But, you CANNOT force mate if the opponent with the K+p knows enough endgame technique to avoid those positions by simply separating the K from the p and just giving it up.  Then there is no mate.  It is mostly when the opponent with the K+p tries to get more from the position by attempting to queen the pawn that he gets in trouble.  If he knows endgame technique he knows that those positions are rare and it is best to just take the draw.

Yes its about the fiftieth time its been said, people still comment how impossible it is. It is VERY UNLIKELY BUT POSSIBLE. TROITZKY LINE.

And Troitzky was famous for "ta da", endgame studies.  How many times is a game you are playing going to result in some esoteric endgame study position? 

It is too easy to demonstrate that you're wrong.

http://www.k4it.de/index.php?topic=egtb&lang=en

You can play around with that all you want. It would also do you some good to read the first page of posts. Natalia posts a link to a wikipedia article on the Troitsky line. It's not just some "ta da" endgame study.

Could you please tell the title of the post, article or blog.  It will save me alot of searching since you seem to know where it is.

Never mind I found the Wikipedia Article.  The article states very clearly that if and when the pawn can be stopped on or before the "Troizsky Line" then checkmate can be forced. But, It text goes on to say:  "...If the defender's pawn is blocked on or before the "Troitzky line", the stronger side can force checkmate, although it may require up to 115 moves with optimal play..."

With the 50 move rule in effect for USCF and FIDE rated tournaments, why would a tournament player be concerned with this endgame.

It is similar to the endgame K+2Bs v. K+N.  In that one which was thought to be a draw for some 300 years, it has been discovered by computers that it is a forced win for the K+2Bs, but it requires some 200 moves to reach checkmate.  Once again the 50 move rule is in effect.  Tournament players don't care except as an interesting fact that a position that was thought to be a draw by Troitzky himself turns out is a forced win for the 2Bs.

I wouldn't be surprised considering that Troizky was wrong about the K+2Bs v K+N, that he might be wrong about the K+2Ns v K+p and one of these days a computer will find that it is a dead draw.

For practical purposes tournament players say, "IDGARA."

I believe K+2B vs. K+N requires at most 70-80 moves with optimal play from both sides, but I'd have to check, and it still exceeds the 50 move rule anyway. For K+2N vs. K+P, it depends on the position, but playing around with the tablebases there seem to be plenty of situations where the 50 moves aren't exceeded with optimal play. Both sides wouldn't play optimally in a tournament setting so mate might be achieved faster or slower than the optimal line of play, or maybe not at all. In a tournament game I would try to play for the win with the two knights, because you can hardly lose and it's a very rare endgame to get the opportunity to play.

I doubt this endgame is worth studying given it's rarity. I don't think I'm even going to bother with it. It's still somewhat interesting though.

@browni3141: Well, check out the Second Trompowsky Line to see which positions are less than 50 moves till mate. The endgame has little practical use, but understanding the ideas will help your chess.

Hm, I sense a contradiction in there somewhere...