Bulletin No.68 – Endgame Corner: Queen vs Minor Pieces

Do you know how a queen fairs against two minor pieces?   And if you know what the result should be, could you achieve it in practice?

Queen vs Two Bishops

This is drawn but only if the defending side can quickly achieve the correct defensive set up.  The king needs to be near but not in a corner and the bishops should be side by side facing the opposing king.   The position below, with White to move, is drawn.  If White plays 1.Qd7+ Black should respond with 1…Kg8/f8 keeping the barrier against the White king.   1…Bf7 would lose.

The positioning of the defensive side needs to be quite precise.   For instance, with White to move the following positions are lost for Black.  Note that in the last example the queen is badly placed on h1 but even then Black cannot get organised in time to set up the barrier formation.

In general, if the position is theoretically won then getting the full point is quite straightforward. If it is theoretically drawn it still requires some care by the defending side.  All in all, not much fun with the two bishops!

Queens vs Bishop and Knight

Like queen vs two bishops this requires a very precise setup to hold.   The diagram below shows the right positioning of the defending side (or mirror images).   You can put the White king and queen anywhere you like, have White to move, and this position is drawn.  Black just shuffles his king between g8 and h7 or his bishop between g7 and h8.  White cannot break the fortress because his king cannot reach f8, f7, f6, g6 or h6.

Pretty much any other arrangement of the black pieces leads to a loss because it is impossible to sustain a barrier to the white king.

Queen vs Two Knights

Perhaps surprisingly there are more positions with a pair of knights against a queen that are theoretically drawn than there are with a pair of bishops against a queen.  Indeed, in his book “Practical Chess Endings” Keres wrote, “the two knights offer better defensive chances than the two bishops and this ending is considered a draw.”   This is probably a fair assessment in practice if the knights are near the king, but tablebases reveal some wins that a human might miss.

A good defensive position is with the king one square from an edge, and the knights close by, preferably not defending each other.   However, the king may need to go to the edge or even the third rank for a move or two, and the knights may need to be defending each other for a move or two.  In fact it is very difficult to make hard and fast rules about the exact positioning of the defensive pieces in this endgame apart from saying it is essential to keep the king next to at least one knight.

The following three positions are drawn (compare them to the examples of Q v BB where only one equivalent endgame is drawn).

However, to understand how tricky this ending might be it is worth looking at the example Keres gave.

Keres gives this as drawn.  In fact 1.Qc7 (only move) followed by bringing the king round to c5 and d6 wins, though the win looks far from easy to me and in practice might be hard for a human to achieve.  Keres’s line starts 1.Qe6 Kg7 2.Kf3 and now 2…Nh8 or 2…Ng8 are theoretical draws but Keres prefers 2…Nh7 which is a theoretical loss!

In summary, a very tricky endgame with good practical drawing chances for the knights.

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