I'm White, and I lost this game because the time was over. What move do I need to do the mate combination?
[FEN "8/6pp/p3R3/5rk1/3B2N1/5P1P/PP3P2/5K2 w - - 0 1"]
You have so much material and positional advantage that in time trouble you just need to make moves that consolidate and defend, and trade your pieces. For instance, moving
Kg2 to protect f3. You don't need to do anything fantastic to win, just gradually close in.
Tony's answer is a solid way to win without taking much time to think. If you're up in material, the more you trade, the better.
1. Re5 will help you out the most, since the fewer pieces Black has, the less likely you are to stumble into a blunder.
1. Bxg7 stands out to me as a good move. It does allow
...Rxf3 but the f-pawns were doubled anyway, so it's a great trade for you. After playing around with the position and toying with
2. Bh6+ (not a great idea), I decided the simple
2 Kg2 is the move I would play.
At this point, I used an engine (Stockfish) which tells me that the original position is mate in 11 beginning with
1. Bxg7 Rxf3 2. Kg2. The full mate it gives is:
[FEN "8/6pp/p3R3/5rk1/3B2N1/5P1P/PP3P2/5K2 w - - 4 1"] 1. Bxg7 Rxf3 2. Kg2 Kf5 3. Rf6+ Ke4 4. Rxf3 Kd5 5. Rf6 a5 6. Ne3+ Kc5 7. Bf8+ Kd4 8. Kf3 Ke5 9. Bg7 Kd4 10. Rf5+ Kd3 11. Rd5# 1-0
But that's far too complicated to figure out in actual play if you're a beginner under time pressure. You would win faster by simply picking off Black pawns and promoting one of yours.
Basically, you did not have a mating net quite yet, if Black played smart. But you had at least the rook. You're probably wondering "what if Black didn't play the moves shown above?" Let's try
1. Bxg7 a5: Stockfish calls this position a mate in 6:
[FEN "8/6pp/p3R3/5rk1/3B2N1/5P1P/PP3P2/5K2 w - - 4 1"] 1. Bxg7 a5 2. Kg2 a4 3. Rh6 a3 4. Kg3 Rxf3+ 5. Kxf3 axb2 6. h4+ Kf5 7. Ne3#
Black's useless pawn moves go to show that he is completely helpless. Anything else he tries results in a quicker mate. For instance,
4... axb2 allows
And trying to escape with his rook is futile too. True, he doesn't have to play
1... Rxf3, but you saw what happens if he leaves his rook on f5. How about
2. Rh6 leaves Black helpless. Notice how the Black king is completely boxed in by the white rook along e6, f6 and g6, and h5 and h4, and the knight takes care of h6 and e5, and the f3 pawn snags e4. The Black king now only has three squares in his box (the f3 pawn is guarded by the White king on White's next move), and Black's rook is helpless because of White's extra bishop and a2 and b2 pawns.
But always, which line you take depends on how much time you have on your clock.
The latter lines might be more advanced of a process than you're used to, but it is always good to study a little deeper than you're comfortable playing.
[FEN "8/6Bp/p6R/1r4k1/6N1/5P1P/PP3P2/5K2 w - - 2 2"]
I don't see a mate. The way forward is to remove his Rook by
1. Re5. Since this pins his Rook against his King he can't move it away. The Rook is coming off the board.
Once his rook is off the board, you have 2 extra pieces and an extra pawn on each side of the board. You really can't lose. Mating with a Knight and Bishop is not easy, so push your Queenside's unopposed pawn - the
b pawn. If you push the
a pawn you allow him to exploit a backward pawn.
Here's one possibility. There are better moves, but this is sure and simple.
[FEN "8/6pp/p3R3/5rk1/3B2N1/5P1P/PP3P2/5K2 w - - 0 1"] 1. Re5 Rxe5 2. Bxe5 g6 3. b4 h5 4. Ne3 Kh4 5.Kg2 Kg5 6. a4
...and it's pretty clear White is going to Queen a pawn. White must be careful not to stalemate black.