The value of pieces that I been led to understand is this -- Queen 9 points, Bishop & Knight both 3 points, rook 5 points, pawn 1 point...as far as advantages go I think that both the bishop & knight each have their own properties & as far as  strengths go with each, it really depends on the situation.

i have known this: queen 9, bishop 3 and both 6.5, knight 2.5 and both 6,  rook 5 and both 10.5, and pawn 1...but despite of these quantitative values i think the real value dependes of the posisition on the board and in wich part of the game youre movig each piece...in the opening the rook practically have no value, even doesnt have so much value until the endgame i think, and for example, bishops and knights have much value on the openings, and the pawns collect their value from the midle to end game!

Hi Vernal, I always thought the bishop was worth one pt. more than the knight, but I imagine the real value is dependent upon the player and which he is best with.(or maybe more comfortable with)...when I play I consider the equal depending on the situation...See you on the board...Glenn

 Vernal, these links might help.

http://www.chess.com/forum/view/game-analysis/knight-or-bishop

http://www.chess.com/forum/view/game-analysis/bishops-or-knights?lc=1

http://www.chess.com/forum/view/general/which-piece-is-the-best-knight-or-bishop?lc=1

I read these discussions and worry that i'm the only person not capable of calculating the value of my position to 3sf. 

IN MY OPINION THE BISHOP IS EVER SO SLIGHTLY STRONGER, BUT LIKE WHAT HAS BEEN SAID I SUPPOSE IT DEPENDS ON THE STATE OF THE GAME.

I find i like the knight better obviously depending on the situation. The queen can do the same diagonal moves as the bishop whereas the knight has something different to offer 

Generally speaking the values of the pieces are such that Queen is 9, Rook is 5, Bishop and Knight 3, Pawns are 1 and the King is infinitely valuable as it is the piece that when captured wins the game.

Generally the Bishops are held with slightly more value than the Knights but as has been said several times it depends on the position on the board. If the game is a very closed game or one such that the bishops can't move then the Knights become more effective. The flip side is a very open game where the Bishops can move freely. Additionally if there is only one Bishop and the opposing pieces are placed on opposite colored squares then that Bishop isn't nearly as effective.

Pawns start out with a value of one but as they progress to the other side of the board they increase in value because of the potential for promotion.

I learned my chess mostly from old timers and they always told me not to trade bishops away for knights unless I had a position that called for it, like a soon to be checkmate or the exchange brought me into a line where I would win material. 2 bishops beats every other pair of minor pieces, I was always told, so keeping your bishop pair intact for the endgame was something you strove for. Winning with knights in the endgame can be a little trickier than winning with bishops so novices should try to retain their bishops, or so I was taught. 

Ok remember that the Bishop and Knight are strong pieces but with different characteristics and depending on the board position, there is a time when one will have a slighter higher value than another.

 The bishop is a long range piece. It  has the ability to jump form one side of the board to the other side of the board quickly but despite this it does have some disadvantages. The first disadvantage is that you have 2 bishops that cover different colors of the board. One bishop covers the white square while the other covers the black squares. Lose one of them and you can no longer attack half the colors of the board.

 The second problem with bishops is that they can be reduced to passivity if they are on the same color as your own pawns. While being on the same color allows the bishop the option of guard duty when necessary, it also might prevent it from being active if the bishop is behind the pawns instead of in front of your own pawns.

The knight is a short range piece and usually you need to provide with support points where the knight can move and be effective. If a knight is attacked, it can not simply go several squares back to get out of harm's way. It needs to find places where it can land and be effective. Thus the old adage of "Knights on the brim are dim".

Knights do have an interesting advantage over bishops in that they are constantly changing both the color that they are on as well as the colors that they are attacking. By this I mean, lets say we have a knight that is on a white color square right now. The knight is attacking squares that are dark colored.

Now lets move the knight and the complete opposite from the previous position exists. Now instead of being on a white square, the knight is on a dark square. Instead of attacking dark squares when it was on a white square, the knight as a result of moving is on a dark square and attacks pieces on white squares.

 Thus no piece is 100% completely safe from a knight since the knight is constantly changing properties. The bishop is restricted to covering whatever squares it started with. If my enemy's king is on a dark square and i only have one bishop that rests on white squares, I can never directly attack the enemy king with my bishop.

Hope you find  that helpful 

Hi John. Whilst playing a coaching game on ChessWorld I was told off for giving away my pair of bishops (I swapped one for a knight early). One thing I've learnt is that in an endgame with pawns on both sides of the board, the bishop is usually superior, as it easily covers squares on both sides of the board, whereas a knight has to shuffle around more. Thanks for telling me about the site, Nick.