Which piece is powerful? Bishop or Knight?

Knight in the early middlegames and the bishop almost everywhere (exp. the endgame where there are pawns on both side of the board, kings and bishop only). Bishops in open games, knights in both. Both are useful in sacs. And lastly, depends upon your choice, management skills as well as OF COURSE, THE SITUATION!!! 

ponz, you wise old bird, I am sure you are right about the 0.17 bit but when I learned I was eight and I had not heard of decimal points - it was three-and-a-half versus three-and-a-quarter

I doubt that. I think queen, the first lady holds the key to victory and is most powerful....

you can checkmate with 2 bishops but not 2 knights, (well you can if your opponent is really dumb...)

not necessarily, as mentioned before it depends on the position.

take this example:

http://www.chess.com/forum/view/fun-with-chess/chess-game-based-riddle

the pawn promotes to a knight which is checkmate, if it promoted to the "all powerful" Queen then it isnt ;-)

The answer to the question is that the Bishops are better at the very start of the game by maybe .07. However after the game progresses a very short time the values of the Bishops and Knights goes up or down depending on opening and Pawn structure.  For example the dark squared Bishop in the Benko Gambit is a very strong piece and its value has gone up.  However the 3 other Bishops--one on the black side and two on the white side have gone down in value.

I normally favor knights over bishops because it is the knight can fork pieces the easiest because any piece can not be right next to it.

It depends on the position and pawn structure.If the game is open the bishop are more powerful because it can move faster than the knight.In a closed position the knights are better because they can hop around the board to find outposts for them.

Q: On an open board knight and bishop can move fluidly around the board. Why is a bishop favored?

A: The bishop can move a lot faster than the knight on a open board. Think:It would take longer for a knight to get to the other side of the board than a bishop.

Q: On a closed board it is really hard to move. Why do they favor knights?

A: Knights can hop around the board and find outposts.If bishops are found in a closed position they are stuck until it clears up.

I did it this way to show that it depends on what position it is at all times.

Yourchess, what you say is correct to a point but not completely.  What opened my thoughts a little was ponz's (sorry to praise you twice old guy, I wont make a habit of it) observation of the black bishop in the benko, where the other 3 identical pieces diminish.  Thats a nice thought.  One other train of thinking would be for example an open Sicilian where there are seven pawns each on the board - the knights are great and the bishops have great potential.  This is not a closed position but the large number of (fluid) pawns favour the knight as the position is still better for their maneuvers, despite the fact the bishops get to make great sweeping moves like Bc4 and Bg5 for white.  I think there is room for a lot more thought on this and certainly do accept the old closed knights/open bishops argument but there is more to it than that.

Bishops and knights are both worth about the same. However, in general, the bishop pair is worth .5 pawn. This means that voluntarily trading a bishop for a knight without any other compensation is giving up some material advantage. 

THEY ARE BOTH EQUAL IN BOARD POINTS

In bullet - a knight

Online - it depends...on the position, on the player, on the amount of pawns, if the opponent has an opposite colour bishop etc.Talking in terms of points is, well, pointless.

I used to believe that a bishop for a knight was favourable,but time and again i have lost out in the late middle and endgame especially against a pair of unpredictable knights vs knight and bishop;the bishop can be made almost irrelevant by position,where the knight easily adapts and repositions.Having said this i still feel better with bishops on the board for myself,but spend a lot of my precious time watching and trying to predict the vector of my opponents knights.An open question!Interesting to note that only the low value knight can hit the queen without being itself in danger from that queen...

sometimes Knight will be better than Bishop when K play wtih Queen, however playing with Bishop is comfortable when exist rook, i said that by experience 

Neither. The Queen is!

Usually when someone exchanges a Bishop for a Knight early in the opening, they get something in exchange like a better pawn structure.

Knights are better in closed position, Bishops like opened ones.  It depends whether you need an arrow or a dagger.  Try to create a position for whatever minor piece(s) you have or plan on having to give yourself the advantageous imbalance. 

I recently played the type of player who likes to trade Everything As soon as possible. I was happy to trade as the center was void of pawns and I had 2 Bishops against 2 Knights. he managed to double pawns from queen trade.. Somehow my fianchetto'd Bishops became useless against the knights.. I was Suprised to see how devistating they can be. Im used to restricting their movement with bishop and then killing.. Maybe I became to comfortable and lost sight and the win.. This guy I play always does the Ruy lopez... takes knight every time.. and likes to develop on the rim.. how do I lose :/ Help a Noob out :D

:D

First of all, I think you meant to ask "Which pieces is more powerful?". 

To answer the question..... there is none.

Both pieces have their own weaknesses that the other can exploit. In a practical game, knights are good "wetboys" while bishops act like cannons to break castles. However, that's only one example.