I am an absolute beginner--but I tried to get an understanding of the
bishop & knight checkmate--perhaps too difficult for a beginner.
Every website I found said "drive the king to an edge and then move
him to the right corner" with no clue as to how to start. I couldn't
get this to work, I followed their examples, but they made no sense
and had long lines with confusing "what if he does this", so I finally
came up with the following technique that I think is easy for
beginners like me (who rarely beat computers at a level 1 ply)--I am
wondering if this is a "normal method" and what the grandmasters here
this of this method. The basic concept is secure a diagonal with
bishop and king, get reinforcement with the knight, and then drive the
king to the next diagonal. With this method I am never at any point
guessing, and I practiced it a few times and can consistently beat the
computer playing on instinct (sometimes 15 seconds to make sure I can
seize a diagonal or if escape is possible).

It is true I do have to still memorize the magic positions for the
knight, but just think, "what position plugs the most holes in the
diagonal" and it will be easy to come up with. Basically, this method
is totally strategy, not a lot of memorization or trying to look four
moves ahead at all points.

Lets say I have a black bishop.

Step 1. Put the knight on B2 (or g7)--Easy enough for a beginner.
This keeps him out of the way for the start, and if you opponent
chases the knight, you can let him while you secure a diagonal and
then retreat you knight "just in time". He will be so deep into your
trap that you have plenty of time to secure the first diagonal if he
chases after the knight.
Step 2. Get the king and bishop to the center. Now, use the bishop
and king to either drive the king to a wrong corner (a8 or h1), or he
will step across the diagonal of a7-g1. If he steps across this
diagonal, I secure it with the bishop and king. He can only either go
to the wrong corner or step across this diagonal; this driving process
is not difficult, but may take a little practice. Often Arasan steps
across this line without realizing its fate, but it does have rather
strong instincts to go to the wrong corner.
Step 3. Keep the diagonal secured until your opponent reverses the
king, which will inevitably happen when he hits into an edge, and
sooner on a clueless opponent. This will give you two moves in which
to move your knight into position. I found that with him on B2, I can
get him into position in two moves regardless of which diagonal is
stepped across and which spot I want him, and I have two moves to
spare when my opponent reverses, but bishop and king control of a
diagonal does keep both men on their toes and will require some
practice.
Step 4. When the opportunity arises, put the knight at d6 or f4 if
the king stepped across the a7-g1 diagonal. If he stepped across the
b8-h2 diagonal, place him c5 or e3 (6 and 4 away from the corner).
This will block most of the diagonal from the king's escape. For this
discussion, I will place him at d6, but mirror images or rotations are
also valid, of course.
Step 5. Now that the knight is blocking the king's escape on this
diagonal, use the bishop and king to push him up the diagonal until he
reaches a4 or b4. I have found it best to "get under" the king, that
is get on a lower rank if you are pushing him up; get to the left of
him if you are pushing him right, etc. Then, move the bishop to b6 to
prevent him going all the way to a5. If the opponent is clueless as
to what you are doing and crosses the A5-F1 diagonal, you can box him
in tighter, but be careful; if he has an escape, you may have to start
completely over, or at least retreat and lost 10 moves. If he gets to
a4 or b4, the bishop on b6 prevents him going further up the diagonal;
he can't retreat because your king is there; he is forced to cross the
a5-f1 diagonal, at which time the bishop moves to a5, and with the
help of the king, keeps him confined on this diagonal while the knight
is brought to d4. After the knight is at d4, the bishop is placed at
B4. Then the king is easily confined. I can force him easily with my
king to as tight as a1,b1,a2,b2.

Step 6. Get your king on c2. If the opponent goes into the a file,
this is trivial, but if he hangs onto b1 and b2, I use a little help
from my bishop, get my king on c2, and retreat the bishop. This
requires fleet-footedness on the part of the bishop, but is not
difficult.
Step 7. Finish off the mate in four or whatever it is while the king
is confined to the corner two squares.

If the king makes it all the way to the wrong corner, I pry him across
the diagonal with my knight and then go to step three. I actually
have a shortcut memorized at present from trying to get this working
and looking on the web, but I will forget the shortcut, but this
technique uses strategy, not just memorization, and I have found that
even without using the shortcut and going to step 3, I still fit
within the 50 moves, barely. Shortcuts will be forgotten, strategy
will remain.

Now, with this method, there is no guess work and all moves can
basically be done by instinct. Here is a sample against Arasan with
comments--this game was easily won and played just for this post.

