Byzantine Chess endgames. Queen vs Pawn

It goes only one square diagonally and (together with bishop) is slightly stronger than a pawn.

The simplest end ‘Q vs P’ may occur rather often and it is reasonable to know what is expected in this endgame.

The white queen may walk only on the light squares, while the dark squares are available to the black queen.
If the pawn stands on the square whose colour corresponds to that of the queen, the queen is called "bad".
Otherwise, the queen is "good".
In fact, there is some resemblance with the endgame ‘bishop vs pawn’  in the Modern Chess.
On the other hand, the pawn of Byzantine Chess is not promoted on the circular board.

Therefore, the partner with the queen always has advantage.

But it is not evident whether he can capture the pawn (that implies the win of the game).

The essential endings may be devided into four classes:

• "Bad" Queen vs flank Pawn
• "Bad" Queen vs central Pawn
• "Good" Queen vs flank Pawn
• "Good" Queen vs Central Pawn

To see the brief results read the Conclusion.

The diagrams are designed in the frames of standard notation on the 16x4 round board accepted by the Circular Chess Society.
 

"Bad" Queen vs flank Pawn

Position of mutual zugzwang

has crucial significance for this endgame.
The black left-going pawn is stopped and the black king can guard it from the two squares: the present stay and h8.

If the black king moves first 1. ... Kg8-h8, he will be deprived of returning to his initial stay g8 by the queen.

If White moves first, he cannot win.
Had White any piece else, the necessary tempo could be obtained immediately.
But the queen is not capable for this trick, because the queen returns to his initial stay in even number of moves (the queen's trajectory consists of the squares of one colour).

"Bad" Queen vs Central Pawn

A central pawn can be also defended against a  “bad” queen.

Here the left-going pawn has blocked the motion of the queen.
If the queen runs around the board and appears behind the pawn, the approach to the pawn will be cut by the black king.

"Good" Queen vs Flank Pawn

The weaker side may push the pawn in order to obtain the game with "bad" queen.
Nevertheless, playing against the "good" queen may also become successful.

The position of mutual zugzwang

is the clue to this endgame.

If Black moves first, the white queen will take the square h7 under control and deprive the king of his initial stay.

If White moves first, the black king is able to defend the pawn.

"Good" Queen vs Central Pawn

The black king guards the left-going pawn

but suffers from zugzwang at his turn to move: the light square behind the pawn will be controlled by the white queen.

Can White succeed if he moves first?

It is clear that the queen can freely come to the blocking square in front of the pawn.

Therefore, the answer is hidden in position

where White wins in any case.

If White moves first, his king comes on e5.

If Black moves first and his king defends the critical square e5, the white queen goes on h5 and controls the square behibd the pawn.

Conclusion

NEVER SURVIVES: the central pawn against the "good" queen.

MAY SURVIVE DUE TO ZUGZWANG: the flank pawn against either "bad" or "good" queen

ALWAYS HAS GOOD CHANCES: the central pawn against the "bad" queen

The weaker side obtains a draw if manages to built a fortress and handle in the proper manner.