Black to move, what can be done?
Derek Grimmell calls this the trapezoid, a key position in the queen-versus-rook endgame. Although it may look innocent enough, black has no move that does not quickly lose.
Rook moves on the eighth rank
Moving the king immediately loses the rook, so the rook must move. Checking the white king with Rb8 allows Kc6 with two mate threats, and white wins the rook or mates. But Ra8 loses the rook to a skewer.
Rook moves on the C-file
These also fail. Rc7 allows Qf8#, followed by Qf7#, winning the rook. What about Rc4 or Rc3 or Rc1? Those rook moves lose to the queen moving to one of the following three squares: d5, f6, g5.
Another use of the trapezoid
Grimmell also points out that if the black pieces are not on the edge of the board it is still to white’s advantage, for black must give ground. In a queen-versus-rook endgame the weaker side does better keeping the king and rook as far from the edge and corner as possible.
Other key positions in queen vs rook
The best known may be the Philidor position, but Max Euwe (world champion decades ago) and his associates came up with their own key position in the mid-20th century. Derek Grimmell has found many key positions, with names like the following:
- third-rank defense