With Black to move, is there a possibility to win in this position?
[FEN "3rk2r/1p2q2p/1Q1p1Bpb/1R1N3n/1P6/5N2/1P3PPP/4R1K1 b k - 0 1"]
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Sign up to join this communityAt a cursory glance you see that...
So no, there is nothing, really nothing in favour of black here. The only thing which needs to be checked is that Qxe1 is not mate, but in a millisecond you see that the rook is protected by the knight on f3.
With Black to move, is there a possibility to win in this position?
Of course there is. If White's flag fell then this would be a win for black.
Here is one simple winning continuation for Black
[FEN "3rk2r/1p2q2p/1Q1p1Bpb/1R1N3n/1P6/5N2/1P3PPP/4R1K1 b k - 0 1"]
1... Nxf6 2. Nd4 Qxe1++
Of course the White move is very bad and only someone who is trying to lose (or teaching a young child to spot back rank mates) would play it but it is one of many possible ways that Black could win.
Of course in a normal competitive game it is never going to happen. With reasonable, half competent play by white black is going to lose.
The position is resignable for Black. White is already up a piece, and is about to win Black's queen for a rook. Technically it's possible White could play some horrible blunder and allow Black to win, but this could be said about any position where the losing side has mating material.
No, this is dead lost. According to stockfish Qxe1 is Black's best move. But even after this, White can force a checkmate in 13 moves.
1... Qxe1+ 2.Nxe1 Rd7 3. Bxh8 Bg5\ 4. Nc7+ Kf7 5. Rxg5 Nf4 6. Rg4 Ne2+ 7. Kf1 h5 8. Qe3 Rxc7 9. Re4 d5 10. Re8 Nf4 11. Rd8 Ne6 12. Qf3+ 13. Qxf4+ Ke6 14. Qf6#