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After thinking for a minute my copy of Stockfish evaluates the position below as +4.7 for white. Why does the computer hate black's position so much?

I know that all things being equal, black should be worse having only a rook for two minor pieces, but black at least has an active queen and white's pieces are all on the back rank. After the simplification 1.axb5 axb5 2.Rxa8 Rxa8 the computer still gives an evaluation of +3. Why does black have no hope to defend this position?

[FEN "r4rk1/2p2ppp/p7/1p1q4/P7/3P4/1PP2PPK/RNBQ4 w - - 0 16"]
[StartFlipped "1"]

For example, after playing out my engine's PV I wind up in the following endgame; presumably I should be to easily see that it is winning for white? (Indeed, the engine seems to say white is winning even if both of white's e-pawns are taken off the board.)

[FEN "3rr1k1/2p2ppp/p7/8/Pp1P4/3PB3/1P2NPP1/R5K1 b - - 0 22"]
[StartFlipped "1"]
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    Convenience information: This is a well-known (47 games on LiChess, even at 2500+, abysmal score for Black) line from the Ruy Lopez Anti-Marshall, after one minute LiChess Stockfish is at +3.0. Still a bit high, but I don't want to play black even for ten dollars :-) (And remember, +3.0 doesn't exist in a game-theoretical sense. If Black is lost in the long run, +infinity.) Commented Nov 13, 2022 at 8:50
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    @HaukeReddmann That is indeed how I got this position :) Commented Nov 13, 2022 at 9:01
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    Two pieces for a rook is usually a winning advantage unless the opponent has something very specific in return.
    – David
    Commented Nov 13, 2022 at 13:49

1 Answer 1

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You are aware that two minor pieces are superior to a Rook in a naive point count but you don't seem to realise why this is so. It is simply that if I attack something with two pieces that you can only defend with one Rook then I can just take it anyway. On the other hand, if a Pawn is attacked by two Rooks, it can be securely defended by just one minor piece. The correct way for White to play is to identify targets that can be exploited in this fashion. And these exist here because Blacks pawns are exposed on the Q-side.

In the first position you note that Black has an active Queen (but no targets and no partners) and Whites pieces are still on the back rank (but with immediate access to stable and influential squares). Present dispositions are only meaningful as they relate to future prospects.

Lets start from your second position and give Black the move. There is still nothing active for Black to do. 1..a5 has the merit of preventing a5 by White, which would artificially isolate Blacks b-pawn. Then 2.Rc1 Rd7 3.Rc5 Ra8 leaves both Rooks passive. After 4.Nc1 and 5.Nb3 the Pa5 is lost. Say 4..Kf8 5.Nb3 Ke8 6.Nxa5 (Better than 6.Rxa5 because it does not allow Black to trade off a useless Rook) ..Kd8 7.b3 and now Nc6 and Rc4 will pick up the Pb4. The role played by the second minor piece (Be3) in this is to completely deny Black any counterplay.

This is good enough to win, but White can very likely win the Pc7 as well. Play the K to c4, N t0 d5, B to f4 etc. As Hauke says, plus infinity.

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