A Bishop is stronger then a Knight !

I like knights better.

However, a bishop pair is worth more than twice the value of a single bishop.

Not if there's nothing else on the board.

And as we all now know, the key to understanding chess is to look at an empty board! ;)

A knight can deliver smothered mate, a bishop cannot. A well placed knight is worth its weight in gold, a blocked up bishop is worthless. It all does depend on position.

(OK not technically smothered but just as cool)

QxQ Black resigns ... faster!  lol

A horse can carry more weight than a pious man or woman of God ever can

To add to Polar_Bear's comment, all those titles have been stripped off Rybka by ICGA

http://icga.uvt.nl/?p=56

Position is key

Resign? With Rook and two pieces for the Queen? Not a bit of it!

(Mind you, Black's got some wriggling to do, but just losing his Queen isn't reason enough to give in)

i knew at least one wouldn't get the joke

For many players the psychological impact of losing the Queen outweighs everything else lol. 

The whole Bishop v Knight argument has been going on for centuries.  The answer basically is, it depends!  Two Bishops may overwhelm Two Knights or Knight and Bishop in one game, and be biting on granite in another situation.  Take, for example, certain lines of the Nimzo-Indian Defense.  White gets the doubled c-pawns on c3 and c4, and let's say Black has achieved the dark-squared wall, so Black pawns on c5, d6, e5, White pawns on c3, c4, d5, e4.  Now, assuming the quantity of pawns are equal (i.e. White didn't win a pawn on a7, Black didn't win White's a-pawn, etc), give White the Bishop pair, give Black the light-squared Bishop and a Knight.  The pawn on c4 can only be covered by one of White's Bishops.  It can be attacked by BOTH of Black's pieces (i.e. B on a6, N on a5).  Even the White King will have trouble helping.  It can't go to b3 to cover the c4-pawn because of the Knight.  If it goes to d3, it blocks the Bishop, or else the Bishop is stuck in the middle of nowhere on a2.  Black can switch gears, and probably win on the Kingside or with a timely f5 push.  So even though White has the Bishop Pair, Black likely has a technically won position because of that Knight!  So even the Bishop Pair isn't always better than B+N or Two Knights.  Positions from the Chigorin Defense (1.d4 d5 2.c4 Nc6) can often lead to favorable scenarios for Black with Two Knights vs White's Two Bishops.

I read one of the best middlegame books ever written, "Bishop v Knight: The Verdict" by Steve Mayer (Copywright 1997).  It's a MUST READ if you really want to understand the ins and outs of the minor pieces.

For example, it often takes a number of tempos, and inititating a trade, to achieve the Bishop pair.  The initiator of any trade always loses a tempo.  So the player that got the Bishop Pair will often be 2 or 3 tempi behind in Development, so the player with the Knights should be trying to increase their speed by gaining tempi via maybe hitting other pieces on the way, and posing threats.  Doing that could get a Knight on c3 over to the Kingside really quickly, like if Nc3-e4 hits a loose bishop on d6, Black moves or protects the Bishop and White hops over to g5.

This, along with many other valuable ideas, are all covered in that excellent book!

Great observation TF

Generally:

(with plenty of exceptions)

Knight's advantages: better in immobilized and compact pawn structures, better cooperation with queen (and king too, btw)

Bishop's advantages: better with mobile and distant pawns, better cooperation with rook, cooperation with own next bishop (of the opposite color - pair)

Knight's disadvantages: can have problems with opponent's distant free pawns, quite often can't make neutral move and kill a tempo this way (so-called "zugzwang")

Bishop's disadvantages: can't change color, can become seriously limited by own immobile pieces or opponent's cooperating compact pawns

So - who is stronger, bishop or knight? It depends which side is played by Karpov.

It's amazing that two pieces so different, actually the antithesis of each other, can find themselves balanced on the chessboard. It's really an example of how great of a game chess is.

I was thinking, it's probably not a case that the chessboard is 8x8. If it was larger, let's say 10x10, then long range pieces would be more powerful and the bishop would always have a decisive advantage over the knight.

"And when there is no Position, such as in the first two Diagrams, the Bishop is by Objectivity Stronger than the Knight.
By Objectivity/Static piece Value, the Bishop is ALWAYS Stronger than a Knight, The Rook is ALWAYS stronger than a Bishop, and the queen is ALWAYS stronger than the Rook."

I don't understand how you can use the lack of a position to determine "objective value" of a piece.

For one thing, if you don't have a chess position, having a queen is not a lick more useful than having a bishop.

You see, if that Queen was a rook white would win. Now it's just a stalemate.

Conclusion: a Rook is more powerful than a Queen.

No, the queen is more powerful, it's just that sometimes, it gives you more power than you wanted!

EDIT: Probably better not to post current games at all.