Pawnless Endings Part 3: KRR vs KR
This ending pops up from time to time. You might see it or a variant of it with pawns as the result of a double Rook late middle game. While not difficult, there are times when the opponent can prolong the game quite a bit.
I will assume that you already know how force mate with KR vs K. The strategy here is aimed at forcing the opponent to trade off his last Rook. This is done with mate threats and other forms of coercion. Along the way you might have to use the Rooks to shield your King from annoying checks.
Here is example of me playing vs Tablebase. Thus, the defending side plays perfectly while I play according to my method. At the start, the position was mate in 22, when the exchange of Rooks was forced, it was mate in 10.