6

How often does each side win in Rook, Bishop and Knight versus Queen endings? It is a 6-piece endgame so the evaluation of each position is known but I could not find statistics on this endgame after searching for a while.

[FEN "8/8/8/3k4/3N4/2q5/5K2/R5B1 w - - 0 46"]
4

The best resource I know for endgame statistics is the ICGA spreadsheet at https://ilk.uvt.nl/icga/games/chess/endgames.php. The spreadsheet posted there contains pretty much all 6-man endgames. So for example KRBNKQ is found in row 277 (assuming White has RBN), with the following percentages:

       wtm    btm   
W win 51.35  9.45       
 draw 45.13 49.27
B win  3.52 41.28

So the result is highly dependent on who has the move.

EDIT: Clarifications (1) This is a tablebase based on computer analysis of all possible positions with these 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".

  • 2
    On the other hand, those black wins would be 95% of the time situations where white loses the rook immediately, so that's effectively just queen vs bishop and knight. Likely the draws would be largely by perpetual check. If white's pieces are sufficiently coordinated and able to protect the white king, white always wins. – user1583209 Mar 18 '18 at 9:13
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The endgame with just those 6 pieces is pretty rare, so I doubt there would be enough games in any database to make good stats. Just judging from the material imbalance though, White is in no danger of losing (unless he blunders his Rook).

Without any blunders, White just has to make sure Black cannot sacrifice his Queen for White's Rook and one minor piece (since K+B vs K is a draw). Then, White can maneuver his pieces and set up one trap after another (pins and forks against the Black King and Queen) until eventually winning the Queen.

The problem Black faces is that he has to watch out for tactics from all 3 of White's pieces, which just so happen to move in all different directions (Rook = vertical, Bishop = diagonal, Knight = L-shape). Meanwhile, Black can only really attack with his Queen, and the Queen alone is not enough to cause serious tactical threats (White just has to watch out for skewers and a few pins from one piece).

  • I agree white will win. But tactics-wise, white is more vulnerable. Q tactics are mainly forks and with an open K, any loose white piece is vulnerable. Black just need to put K and Q wide apart on different colours to avoid any tactics (but he might be mated quickly if white plays correctly) – jf328 Mar 19 '18 at 16:16
  • @jf328 I think White is only more vulnerable if he leaves any of his pieces undefended. If White keeps all his pieces protected, Black cannot do much other than attempt a perpetual check. Meanwhile, Black will not get anywhere by protecting his Queen with his King, since White is happy to exchange any of his pieces for it. If Black kept his K and Q far apart, tactics would be difficult (but still possible). White's Rook and Bishop can form nice long-range tactical traps. – Inertial Ignorance Mar 19 '18 at 18:24

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