Chess problems and studies

[cuBerBruce]

King and queen vs. king and queen endgames are mostly draws unless there is a rather immediate safe capture or mate for one side. There are, however, some cases that the losing side can keep its queen for a number of moves.

I'm pretty sure the following position is a "worst case" winning KQ vs. KQ position for white in terms of the number of moves it takes white to force a winning capture or checkmate.

White to move and (eventually) win:

[Brian-E]

Originally Posted by cuBerBruce

White to move and (eventually) win:

The moves required seem fairly obvious, unless I've missed a defence by Black. The length of the longest line seems to be a series of checks down two files by the white queen to manoeuvre down the board.
1.Kd2+ Kb2 seems to lose quickly: 2.Qb6+ Ka3 (2...Ka2 3.Kc2) 3.Kc2 Qa2+ 4.Kc3.

1...Ka2 forces White to approach down the a and b files with check, for example 2.Qa7+ Kb3 3.Qb6+ Ka3 4.Qa5+ Kb2 5.Qb4+ Ka2 6.Kc2.

Have I missed anything?

[cuBerBruce]

Originally Posted by Brian-E

The moves required seem fairly obvious, unless I've missed a defence by Black. The length of the longest line seems to be a series of checks down two files by the white queen to manoeuvre down the board.
1.Kd2+ Kb2 seems to lose quickly: 2.Qb6+ Ka3 (2...Ka2 3.Kc2) 3.Kc2 Qa2+ 4.Kc3.

1...Ka2 forces White to approach down the a and b files with check, for example 2.Qa7+ Kb3 3.Qb6+ Ka3 4.Qa5+ Kb2 5.Qb4+ Ka2 6.Kc2.

Have I missed anything?

2. Qa7+ is non-optimal, as 2 Qa7+ Kb1 forces the white queen away from the a and b files. 3. Qb6+? Qb2+ draws, so white must play 3. Qh7+. Better for white is to play 2. Qg8+.

Edit: Oh, by the way... If ... 1. Kd2+ Ka2 2. Qa7+ Kb3? then 3. Qxa1 wins.

[Brian-E]

Yes, it's clearly much more subtle than my attempt. White has to watch out for Black's cross checks swapping the queens.

The problem is still open then. Best play needs to be demonstrated after 1.Kd2+ Ka2 2.Qg8+.

[cuBerBruce]

Assuming black's strategy is to keep the game KQ vs. KQ as long as possible, then I get these as the main lines. (I am guessing that table bases might instead assume black tries to avoid mate for as many moves as possible.)

1. Kd2 Ka2 2. Qg8+ Kb1 3. Qg6+ Ka2 4. Qe6+ Ka3 5. Qa6+ Kb2 6. Qb5+ Ka3 7.Qa5+ Kb2 8. Qb4+ Ka2 9.Kc2 Qc3+ 10. Kxc3 (obviously not Qxc3 stalemate)

1. Kd2 Ka2 2. Qg8+ Ka3 3. Qa8+ Kb2 4. Qb7+ Ka3 (if 4 .. Ka2 then 5. Kc2) 5. Qa6+ (and continue as in the previous line)

Of course, black has other options for the 9th move, but baiting stalemate is probably the best option.

My analysis also found this white-to-move position allowing black to keep the game KQ vs. KQ until white's 10th move.
(It found 3 other such white-to-move positions, up to symmetry, but the others immediately go into the same lines as one of these other two.)

[Brian-E]

Originally Posted by cuBerBruce

My analysis also found this white-to-move position allowing black to keep the game KQ vs. KQ until white's 10th move.
(It found 3 other such white-to-move positions, up to symmetry, but the others immediately go into the same lines as one of these other two.)

All very interesting. Can I ask what you were using to find these positions and to ascertain that they are the "worst-case winning positions" of KQ vs KQ? Was it publicly available software or your own written code?

PS About whether table bases would regard the "best" lines for the defence as the ones which avoid mate for as long as possible, I believe they can be used to indicate maximum "time to conversion" rather than necessarily to mate, which in this case would mean maximum time before having to either be mated or lose the queen (converting to KQ vs K).

[cuBerBruce]

Originally Posted by Brian-E

All very interesting. Can I ask what you were using to find these positions and to ascertain that they are the "worst-case winning positions" of KQ vs KQ? Was it publicly available software or your own written code?

I wrote my own code for this. So there could be a possibility of error. But I haven't found any inconsistencies, and I had done the same analysis many years ago, from which I remember the position with everything along one edge as being a worst case position. So I believe it's correct.

Originally Posted by Brian-E

PS About whether table bases would regard the "best" lines for the defence as the ones which avoid mate for as long as possible, I believe they can be used to indicate maximum "time to conversion" rather than necessarily to mate, which in this case would mean maximum time before having to either be mated or lose the queen (converting to KQ vs K).

OK, I just wanted to point out that table bases might not agree with my lines if they (the table bases) were based upon moves until mate.