Start: 1B5N/8/8/4k/8/8/8/7K w - - 0 1

Computer plays black, I play white, white to move--Here is the *.pgn
file.
1. Nf7+ Kd5 2. Nd6 Kc6 3. Nc4 Kb7 4. Be5 Kc6 5. Nb2 Kd5 6. Bh8 Kc6
7. Kg2 Kb6 8. Kf3 Kb7 9. Ke4 Kc6 10. Be5 Kc5 11. Bf4 Kb6 12. Kd5 Kb7
13. Bd6 Ka7 14. Kc6 Ka8 15. Na4 Ka7 16. Nb6 Ka6 17. Bb8 Ka5 18. Nc8
Kb4 19. Ba7 Kc3 20. Kd5 Kd2 21. Ke4 Kc3 22. Nd6 Kd2 23. Kf3 Kc3
24. Ke2 Kb4 25. Bb6 Kc3 26. Bc5 Kb3 27. Kd3 Ka4 28. Bb6 Kb4 29. Kd4
Kb3 30. Ba5 Ka4 31. Bd2 Kb3 32. Kd3 Ka2 33. Nf5 Ka3 34. Nd4 Kb2
35. Kc4 Ka2 36. Bc1 Kb1 37. Ba3 Ka1 38. Kb3 Kb1 39. Nb5 Ka1 40. Bc1
Kb1 41. Bd2 Ka1 42. Be3 Kb1 43. Na3+ Ka1 44. Bd4# 1-0 {White mates}

Comments:
First four moves position the knight on B2, except one move to safety
for the bishop
Up to move 10, I move my king and bishop to the center; I keep the
bishop out of harm's way until a king is closeby
At move 14, he is in the wrong corner; the bishop and king were
always where if he stepped over the line, I could seize the diagonal,
but Arasan chose to go to the wrong diagonal. Now, some sites I found
show a memorized sequence to finish him off quickly from this point,
but for the sake of demonstration, and because I will forget these
moves, I continue with my plan; get my knight over to force him out.
At move 17, the bishop is both blocking retreat and waiting for its
chance to secure the diagonal.
19--diagonal secured, knight one jump away from the magic spot.
20+21--Chasing the king; he backtracked; obviously Arasan was
clueless to what I was doing, so I get the knight in; worst case if he
would have gone all the way to g1
21-30--I use the bishop and king to seize the next diagonal.
I don't need the king to confine him on the diagonal because of the
knight, so the king helps push him. I am sure the grandmasters here
could have done it better, but it is now secured. His king wants my
bishop, but I am not worried; the knight is keeping him contained and
moving the bishop to safety is easy.
33+34--I observe Arasan is well enough contained because it
didn't understand what I was doing; I easily moved my knight into
position. Now, the rest is getting my king into position for the
final mate, a little fleet-footedness of the bishop helps get him
there.
39--A tempo adjusting move; the knight is no longer needed at D4, but
I want my bishop at D2, but can't do it right now.
42--Another tempo adjusting move, mate in two.

Anyone seen a method like this?--I used 44 moves and likely could have
reached 50 if the computer had fought me harder, but I would rather
risk 44 moves on an easy method and have something to work with than
be clueless if I ever need this checkmate.

[snip]


Start: 1B5N/8/8/4k/8/8/8/7K w - - 0 1

This position is illegal.


Computer plays black, I play white, white to move--Here is the *.pgn
file.
1. Nf7+ Kd5 2. Nd6 Kc6 3. Nc4 Kb7 4. Be5 Kc6 5. Nb2 Kd5 6. Bh8 Kc6
7. Kg2 Kb6 8. Kf3 Kb7 9. Ke4 Kc6 10. Be5 Kc5 11. Bf4 Kb6 12. Kd5 Kb7
13. Bd6 Ka7 14. Kc6 Ka8 15. Na4 Ka7 16. Nb6 Ka6 17. Bb8 Ka5 18. Nc8
Kb4 19. Ba7 Kc3 20. Kd5 Kd2 21. Ke4 Kc3 22. Nd6 Kd2 23. Kf3 Kc3
24. Ke2 Kb4 25. Bb6 Kc3 26. Bc5 Kb3 27. Kd3 Ka4 28. Bb6 Kb4 29. Kd4
Kb3 30. Ba5 Ka4 31. Bd2 Kb3 32. Kd3 Ka2 33. Nf5 Ka3 34. Nd4 Kb2
35. Kc4 Ka2 36. Bc1 Kb1 37. Ba3 Ka1 38. Kb3 Kb1 39. Nb5 Ka1 40. Bc1
Kb1 41. Bd2 Ka1 42. Be3 Kb1 43. Na3+ Ka1 44. Bd4# 1-0 {White mates}

