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I have always thought that bishops and knights are of equal value and can be traded off, as I personally prefer to use knights in an endgame I tend to trade my bishops for opponents knights early on in a game. Has it been proven (with whatever wonderful chess programs that are on the market) that one is statistically more beneficial to a game of chess than the other?

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Originally posted by Sicilian Smaug
depends on the position
Yes, but even before a game gets going I would normally trade off in this way, I just prefer the wild and wonderful way a knight moves compared to the drab linear way a bishop does i guess.

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Originally posted by Sicilian Smaug
depends on the position
True.

However, the bishop prevails in more endgames than the knight. The bishop can move without altering the critical position, but the knight can visit every square.

Knights work better with queens, while bishops work better with rooks.

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In a locked-pawn position, knights are vastly superior. Suffered this ignominy several times. ;-)

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Originally posted by cadwah
I have always thought that bishops and knights are of equal value and can be traded off, as I personally prefer to use knights in an endgame I tend to trade my bishops for opponents knights early on in a game. Has it been proven (with whatever wonderful chess programs that are on the market) that one is statistically more beneficial to a game of chess than the other?
As a general rule, in the middle and endgame, knights work best in closed positions and bishops in open positions. However, it really depends upon the layout of the position. To be effective, knights need outposts while bishops need open diagonals. Also, a bishop can become bad if a majority of the pawns are on the same color. In the endgame with spread out pawns, the bishop is generally more effective since it can move from one side of the board to the other much faster than a knight and also can control a longer range of squares. To be effective, knights have to be in the thick of things (like the knights of medieval warefare), while the bishop (archer) can be effective from long range. However, a single bishop does have the disadvantage of only controlling one color on the board; thus, the general advantage of two bishops. Also, note that in the endgame, a king and two bishops vs king can be forced into a checkmate (it is difficult) while a king and two knights vs king cannot be forced into checkmate (although with pawns on the board it can be possible).

For a good reference on bishops versus knights, I would suggest either "The Amateur's Mind" (beginner level) or "Reassess Your Chess" (intermediate level) by Jeremy Silman.

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Originally posted by Sicilian Smaug
absolutely, Game 1816922 4 pawns up here from move 32, but with knight against bishop was a real struggle to not slip up and draw, shows the advantage of having bishop in the endgame against a knight.
The bishop is better than the knight in that example, certainly. Although four pawns are too much to overcome. I wonder, however, why you missed the easier knockout in the middlegame:

White to move

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Originally posted by Sicilian Smaug
Remember black has a mating eye on g2, so i can tmove the knight at that point.

Move 22 b5 maybe, then if Qe4, Re1
I saw a sequence in which the knight can move with security, but there is a better sequence. Your mating threats eventually could have won the queen:

22.Qh8+ Ke7 23.Bf6+ Kd7 24.Rd1+ ( the knight could move here 24.Ne5+ Kc7 25.Bxd8+ Rxd8 26.Qxd8+ Kxd8 27.Nxc6+ Bxc6+-) 24...Kc7 25.Bxd8+ Kb8 26.Be7+ Bc8 27.b5+-

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A general engame rule is that if there are pawns on both sides of the board, the bishop is better (as it can affect both sides at once, or shoot between them quickly). If all the pawns are on one side, the knight is probably better as it can attack both the light and dark squares.

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Bishops have the range - they can quickly move, and can quickly deal with threats....

but they can become somewhat useless - having A black squared bishop with all your openants pieces on white squares mean it wont be that helpful

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Originally posted by cadwah
I have always thought that bishops and knights are of equal value and can be traded off, as I personally prefer to use knights in an endgame I tend to trade my bishops for opponents knights early on in a game. Has it been proven (with whatever wonderful chess programs that are on the market) that one is statistically more beneficial to a game of chess than the other?
I spend a lot of time teaching chess to others, a while ago I summarized the main differences (strengths and weaknesses) of the bishop and knight.

http://blueeyedrook.blogspot.com/2005/12/bishops-versus-knights-general.html

I agree with everyone's sentiments.... which is better depends entirely on the situation.