Question: Can you mate with just a Knight + Bishop?

Yes, I didn't see from this point of view!!

On the standard 8x8 board the lone king can be mated if he is confined behind a seven square diagonal of opposite colour to the bishop. He can be mated without ever being allowed to venture to or beyond the seven square diagonal (optimally in fact). These positions will be won on any finite rectangular board with edges greater than 8 if the bishop is the same colour as the relevant corner.

But I think that on large boards almost all positions will be drawn by repetition. The positions behind the seven square diagonals will form a progressively smaller percentage of the total.

For a win the king need not be behind a seven square diagonal to a mating corner. See posts #114(p.6) and #147(p8) in this topic: https://www.chess.com/forum/view/endgames/bishop-knight-amp-king-versus-king , but for twelve squares and beyond I think winnable positions are progressively more rarities than the norm.

Thank you Eric!

Interesting, but I think that the 50 move rule was introduced because of endgames like these on a 8x8 board. Adjusments may probably be made (eg, 75 or 100 moves) for boards of higher order.

Actually Bishop + Knight can force mate against a bare King from any position where B or N are not immediately lost, on boards of any size with a corner of the right color. It might take longer than 50 moves, if the board is large enough. Even KQK would be a draw if the King is more than 50 steps away from any edge. But there is no reason to believe the 50-move rule would apply in variants with larger board. Exactly for that reason. Why would anyone want frequently occurring winnable end-games turn into draws because of a move limitation? The 50-move rule was made to force subborn people into accepting a draw when it is one.

For a few examples on larger board, see for instance: https://chess.stackexchange.com/questions/1432/kbn-vs-k-checkmate-on-nonstandard-boards . The guy there is right; I checked it with my own EGT generator, upto 14x14. From the optimal lines on the larger boards you can see that there is a very interesting general technique to drive up the King along an edge to the corner where you want him, without giving him the chance to ever flee into the open. It is a bit slower than the W method popular on 8x8. (It works there because by the time the bare King has escaped the confinement there it is so close to the corner that it actually runs into the perpendicular edge, and thus gained nothing.)

 Confinement to a triangular area in a corner can actualy be done along diagonals of any length, because you can use dynamic confinement, rather than static. You just need King and Bishop for that. The idea is that when the bare King is next to the diagonal (on a square of the opposite shade), and threatens to cross it, you cover that square with your own King by taking opposition on the side of you Bishop. If he runs further along the diagonal, you follow him with your King.

The point is that reversing the direction in which he is running along the diagonal takes 4 moves before he reaches the point on the other side of your King where he could cross it again. And there is no need to take action before his 3rd move; at that point he still cannot cross, and you move your Bishop to the 'safe' side of your King. The other two moves you can use to approach your Knight (or whatever second piece you have, no matter how weak or slow). Sooner or later he has to reverse, because he reaches the end of the diagonal (where the Bishop is not). Once your second piece reaches the diagonal, you can use it to make that he has to step away from the diagonal to pass it so much that the Bishop can 'tighten the noose'. Through this technique a Bishop can pretty much checkmate in combination with any other piece on boards of any size.

Yes you can

You can checkmate on the edge of the board too...

I did this against my brother. Hope I can find the game... stay tuned.

That's true, it can be done on the edge of the board but only if the opponent makes a mistake. In your example I dont think that counts as edge of the board forced win because the king had to be cornered on a8 first for this to happen. Post number 152 shows a very similar situation. The king was not forced to where it is now from a6 or b6 because it could escape. To be forced to a7 it had to come from the corner.

True, true, I was just making a point, though.

I have faced it WITH the pieces and am 0 - 3 with 3 draws:  50 moves twice and a repetition

it comes up 1 in 6,000 games so why bother I'll take the draw; got better things to learn

too deep 4 me

Probably though if some huckster gets up two pieces on me and completes it (still haven't faced it yet), then maybe just maybe I'll take the time, but as of now I prefer sex sports &rock n roll 

I actually use it as a "drawing technique" in blitz on the rare occasion I can - because I know that there is no way in hell anyone under 2200 will be able to force it in 3/2 time limit. It's hilarious watching them flail about trying to pull it off in blitz. Not a single one I ever came across can. I think once ever many years ago I got really careless and a guy did it though lol, but that was my own fault, I got into a corner somehow, unless I'm confusing it for another situation. 

I also enjoy the irony of attempting to secure my draw by getting a technically lost position. Not a single person lol. 

Really? Just gave me 60 secs and I will checkmate you. 

So I tested vs Stockfish level 8(highest level ) in 60 secs time control. And I checkmated him in 40 secs!! I am 2000+ player, @Uhohspaghettio1, your claim is false! People get 2000 due to hardwork and skill and I defended for the pride of 2000  rated players, lol. 

https://www.youtube.com/watch?v=S3cxKyoDEMc&feature=youtu.be

P.s . Sorry for microphone error

https://lichess.org/TaO50upj#53

I'd just offer a draw and move on I think if I reached an endgame with Knight and Bishop vs King!

I think associating an ability to do it or not with rating though is spurious.  It's basically just memorising a technique and the patterns.  It has very little to do with chess ability in a sense, though obviously people better at chess are more likely to understand the technique.  My point is more though that if someone wants to learn it, then they can. Even a 1200 rated player, if they decide they really want to learn Bishop and Knight mate could do so because there are only 4 pieces on the board to consider.  Most won't choose to do so though, of course.  And on the flip side some much higher rated players simply won't bother to learn it and will fail to work out the technique 'on the fly' in a game.

Your assumption is not correct. Of course there is a possibility that 2100 player cant checkmate with KNB vs K, but the chance is very very small. Meanwhile 1200 player can also checkmate , but the chance is very slim. 

In fact 2100 players have much much memorized shortcuts , patterns to understand chess., and they cant become 2000+ without serious hard work or experience. After learning serious things in chess, KVB vs K become a piece of cake. That is why I checkmated Stockfish Level 8, within 40 secs.

For me, the book I read about how to checkmake was incomplete and flawed, I figured out by myself since my teenage. My tip is here, please check this 3  positions

,,

This is position 1, the main position. Check out how many squares , these two pieces have been covered. There are only a few uncovered squares, that need to be covered by your king and push enemy king. You will need to twist your pieces like position 2.

Position 2 is alternate of position 1, not strong but still bar the king a lot.

Position 3, Failed, Never put your Kt and B in different color..

Now you can see the difference, how easy to become top player in chess with patterns and shortcuts. In other words, no one can be a top player without patterns and shortcuts.

The first chess book I had as a kid included 3 Knights in the core mates!

I completely disagree. The knight and bishop checkmate is difficult, but not THAT difficult. I guess everyone is different. For me the two bishop checkmate is easy, much like the lone rook checkmate or the lone queen checkmate. I think there are much more challenging endgame forced mates, like king and rook versus king and bishop or king and rook and bishop versus king and rook. Draws everywhere but also forced mates everywhere. Those are much more difficult for me.

Bishop and knight checkmate is a piece of cake compared to Queen vs two bishops endgame.

yes