Is this endgame a draw? 2 Bishops + 4 Pawns vs Queen + 1 Pawn

Question

I had this position playing as Black, with Black to move:

[FEN "8/5pk1/6p1/2pQ1b2/1p1b1P2/5K2/8/8 b - - 0 1"]

I had both bishops + 4 pawns = 6.5 points + 4 points = 10.5 points. The opponent has a queen + 1 pawn = 10 points.

I know how to challenge a queen with 2 rooks but not with 2 bishops supported with pawns. That's why I played to get the draw and I got it by claiming repetition.

My Questions:

• Do black or white have a way to force a win, or is it a draw?

• Does comparing with points matter here, with the “score” being 10.5 vs 10?

The whole game is here:

[FEN ""]
[Event "Live Chess"]
[Site "Chess.com"]
[Date "2015.07.06"]
[White "IRINA777"]
[Black "bigother"]
[Result "1/2-1/2"]
[WhiteElo "1396"]
[BlackElo "1427"]
[TimeControl "5|0"]
[Termination "Game drawn by repetition"]

1.e4 d6 2.d4 g6 3.Nf3 Bg7 4.c3 Nf6 5.Bd3 O-O 6.O-O b6 7.Be3 Bb7 8.Qd2 Nbd7 9.Na3 c5 10.d5 Re8
 11.Nc4 Qc7 12.a4 e6 13.e5 dxe5 14.Ncxe5 Nxe5 15.Nxe5 Qxe5 16.dxe6 Qxe6 17.Rae1 Qc6 18.f3 Nd5 19.Bh6 Rxe1 20.Rxe1 Re8
 21.Bb5 Rxe1+ 22.Qxe1 Bxh6 23.Bxc6 Bxc6 24.c4 Be3+ 25.Kh1 Bd4 26.cxd5 Bxd5 27.a5 Bxb2 28.axb6 axb6 29.Qd2 Bd4 30.Qd3 Bc6
 31.h4 b5 32.h5 b4 33.hxg6 hxg6 34.f4 Bd7 35.Kh2 Bf5 36.Qc4 Kg7 37.g3 Kg8 38.Kg2 Kg7 39.Kf3 Kg8 40.g4 Be6
 41.Qa6 Kg7 42.Ke4 Bxg4 43.Qb7 Bh3 44.Qb5 Bf5+ 45.Kf3 Kg8 46.Qe8+ Kg7 47.Qb8 Kh7 48.Qb7 Kg7 49.Qb5 Kg8 50.Qc4 Kg7
 51.Qb3 Kg8 52.Qc4 Kg7 53.Qd5 Kg8 54.Qd8+ Kg7 55.Qd5 Kg8 56.Qa8+ Kg7 57.Qd5 1/2-1/2

Answer 1

Black is winning handily from the diagram position, and has a fairly straightforward strategy going forward: force the b-pawn's advance to b2 with the support of the bishops (starting with 1...Be6 to gain control of the b3 square), and then slowly push for a new queen, making use of the facts that (1) White must always keep guard over b1, and (2) Black has plenty of material to shield from a potential perpetual.

The following is lightly annotated over the first few moves, and from move 5 on is just one line illustrating how Black can make steady progress with nothing to fear from the White queen.

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[FEN "8/5pk1/6p1/2pQ1b2/1p1b1P2/5K2/8/8 b - - 0 1"]

1...Be6 
    {Taking control of the b3 square with tempo, preparing to advance the 
    b-pawn.}
2.Qb7 b3 3.f5 
    {White needs to try this, as otherwise Black can simply follow with 
    ...b2, ...Bf5 and queening. Playing this immediately forces Black to 
    occupy f5 with the pawn, since ...Bxf5 drops the b3 pawn.}
    ( 3.Ke2 $2 b2 4.Kd2 Bf5 )
3...gxf5 
    {Still, Black will be able to get in ...b2 from here, which will tie 
    White to guarding against promotion on b1. The only hope for White 
    would be a perpetual, but Black has plenty of material with which to 
    shelter the king.}
4.Kf4 b2 
    {What follows is just one illustrative line showing how Black can keep
    the king safe while pushing toward a new queen.}
5.Qg2+ Kf8 6.Qa8+ Ke7 7.Qb8 c4 8.Qc7+ Bd7 9.Qb7 f6 10.Qb4+ Ke8 11.Qb8+ Kf7
12.Qb7 Be5+ 13.Ke3 f4+ 14.Kd2 Kg6 15.Qg2+ Kh5 16.Qh1+ Kg5 17.Qg2+ Bg4 18.
Qb7 c3+ 19.Ke1 f3 20.Qg7+ Kf4 21.Qh6+ Kg3 22.Qg6 f2+ 23.Kf1 b1=Q+ 24.Qxb1 
Bh3+ 25.Ke2 f1=Q+ 26.Qxf1 Bxf1+ 27.Kxf1 c2 *

Answer 2

Actually, looks to me like black is winning. For example:

8/5pk1/6p1/2pQ1b2/1p1b1P2/5K2/8/8 b - - 0 1

1... Be6 2. Qb7 b3 3. f5 {only move - opening black's position up} gxf5 (3... Bxf5?!) Kf4 b2 {now black has to escape queen's checks...}

From here, white can go on with some checking sequence, but it looks to me that black will be able to escape a draw by perpetual check eventually and promote.

The piece point scoring systems are subjective by default and also often heavily dependent on the position and number of pieces left. I do not think exact point comparison is useful in this particular case, however. The position is roughly equal, yes - black just happens to have his king safeguarded from checks and two well supported, passed pawns and thereby excellent winning chances. Suppose though, that both black and white f-pawns were gone. Point-difference-wise nothing has changed - 9.5 to 9 now, but it would be much more difficult, if not impossible, for black to force a win, since his king is now much more exposed to checks. What I mean, is that with this same material imbalance (Q+P vs B+B+4P), one could easily set up positions with any possible end result as an outcome - all depending on how the pieces are positioned and coordinated.

There are also many fortress scenarios in queen vs rook/minor piece(s) endings, where the point system can be misleading. Suppose, for example, the c and b pawns were to be removed - now, in theory, white is ahead - 10 to 8.5 points. I haven't checked, but black should be able to set up a fortress and hold a draw despite the material disadvantage.