2 Bishops vs Knight Endgame

How does white force mate? I read that it could take up to 78 moves.

What is this?

For the longest time, it was assumed that Black could exchange his knight for a bishop, leading to draw by insufficient material. But with the advent of tablebases, it was found that White can force the win except that in many (most) cases it takes more than 50 moves, a draw by the rules of chess. See this site to try it out: http://k4it.de/index.php?topic=egtb&lang=en

This is a perfect example of why the 50 move shouldn't exist. It shouldn't be a draw just because it takes a long time to win. A win is still a win. That's what happens when you get yourself into a losing endgame, u end up having to defend for a very long time! U face a long, slow, but sure destruction...

the 50 move rule would haunt my thoughts every move...is it possible to win in 50 moves with perfect play....im crazy and would study the technique....last month I studied the KBN vs K position with both colors....both bishops...and pieces spread everywhere....there was a time I had a whole crowd watching my otb game and I had a knight and pawn queening vs bare king and wish I coulda promoted to a bishop and give em a show....I am able to do it now confidently but I wont practice unless I know its worth it....or maybe I will try vs fritz now

I witness an expert in my club choke the bishop and knight and wasn't able to deliver mate within 50 move rule. That is why every expert should learn this mate and once learned you never forget it.

The king+Bishop+Knight endgame can always be forced in under 40 moves from the worst positions with perfect play. It is also easy. However, the 2 Bishops vs Knight endgame can take up to 66 moves from an average position with BEST PLAY! That's not even giving anyone a chance to win in those positions. It's an automatic draw in that case because you are saying that it takes over 50 moves, but there's still a win. It should be increased to 100 moves for those endgames to give the winning side a chance to checkmate.

When you say 66 moves, is that on an 8x8 board or a 9x8 board?

According to Nalimov the maximum mate depth on an 8x8 board is 157 plies - Black to move and White needs 78 moves to mate. E.g.:

8*8 obviously. A tablebase said that. Even 78 moves is well over 50 moves. That is, assuming the capture of the black knight is after move 50.

Also according to Nalimov, the maximum black to play mate depth in KBBK is 39 plies, so the position I showed can't be won within the 50 move rule. There is online access to the Syzygy DTZ50 databases that will tell you about the position you posted. If you can't find it I will fish out a link.

That's exactly why the rule shouldn't exist. A won position shouldn't be a draw because it takes a long time to actually force mate. These are what make chess so complex and interesting, and the 50 move rule ruins it.

BTW, it also depends on what move the knight is taken (if at all), but that's besides the point.

It does depend in the position you showed but not in the maximal position I showed because in the latter the arithmetic can't work. The Syzygy databases would answer both. 

If Black plays accurately then clearly any mate by White that doesn't involve the capture of the knight would be a draw under the 50 move rule in both positions.

I think White tries to herd both the Black king and knight into a corner, and then cut the knight off.  Black is probably trying to keep his king and knight close together, so he won't need to worry about forks or skewers, but the tough part for White is herding them into a corner without letting them come back out.  I think even in the fastest lines, Black's king escapes out to near the centre a few times first.

I totally agree.

There must be many people that put in a lot of time acquiring the technique to win from KNNKP positions that exceed the 50 move rule limit, in the time when the 50 move rule was waived for this endgame, only for FIDE to render the effort useless by reimposing the 50 move rule limit.

But some limit is needed. You don't want to hang around for ever while someone persists in trying to mate your lone king with two knights, or even while they wander aimlessly about the board trying to mate it with a bishop and knight without making any progress.

I think the limit should be based on the maxima already calculated for positions with up to 7 men together with an extrapolation to higher numbers of men. This would make it approximately infinite in the middle game, but the 50 move rule is hardly ever invoked in the middle game anyway.

Regarding the 50-move rule: It has become clear that there is no great way to figure out the maximum number of moves that should be allowed to win a "won" endgame. Consider this position:

Endgame tablebases show that in most open positions, the B+R win over N+N. On this particular example, the Distance-To-Mate (DTM) is 151 moves. Should the rules of chess be changed to allow the shortest DTM + X moves (X moves to allow for fallible human play)? Seems like there is no one good answer...

Just looking at that position I would never guess it's 151 moves. It seems to me in this modern computer age the rules could easily accomodate the couple dozen (or however many it is) endgames that require more than 50 moves to mate. Golf is undergoing it's biggest rules change since the 1700s. 300 years is a long time, but long overdue. The purpose is to accomodate modern players and make the activity more enjoyable for the average person. I dont see why chess cant make similar rules changes and allow these rare endgame possibilities.

It should be at least 100 moves. Endgames like 2 Knights vs Pawn, can take up to 145 moves (the pawn will probably move) but anyway. BTW, 2 knights vs king will be declared a draw by the director.

At one point, FIDE allowed more moves for the longer mates. They reversed course and went back to the previous rule and added the 75 move automatic one.

edit: I see someone has already posted about it. Guess I should read the whole topic first