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Rook endgame. Help needed.

http://el.lichess.org/iC23fHadwVhO

Here is the position taken from Silman's endgame course. It makes sense when I study it but in practice Its clear that something vital and basic skips my understanding. I can't make it a clear win when I play white and can't defend at all when I play black. Does anyone really gets this Position from beginning to end?
I'm not an endgame expert or anything, but this seemed fairly straightforward to me:



With 5. Re6 (instead of Ra6), I kept the rook in the center where I can use it to block against checks, and it's easier to stop black's g pawn that way. Then I used my king to escort the b pawn.

In your game, you ended up having a passive rook on a7 that had to protect your b pawn, but the rook itself couldn't support a further pawn advance.
Stockfish says it was still winning until move 10. But if you follow the engine line at that point, you'll see that in the end, it has to be the king that protects your b pawn. So, you basically lost time with your rook moves and allowed black's g pawn to become unneccessarily dangerous.
http://fa.lichess.org/wmxO3Cn5/white#0
nice endgame training for me
thank U :)
I think 2.Kd3 is clearly better than 2.Kd4 ; Because after :
2.Kd3 Rc5 3.Rxb6 Rxg4
its possible to play 4.Ra6 and winning the a pawn; but in 2.Kd4 line, it was not possible; Because of Rg5+ and then Rxa4

Thank you for the replies! Dr King Schultz the idea with the centered rook was really helpful. I totally missed that even after a rook exchange and a free black g pawn for my king to deal with my pawns are totally safe.

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