The chances of a draw are even greater in endings of Q against Q, as the King on the stronger side can seldom evade perpetual check. For the sake of completeness I will show a few cases in which Q or R cannot win against an advanced pawn.
In Diagram 80 White can still draw, for in five moves the pawn reaches Kt7, supported by the King at R7, and in that time Black cannot come up with his King, so that he must give up the Rook for the pawn. Two passed pawns win, even when the King is away from them, if they have reached their sixth square. In Diagram 81, for instance, White is lost,
Diag. 80
as Black gives up his Rook at Q7 and plays P-Kt6, after which one of the pawns queens.
The Queen wins against an advanced pawn, even when the latter is supported by the King; only the R or B pawn can
Diag. 81
draw sometimes, when the pawn is on the seventh supported by the King, and the opposing Q cannot move to the queening square.
The following illustrates the three principal cases: