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In a game I recently played, I was playing White and I blundered quite a bit to reach this position.
[FEN "8/R1N4p/2k5/1pn1K3/8/3r4/P4r2/8 w - - 0 1"]
Is it possible for White to win at all? I had four minutes at hand, and I sat down thinking about all the possible moves I could make by giving the Black king constant checks to win. However, I could not think of anything here.
No matter what, White is doomed. Black has much more material and there is no immediate threat to the Black king that White can cook up. The only checks available are futile ones. Additionally, the White king is in the hole, deep into a mating net and constricted by two Black rooks. Checkmate is inevitable in this position.
In fact, according to Stockfish analysis, Black has a mate in 7 here with White's best play.
[FEN "8/R1N4p/2k5/1pn1K3/8/3r4/P4r2/8 w - - 0 1"]
1. Ra3 Rxa3 2. Nd5 Re2+ 3. Kf6 Re6+ 4. Kf7 Kxd5 5. Kg7 Ra7+ 6. Kf8 Rb6 7. Ke8 Rb8#
Pretty hopeless unless your opponent blunders. Your only strategy is to avoid rook trades and use your knight to set up a fork. Unfortunately, you have no immediate move that proceeds with this strategy. If your rook moves, you well lose your knight. Your king has no legal moves. And if you move your night then Rd5 is mate. Your only hope is to play Na6, in the hope that your opponent misses mate in 1!
Black mates in 3 moves. White king is already in check and king has only one legal move that is Ke5 So 1.Ke5 Re3+ again king has only one legal move i.e. Kd4. 2.Kd4 Re4+ again king has only one legal move i.e. Kc3 3.Kc3 b4#.