7

Other than specific scenarios where the side with the rook can draw, is it always possible to win as the side with the queen in rook and queen endgames?

  • 2
    Don't forget the scenarios where the side with the rook can win! – D M Apr 27 '18 at 19:59
  • 1
    I believe the only way for the rook to win/draw this is, if the queen is obviously won/exchanged within the next couple of moves. – user1583209 Apr 27 '18 at 20:21
  • There are also some perpetual checks where the stronger side can avoid the checks only by allowing a pin or skewer (Kh2,Qf2/Kg8,Rh7+), or sometimes stalemate (Kh2(a2),Qf7/Kh8,Rh1(a1)+; Kh1,Qe6/Kf8,Rh7+). But those exceptions are all known. In particular, if the stronger side is to move and is not in check then it's always a forced win. – Noam D. Elkies May 2 '18 at 1:15
  • Take a look at my answer to this question. – AlwaysLearningNewStuff May 9 '18 at 17:48
6

The best resource I know for endgame statistics remains the ICGA endgame stats. The spreadsheet posted there contains pretty much all endgames up to 6 men. So for example KQKR is found in row 27 (assuming White has KQ), with the following percentages:

       wtm    btm   
W win 99.01 65.51
 draw  0.80  5.83
B win  0.19 28.65

So as long as White has the move, KQ is almost certain to win. Black victories with Black to move are likely due to be immediate capture or skewer. (Pin or fork of the queen leads at best to a draw, of course.)

Interesting to compare with KRBKR, row 107:

       wtm    btm   
W win 41.25  5.09   
 draw 58.70 94.06
B win  0.05  0.85

With White to move, Black does much better than in KQKR, which is curious since all that has happened is that the queen has been "unpacked" into its "constituent rook and bishop". With Black to move, the position is an almost certain draw: Black has lost the quick steals, but equally can protect himself from most of the situations where he might end up losing.

Note: (1) This is a tablebase based on computer analysis of all possible positions with up to 6 pieces. It does not refer to actual games played over the board. (2) The spreadsheet refers to "non-broken positions" which approximates to "legal positions".

5

According to Wikipedia, citing Fundamental Chess Endings, such endgames are wins for the side with the queen, unless there's an immediate draw or win for the side with the rook.

However, such endgames are complex enough that even a grandmaster may not necessarily win before 50 moves.

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