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

MARattigan
torrubirubi wrote:

Capablanca's board is 10 x 10, perhaps the future of chess. Funny that in this variant check mate is easier and quicker - we could expect the opposite of it.

Mate on a 10x10 board is typically neither easier nor quicker (and less often possible I believe). Mate on a 9x9 board is easier so long as your bishop is the colour of the corners, because there are mating corners in all directions and the lone king is never more than four moves away from one.  

torrubirubi
MARattigan wrote:
chadnilsen wrote:
...

Why don't you play games on chess.com? Chess.com is the BEST.

Because I'm a rubbish chess player. Look at my rating.

How is your rating? Play some games and you soon will find it out...

torrubirubi
MARattigan wrote:
torrubirubi wrote:
MARattigan wrote:
torrubirubi wrote:
chadnilsen wrote:

I still haven't figured out how to do it from a random position. And so far, this is the only "edge" position I've seen! I'm getting tired of this exact position! It isn't that easy to get the bishop and knight onto those two squares...

From a random position: move first slowest pieces, towards the enemy king. This means, move first the king to the center, then the knight to the centre (and pushing the enemy king with the king and knight as far as possible), and at the end you come with the bishop. You will be probably in the wrong corner, so you will have soon the setup to bring the enemy king to the other corner.

I would disagree with much of that.

It is generally unnecessary to move the knight and sometimes also the bishop, but if the intention is to exclude the lone king from the centre a knight in the centre is not very effective. Also if the lone king is played correctly (as opposed to accurately) the lone king will refuse to go to the wrong corner from the great majority of positions. A computer program with an attached EGTB will almost always move his king to the wrong corner in preference to abandoning the wrong diagonal, but the EGTBs do not play the lone king in this endgame correctly. See my post #116 in https://www.chess.com/forum/view/endgames/bishop-knight-amp-king-versus-king  

If the player with the knights wants the quickest mate he should look to permanently exclude the lone king from the wrong diagonal at the earliest opportunity rather than actively seeking to manoeuvre the king to the wrong corner. This can be done from the middle of the wrong diagonal in some cases.   

I don't try to make the quickest mate, but I chose a mate that makes sense for me and is therefore easier (for me). I learned two  different systems, but know I tried only the method showed in the book "100 Endgames You Must Know". You can train it by spaced repetition in Chessable. The method described is rather straightforward:

"1 ) Transferring our king to the centre, to drive the black king off.

2) Transferring the knight to the centre as well, since it is a short-range piece.

3 ) Pushing the black king to the edge, where he will head for a corner opposite to the bishop's colour (otherwise, checkmate comes sooner). We will call this corner a Safe Corner. Here, it is the a8-square.

4 ) Our king occupies a square on the long diagonal opposite to the corner (here, the c6-square). We will call this spot the Pivotal Square.

5 ) The knight drives the black king off the Safe Corner from c7 or b6.

6 ) The bishop drives the black king off the square adjacent to the corner from a7 or b8.

7 ) We force the black king to a corner of the bishop's colour (Mating Corner) by means of an accurate manoeuvre. We will give more details when the moment comes.

8 ) The black king is locked in the cage. (you have to buy the book to see what the author means with this).

9 ) The white king stays a knight's jump away from the corner (f7 or g6). We will call this spot the Mating Square.

10 ) We arrange the checkmate, which will come by two consecutive checks, one with each piece.

The execution of Step 7 requires special attention."

 

 

As I said, I prefer to learn the whole thing with spaced repetition, so I will memorize all the steps and review them from time to time.

 

It's a reasonable overview as these things go but step 2 I think is misguided as mentioned previously and step 3 begs a few questions such as, "What if he doesn't want to go?" and "What if he heads back out again instead of heading for the wrong corner?".

I had intended some changes to the Wikipedia page for this and looked at several possible sources. The great majority of positions are what I've called "open" positions where the lone king can reach the wrong diagonal but neither in the manuals nor games could I find any extended accurate play in these positions, nor anything but the kind of generality in 3. Most agree that you should use all your pieces to drive the king to the edge or sometimes wrong corner, but it doesn't translate into accurate examples.

I worked out my own (mindless) method when I first learned the ending which works from any won position but is not necessarily optimal. I would recommend that approach rather than reading.

These days I practice against the Nalimov EGTBs with the aim of reaching the DTM (as either colour). It's not necessary to play the ending but I'm hoping to come up with a similar mindless method of mating optimally this year. 

 

By the way if you're not interested in optimality you can also dispense with 7. From the wrong corner you can reach Delétang's first net in a few moves, so if you want to learn a method that would probably be more useful. Philidor's method and similar are only methods of driving the king from a wrong to a right corner. 

Actually I just learn this mate because chess culture, and also perhaps to learn more about this specific coordination of pieces. I only played twice this ending. The first time with king alone, and my opponent said it is a forced draw, I said he is wrong, so I took his side and won (it was easy for me, as he went first to the wrong corner, and was trying always to go back there, who make things easy for me). The second time I was again with the king alone, but the guy was not able to mate in 50 in a blitz. I didn't spend much time working out the details of this ending, and I just hope to be able to mate when I have the opportunity after learning the system proposed in the 100 endgames-book.

eric0022
chadnilsen wrote:

Your rating is 800 because you haven't played...

 

Therefore, we can say that MARattigan is undefeated in all time controls and game formats on Chess.com so far.

eric0022
torrubirubi wrote:
eric0022 wrote:

How about on a 12x12 board (or even higher dimensions)?

Why?

 

 

Just purely out of curiosity.

Piperose

This is one of things I'm determined to have competence in 50 moves and less.

torrubirubi
eric0022 wrote:
chadnilsen wrote:

Your rating is 800 because you haven't played...

 

Therefore, we can say that MARattigan is undefeated in all time controls and game formats on Chess.com so far.

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

MARattigan
eric0022 wrote:
torrubirubi wrote:
eric0022 wrote:

How about on a 12x12 board (or even higher dimensions)?

Why?

 

 

Just purely out of curiosity.

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.

MARattigan
[COMMENT DELETED]
MARattigan
eric0022 wrote:
chadnilsen wrote:

Your rating is 800 because you haven't played...

 

Therefore, we can say that MARattigan is undefeated in all time controls and game formats on Chess.com so far.

Thank you Eric!

eric0022
MARattigan wrote:
eric0022 wrote:
torrubirubi wrote:
eric0022 wrote:

How about on a 12x12 board (or even higher dimensions)?

Why?

 

 

Just purely out of curiosity.

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.

 

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.

HGMuller

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.

Shubhamo7

Yes you can

Kwolverine04

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

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

lfPatriotGames
Kwolverine04 wrote:

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.

Kwolverine04

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