The Art of the Checkmate, Quiz 24: Is there a win? This is quiz 24 from The Art of the Checkmate by Renaud &amp; Kahn.

Black to play and win

rn3rk1/pp3ppp/3b1n2/2pPq3/2B1P3/1NN2bP1/PPPQ1P1P/R1B2RK1 b - - 0 1


The authors give this as the winning line:


   1... Qh5 2. Be2 (as Black was threatening Qh3-g2#) Ng4 (threatening mate on h2) 3. h4 Qxh4 4. gxh4 Bh2#


However, I think White has a simple refutation:


   2. Re1 prepares Bf1, stopping the Qh3-g2 threat, and Ng4 threats can be nullified with h4, as the Queen sacrifice doesn't work now as the King has a flight square


So, my questions are:


Is there a forced win (mate or material)?
If so, what is it?
If not, what's the best move?
Yes, you're right, there is no forced win. With correct play, White avoids the mate, and Black can only win one of the two pawns he is currently behind. White will have a healthy pawn more with best play from both sides:

rn3rk1/pp3ppp/3b1n2/2pPq3/2B1P3/1NN2bP1/PPPQ1P1P/R1B2RK1 b - - 0 1

1... Qh5 2. Re1 Ng4 3. h4 Ne5 4. Bf1 Bxe4