KNNKP position: can Black avoid a legal Mate?

[ernest]

In the CCC-Forum, I came upon this KNNKP position:

8/k7/8/4Kn2/8/P7/8/1n6 b - - 01


The Nalimov DTM show this is a Mate-in-115, and this shortest Mate-in-115 is indeed legal by the 50-move rule (White pushes his Pawn after less than 50 moves)

Is it possible to search, starting from this given position, if White can hold his Pawn still during 50 moves, allowing a non-optimal (shorter than 115) Mate for Black, but in fact obtaining a legal Draw.

Can the DTZ50 table be of any help? Why and how?

Guy Haworth?
Anybody else?

[guyhaw]

DTM = 115 sounds familiar: maybe the maxDTM figure, or a position from an old KNNKP paper involving JvdH.

wtm draws, and indeed, btm - Black wins in DTM = 115.

The DTZ50 EGT only signals a win if the defender cannot claim a 50-move draw. That's how it helps!

I'll be making my holding of DTZ50 EGTs available shortly so you will be able to check this out for yourself.

g

[kronsteen]

This position is indeed the maximal knnkp position for DTM.

DTZ50 is exactly the metric needed for this problem. I’ve explored a bit the DTZ50 knnkp table (at http://www.chess.jaet.org/endings - the site offered online multimetric access, but unfortunately it is down nowadays) and I’m sure that this position is a 50-move rule draw. That means, white has the resources to last 50 moves without being mated or forced to move his pawn with his king stalemated by black forces. This can be true even if the optimal DTM line has less than 50 moves between all successive zeroing moves.

In fact, some DTZ50 optimal lines are significantly different from DTM optimal lines in this *very* special ending of knnkp. In DTZ50, black often tries to first stalemate the white king at the edge to force a pawn push thus resetting the move counter, then goes back to the normal mate-seeking pattern.

DTZ50 would be a very nice upgrade for the existing DTM tables, giving lines that are absolutely certain to win (albeit non DTM-optimal) without any risk of 50-move rule draws. The ultimate metric would be DTM50 (particularly attractive for knnkp), but the tables would be huge.

[ernest]

The DTZ50 EGT only signals a win if the defender cannot claim a 50-move draw. That's how it helps!
g

Can somebody explain that a little further?...

[kronsteen]

It means that winning positions where the losing side - before being mated - can always force a 50-move sequence without a capture or pawn move are regarded as draws by the DTZ50 table. If you play with 50-move rule it is the DTZ50 table, not the DTM table, who gives the correct result. The above knnkp position is one of these : the DTM table says “mate in 115”, the DTZ50 table says “draw”.