Comments:
First four moves position the knight on B2, except one move to safety
for the bishop
Up to move 10, I move my king and bishop to the center; I keep the
bishop out of harm's way until a king is closeby
At move 14, he is in the wrong corner; the bishop and king were
always where if he stepped over the line, I could seize the diagonal,
but Arasan chose to go to the wrong diagonal. Now, some sites I found
show a memorized sequence to finish him off quickly from this point,
but for the sake of demonstration, and because I will forget these
moves, I continue with my plan; get my knight over to force him out.
At move 17, the bishop is both blocking retreat and waiting for its
chance to secure the diagonal.
19--diagonal secured, knight one jump away from the magic spot.
20+21--Chasing the king; he backtracked; obviously Arasan was
clueless to what I was doing, so I get the knight in; worst case if he
would have gone all the way to g1
21-30--I use the bishop and king to seize the next diagonal.
I don't need the king to confine him on the diagonal because of the
knight, so the king helps push him. I am sure the grandmasters here
could have done it better, but it is now secured. His king wants my
bishop, but I am not worried; the knight is keeping him contained and
moving the bishop to safety is easy.
33+34--I observe Arasan is well enough contained because it
didn't understand what I was doing; I easily moved my knight into
position. Now, the rest is getting my king into position for the
final mate, a little fleet-footedness of the bishop helps get him
there.
39--A tempo adjusting move; the knight is no longer needed at D4, but
I want my bishop at D2, but can't do it right now.
42--Another tempo adjusting move, mate in two.

Anyone seen a method like this?--I used 44 moves and likely could have
reached 50 if the computer had fought me harder, but I would rather
risk 44 moves on an easy method and have something to work with than
be clueless if I ever need this checkmate.

If you adopt the policy of always resigning this ending (playing either side), the net impact on your rating on average will be less
than 1 rating point amortized over time. It has little to do with your strength as a player. I've never encountered the ending in a
tournament game of mine and very rarely in blitz. It is one of the least important endings one could ever study. It probably occurs
less than once in a thousand games.

I've heard people say that learning how to play this ending will teach them how to handle minor pieces in the endgame, but it won't
do this because the ending is so abnormal (no pawns and the opponent has zero pieces against your 2).

Practicality is an important consideration if you want to be a strong player. In any case, despite the issue of practicality, I
suspect you are fascinated by the ending for reasons similar to those of mountains climbers have about Everest. All I can say then
is good luck!

I've made similar points to students -- I'd much rather they spent the same
amount of time on crucial rook and pawn endings, because they are much more
likely to occur in their games. In 30 years of tournament play, I've never
come across this ending. As a 2300 rated player, I'm not sure I could win
it if I did (although I think I probably would). Still, I also agree that
chess is a fascinating game, and there is nothing wrong with studying and
analyzing aspects of the game that interest you.

Randy Bauer

"Ricardo Gibert" wrote in message
news:Rht6c.38711$Zp.34493@fed1read07...

If you adopt the policy of always resigning this ending (playing either
side), the net impact on your rating on average will be less
than 1 rating point amortized over time. It has little to do with your
strength as a player. I've never encountered the ending in a
tournament game of mine and very rarely in blitz. It is one of the least
important endings one could ever study. It probably occurs
less than once in a thousand games.

I've heard people say that learning how to play this ending will teach
them how to handle minor pieces in the endgame, but it won't
do this because the ending is so abnormal (no pawns and the opponent has
zero pieces against your 2).

Practicality is an important consideration if you want to be a strong
player. In any case, despite the issue of practicality, I
suspect you are fascinated by the ending for reasons similar to those of
mountains climbers have about Everest. All I can say then
is good luck!

Its a tedious win and requires concetration with so little pieces. The key
is to drive the Black King into a dark colored corner then keep him from
moving far from it, then you have to time your check with each piece so that
the King is driven to the remaining dark colored corner square where he can
then be mated. You have to literally drive the King to the corner (he won't
go willingly), corral him, then box him into his 2 squares, then its
important to check the King on the light colored square 1st, then the dark
square to complete the mate. Its not easy at all because you have to make
sure there are no escape routes for the King while doing this. I didn't
actually read this in any books, but I was able to see it after some trial
and error. I setup the pieces almost like your example, except the Black
King is not starting out in check. Maybe with refinement these moves can be
shortened, but I don't know that for sure. If you can see the principles of
how this works it will make it easier to play later. Protecting your own
pieces while doing all the above is of course essential.

