repetition (indeed, it's possible for White to stave this off for more than 50 moves) and thinks the b7 pawn is worth almost 6 pawns because it is on the verge of queening.

3

The 7-piece tablebase says that the position without the pawn on h6 is draw, so I believe this position is also a draw (by perpetual check).

A typical winning attempt in queen+pawn vs queen endgames is to find a position where white can block a check with his queen while at the same time giving check. This is not possible here since the black king is protected by pawns.

Another option is to hide behind the pawn somehow. A somewhat ideal situation would be if white could move the king to a8, and to have the white queen on the a-file (e.g. on a5). In this position there is no check on the a-file and if black checked on the 8th row, white could respond by queening the pawn. However even in this ideal position black has the single (but sufficient) resource of pinning the pawn along the h1-a8 diagonal.

So yes this position with the b-pawn is draw and you can almost freely arrange white king and queen and it still stays a draw.

If it was a c-pawn though it would be more difficult for black to hold this.

  • Thanks! Why c-pawn is better than b-pawn? – jf328 Feb 21 '17 at 10:50
  • @jf328 Actually I am not sure about the c-pawn. It might in fact still be a draw with the h pawn included. But it certainly looks more difficult to hold for black. in this case. One reason is that there is less space for checks from the right. E.g. if you put the pawn on c7, queen on d7 and king on e8 and black queen checks from g8, then after Ke7 there is no more check. – user1583209 Feb 21 '17 at 11:01

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