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silverq 10 ( +1 | -1 )
R vs P Does anyone have any general or specific tips on rook and pawn endgames?

atrifix 18 ( +1 | -1 )
Is that KR + pawns vs. KR + pawns or KR vs. K + pawns?

Two connected passed pawns on the sixth usually (not always) beat a rook; for KR vs. KR, see Philidor and Lucena positions. Always try to activate your rook.
zdrak 74 ( +1 | -1 )
The most important tip is: "Rook behind the pawn!" - this is true for supporting your own pawns from behind, as well as attacking your enemy pawns from behind.

For example, consider this sample position:

White: Rc4, Kh1, pawns a6, g2, h3
Black: Rd8, Kh7, pawns g7, h6

If White is to play, he gains a winning advantage with 1.Ra4 (rook behind the pawn!)

If Black is to play, he should play 1...Rd1+ 2.Kh2 Ra1 (rook behind the pawn!) - and black has significant drawing chances.

Another related tip is: "The advantage of one pawn is often not enough for a win if the weak side has an active rook"

Yet another tip: "Connected pawns good, separated pawns bad" (this is actually true for all positions, but becomes an especially important factor in rook endgames)
macheide 88 ( +1 | -1 )
silverq All of the above are very good advices! If you want to begin a systematic study of this important kind of endgame (Maybe 50% of the endings are Rook endings), I'll recommend the following books:

"A Survival Guide to Rook Endgames" by John Emms
"Rook Endgames" by Smyslov and Levenfish (A very rare superbclassic, I have it in spanish)
"Capablanca's Best Chess Endgames" by Irving Chernev. (This book deals not only with Rook endgames, but you should study it, because of the practical examples and because it is A GREAT BOOK)
"Secrets of Rook Endings" by John Nunn (A little advanced and deals with only one kind od Rook endgame, but is the definitive treatise on this one)

The list isn't exhaustive but hopefuly it will help you.

Post data: Study Rubinstein's games, he was the supreme master of Rook endgames.

Best wishes,