Originally posted by wormwoodIf I may add to this, the side with the rook merely has to exchange the rook for one of the pieces, and the side with the remaining piece can only draw at best, if there is no other material.
in the endgame, R+p can win, there's winning potential left.
with B+N, even winning against the lone king is nontrivial. give the defending king anything, let alone R+p, and it's quickly almost impossible to mate him.
the numerical value of pieces has little to do with the question.
My OTB club (the Clermont Chess Club) has debated this for years in various positions, and our conclusive answer is "it depends".