It could go like this.

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "1B5N/8/8/3k4/8/8/8/7K w - - 0 1"]

1. Kg2 Kc6 2. Kf3 Kb7 3. Be5 Kc6 4. Ke4 Kb7 5. Nf7 Kc6 6. Kd4 Kb7 7. Kc4 Ka8
8.
Kb5 Kb7 9. Nd6+ Kc7 10. Bf4 Kb8 11. Kb6 Ka8 12. Ka6 Kb8 13. Nc4+ Kc8 14. Kb5
Kb7
15. Nd2 Ka8 16. Nc4 Ka7 17. Kc6 Ka8 18. Nb6+ Ka7 19. Bc7 Ka6 20. Bb8 Ka5 21.
Nd5
Ka4 22. Be5 Ka5 23. Bd4 Ka6 24. Nb4+ Ka5 25. Kc5 Ka4 26. Be5 Ka5 27. Bc7+
Ka4
28. Kc4 Ka3 29. Nd3 Ka4 30. Nc5+ Ka3 31. Kc3 Ka2 32. Kc2 Ka3 33. Ba5 Ka2 34.
Bb4
Ka1 35. Nb3+ Ka2 36. Nc1+ Ka1 37. Bc3# *

Robert Richter wrote:

The basic concept is secure a diagonal with
bishop and king, get reinforcement with the knight, and then drive the
king to the next diagonal.

Looks like the method described he

http://bobbyfischer.net/bnvk.html

Claus-Juergen

Claus-Jürgen Heigl wrote in message ...
Robert Richter wrote:

The basic concept is secure a diagonal with
bishop and king, get reinforcement with the knight, and then drive the
king to the next diagonal.

Looks like the method described he

http://bobbyfischer.net/bnvk.html

Claus-Juergen

OK, so this method is used somewhere else. I thought it easy enough
to be taught to people. I am wondering if the worst case exceeds 50
moves with this method.

As far as the starting position being illegal, it may be illegal
because after I mated, I noticed the *.pgn file had all black moves
first instead of white; I put black with the bishop, knight, and king,
but since the pgn file was backwards, I switched around the initial
starting position and said "I played white" but thought I modified the
file correctly; then I said I played white. Or, maybe I used the
wrong starting file compared to what I used in Arasan, as I have
numerous starting positions for this mate as I was trying to figure it
out.

This method on the Bobby Fisher site shows nets much similar to this
technique, so it apparently is a legitimate method. Anyway, I felt
kind of proud of myself for even getting it to work, especially when I
am a beginner and the web makes it appear that the only person to be
capable of such a mate would be Kasparov.

I never rate myself or play in tournaments. I simply found that my
style of play can no longer be to catch my brother in the middle game
unaware--he can smell checkmates now; I must go clear to the end and
strip him of all his men now, and I found by reading the web that
bishop and knight can mate, but couldn't make heads or tails of the
examples on the sites I found. I have not bought any good books or
taken formal lessons.

Also, where can I buy a chess timer? I think I want one that is
electronic with an initial time and a time bonus per move.

I am now trying to learn how to pick off a rook with a queen. I don't
know if I will ever figure this one out; after I get this one, I will
learn how to pick off the bishop, and then the knight. Maybe I should
start the other way around.

Can a lone queen pick off two bishops, two knights, or one bishop and
one knight; assuming all pawns on both sides are stripped?

PS. The two bishop mate is also wacky on the web--the bishops are out
in the middle under constant attack by the king. I found that with
the two bishops perpendicular to an edge and against the edge, they
protect each other from the enemy king and my king can concentrate on
securing another diagonal instead of keeping them under protection;
the web examples are very disorganized on this mate, too.

"Ricardo Gibert" wrote in message news:Rht6c.38711$Zp.34493@fed1read07...
[snip]


Start: 1B5N/8/8/4k/8/8/8/7K w - - 0 1

This position is illegal.

You're right; I wonder why Arasan didn't object to that, and why I
didn't see that, but it did get out of check on its first move, so
apparently, you need the starting position after my first move and his
first move if your chess program is objecting.

"Randy Bauer" writes:

I've made similar points to students -- I'd much rather they spent the same
amount of time on crucial rook and pawn endings, because they are much more
likely to occur in their games.

In my opinion, that's not the point of studying KBNk. I view it as
analogous to what are called "small-sided games" in soccer. The key
skill being developed is the ability to visualize, and use, interactions
between the piece. Coordinating N and B is a crucial skill in the
opening and middlegame - but it's hard to distill those positions to the
point where the N+B interaction is obvious to the student.

