2 Bishops vs Knight Endgame

wayne_thomas

Move 9 for Black

Your move Nh5

Tablebase   Ne8

The link Liburkin gives in post #4 has both ...Nh5 and ...Ne8 leading to mate in 58 moves.

I just noticed that.  Unfortunately, it's not possible to make a further comparison.  I did a brute force count of the moves a couple of times.  I still get Knight capture on move 51.  I guess we will never know why the difference.

Perhaps both routes lead to mate in 67, the Knight capture just occurs on a different move.

Yeah, I think Black can avoid having his knight captured on move 51 in certain lines.  That's why I had those sublines in my diagram.

 From my perspective, it was an interesting exercise.  I've heard of tablebases, but this is the first time that I've experimented with one.

John Nunn uses tablebases in some of his endgame books.  Sometimes as in this endgame, it's a bit hard to understand the best moves.  White has to let the Black king escape to the centre, and it's not so easy to figure out why one way of doing this might be better than another.

For simpler endgames though, you can sometimes come up with simpler heuristics, like forcing Black's king to the edge of the board, or there are specific positions you can aim for like Philidor or Lolli's positions in R+B vs. R.

With best play, 145 moves. Look on wikipedia

In Fundamental Chess Endings page 20, Muller and Lamprecht claim that the longest win takes 115 moves.

Yeah, I saw 115 also. I also saw 145. Wiki probably incorrect

I also saw that 2 bishops can also win against 2 knights. Is that true?

Lewis Stiller says the two bishops win against two knights in 63% of positions with the longest win taking 38 moves.

http://library.msri.org/books/Book29/files/stiller.pdf

Only 63%, so it's virtually even. That makes sense. In a position where the king is already trapped, or the knights forked, skewered..etc, the bishops can win, but mostly, it's just a solid draw.

Never believe what you read on Wikipaedia. Troitzky said 115, Nalimov says 115. I think they are more reliable. (Even less if it's the side with the pawn that has a win - Troitzky didn't consider those but Nalimov does.)

Wikipaedia says 115 here https://en.wikipedia.org/wiki/Two_knights_endgame#Troitsky_line so if you know where it says 145, perhaps you could correct it. (Just click on edit - you don't need an ID.)

How many Pawns does it take to draw, and WIN against 2 knights?

I think 2 knights can beat up to 4 pawns. Not sure if 5 pawns is a draw or a win for the 2 knights, depending on how advanced the pawns are and the position of the knights. In the position shown above, it said White mates in 146 moves. I'm assuming the 1st move is Nxa7 to eliminate that pawn, so after, is it 145? It said it was from the "Lomonosov" Tablebases

OK, I tried to fix it.

What does that position have to do with it?

EndgameStudy wrote:

"How many Pawns does it take to draw, and WIN against 2 knights?"

To win, the answer would seem to be at least one pawn.

To draw any number between 0 and 8, similarly to lose (but from very few positions with 0).