White to play and mate in 21.

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MARattigan
Arisktotle wrote:

Of course, there is the little issue of what the "mating phase" exactly constitutes. Roughly I would say the last 8 moves or the black king being locked in his final corner.

Note that these principles fully apply to your post #1. Once the pawn is blockaded, it remains so until 4 moves before the mate. I never stated that the blockade had to start before (or on) the Troitsky line.

I may be losing track of the conversation here.

My comments regarding lifting and reinstating the blockade related to your paragraphs:

I am not sure what you are saying but it is clear to me that the Troitsky line must be associated with a blockaded pawn. Otherwise the pawn would just keep on pushing until it is over that line (as far as it can).

And obviously that blockade must be lifted at some point, since you can't mate the king with just one knight. But that's when we entered the phase of the checkmate count-down.

By "that blockade", I assumed you meant the blockade referred to in the rule (on or behind the Troitsky line), and by "the phase of the checkmate count-down", I assumed you meant the point (should it exist) where a blockade is removed without further hindrance to the pawn's progress other than checks on its king.

In #1 "that blockade" would then refer to the blockade shown in the diagram (with the pawn on c7) and "the phase of the checkmate count-down", assuming accurate play by both sides would begin 4 moves before white checkmates.

But if white is to win against accurate Black defense in #1 he must lift the initial blockade on move 1, which is not in the checkmate count-down, so I don't agree with the final paragraph of the post. The lifting of this blockade is also not in the mating phase as you have defined it.

Incidentally, the Black king's final corner referred to in your definition of "the mating phase" need also  not exist, even in White won positions. There are forced mates in this ending where the Black king may finish on any of the squares on the rook's files or White's first rank with the exception of White's king and queen squares. (There are also forced mates on c8/f8 but only from illegal starting positions.) It is the case that from the vast majority of White won positions the Black king will finish up either in a corner or on c1/f1 (with accurate play by both sides). The squares b1/g1 could also be counted as "respectable", e.g. the mates in 11 position I posted earlier.

 

Arisktotle

hm, one of those days where my comments mysteriously disappear. Do it again when I feel like it.

MARattigan

Sorry, that was probably me inserting the previous post. I've lost a couple that way as well.

MARattigan

OK I see what you were saying now. I think you intended the phrase "that blockade" to refer not only to the specific blockade referred to in your previous paragraph, but also to any subsequent blockades, and yes, the lifting of all blockades would generally begin the "checkmate count down".