A player who has studied KBNk will play better openings and middlegames.

Of course, R endings come first! but...I think the right reason is
*understanding* how the pieces work together, and NOT memorizing classic
positions and the cookbook methods of winning/drawing from those positions.

--
Kenneth Sloan
Computer and Information Sciences (205) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/

"Ricardo Gibert" wrote in message news:Rht6c.38711$Zp.34493@fed1read07...
[snip]


Start: 1B5N/8/8/4k/8/8/8/7K w - - 0 1

This position is illegal.

I corrected the check problem and tried again. Arasan doesn't have a
Visual setup mode; I entered this position in with Window's Notepad
and never noticed the initial check. I move the king over by one.
Here is another sample game; this time, Arasan stepped over the line
before his king got to the wrong corner; Arasan stepped over at move
13, so I instantly seized the diagonal. For some reason, it appeared
more clueless on this checkmate than the usual fight it has given me.

1B5N/8/8/3k1/8/8/8/7K w - - 0 1

[Event "?"]
[Site "?"]
[Date "2004.03.19"]
[Round "?"]
[White "?"]
[Black "Arasan 7.3"]
[Result "1-0"]

1. Nf7 Kc6 2. Ng5 Kb7 3. Be5 Kc6 4. Bb2 Kc5 5. Ne6+ Kd6 6. Ng7 Kd5
7. Kg2 Kc6 8. Kf3 Kd5 9. Kf4 Kc6 10. Ke4 Kb7 11. Kd5 Kb6 12. Ba3 Kc7
13. Bd6+ Kb6 14. Be5 Kb5 15. Bd4 Kb4 16. Ne8 Kb3 17. Nd6 Kc2 18. Ke4
Kb3 19. Kd3 Kb4 20. Bb6 Kb3 21. Ba5 Ka4 22. Bd2 Kb3 23. Nf5 Ka4
24. Nd4 Ka3 25. Kc4 Kb2 26. Kb4 Ka2 27. Bc1 Ka1 28. Kb3 Kb1 29. Bd2
Ka1 30. Nb5 Kb1 31. Na3+ Ka1 32. Bc3# 1-0 {White mates}

Comments:
1-6: Position my knight for springing into action when the time
arrives.
13: An idle move forcing the king to retreat because I didn't want to
move my king, but rather than retreat into the wrong corner, he
crossed the line here.
15: Diagonal secured. Arasan makes it easy by not making me chase
his king, so I have time to position my knight.
17: Knight positioned (two move was all I had, but he was
conveniently positioned to get there in two moves); Arasan's King
almost escapes, but my king can still reach him in time.
18-21: Arasan was clueless; seizing the next diagonal wasn't even a
challenge, but it has been a challenge at times when trying to master
this mate. Main problem here is watching out for the stalemate where
his king, my bishop, and my king are lined up perpendicular to an
edge; Arasan has caught me unaware a few times on this.
22-23: I notice that the only escape is out b5, but my knight will be
into its new position and block this escape in time, so I don't try to
block it with my king; it's safe to move the knight--Arasan attempts
the escape, but is driven back when my knight is in the new position
on the second knight move.
25-29: No difficulty confining the king to the corner two squares,
after which he is shortly mated.
29-32: Mate finalized.

"Kenneth Sloan" wrote in message ...
"Randy Bauer" writes:

I've made similar points to students -- I'd much rather they spent the same
amount of time on crucial rook and pawn endings, because they are much more
likely to occur in their games.

In my opinion, that's not the point of studying KBNk. I view it as
analogous to what are called "small-sided games" in soccer. The key
skill being developed is the ability to visualize, and use, interactions
between the piece. Coordinating N and B is a crucial skill in the
opening and middlegame - but it's hard to distill those positions to the
point where the N+B interaction is obvious to the student.

A player who has studied KBNk will play better openings and middlegames.

I'm baffled as to why you would think this is true. I'm an NM who can very easily win this ending with less than 30 secs on the
clock and I can assure that playing this ending well is of negligible benefit to playing the opening and middlegame better. I
understand your point about "small-sided games" and I agree that the study of chess in such "chunks" is useful, but this particular
ending is not effective in that way.


Of course, R endings come first! but...I think the right reason is
*understanding* how the pieces work together, and NOT memorizing classic
positions and the cookbook methods of winning/drawing from those positions.

--
Kenneth Sloan
Computer and Information Sciences (205) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/