Yes.
Knight vrs bishop
It all depends on the position.
TheGrobe is correct.
Of course, more can be said, but books have been written on the topic. Any answers offered in the brief confines of this forum will be partial and incomplete.
I can offer two games against the same opponent. Both games were played at correspondence time controls, both featured an imbalance of bishop versus knight. In both cases, my minor piece proved superior--a knight in one game, a bishop in the other.
The knight prevails:
The bishop prevails:
It is wise to not blunder pieces before deciding what is better Knight or Bishop. Both are generally equal and can be exchanged back and forth if the position allows for it. Knight is better in closed positions, and Bishop is better in open positions. The simple fact that it's easier to open a position than to close it lends to the idea that a Bishop has advantages slightly more often than a Knight. Finding an A or B answer is the wrong way to go about playing Chess though, so don't go just kamikazeing your Knights for his Bishops at every opportunity. The "knight or bishop" question is when you're at higher levels of play and have long stopped blundering pieces, made large positional errors, or missed tactical opportunities. And once you get to that level you will have discovered the answer for yourself and that answer will be:
It depends on the position.
Bishops are usually worth about a half point more than knights, but it depends on the position and if you get any compensation. For example, in the exchange spanish, White gives up a bishop pair for the knight and doubeld pawns. Most masters do not like this approach, it trade a bishop for a knight. I try not to make the trade too often, but it really depends on the position
I knew that in the anti-Meran, Kramnik often trades his bishop for a knight very early in the game, so it took me fifteen seconds to locate:
A bishop (a high up clergyman) has taken vows not to fight. A knight (a mounted and armored warrior) is very good in a fight. I would choose the knight for a battle.
I'm making a joke because we have had this discussion dozens of times.
A humorous thought I had while seeing this topic appear again. A list of these topics would be useful in the repertoire of a chess hustler. Throw in a few questions about bishop or knight preferences, ask about the 15 move rule and how en-passant isn't recognized outside of france.... ok not that blatant, just stick to these threads and you'll be a great hustler in no time.
To the OP, their value is very nearly equal. Not nearly as huge as one being half a point more than the other. It's more like one is worth 3 and one is worth 3.001 When these values change (as with any of the relative values) it's because of strategic factors that can't be learned by reading a paragraph long forum post. Just like every one else, it will take you experience, practice, and learning to refine the skill of knowing which is better in a given situation.
Like when Bobby traded his knight for Petrosian's bishop, and the GM spectators scoffed. The move turned out to be correct. This question in the context of specific positions will never be fully answered. In purely general terms though, the answer is they're equal.
sometimes knights are better than rooks; bishops never are. However, most of the time the bishop is better than the knight, although sometimes it is vastly inferior.
Most people prefer bishops over knights, some think that they are about the same, and few people (myself included) think that knights are more valuable than rooks.
In my experience, both peices are equally important, @ReasonableDoubt is right, sometimes the bishop seems more effective but one thing is certain. it is better to play with at least a knight and a bishop on the board than to loose both bishops or both knights.
Is it wise to trade bishops for knights? Please let me know what you think.