The bishop is superior to the knight.

No need to apologize. I realize how frustrating that is (I tried to use photos as well, and ended up having to remove them because of the formatting problems).The Most Important PieceTrue, the king is the most important piece, but in terms of actual merit, which, for all practical purposes, is what is being debated here, the king is typically only ranked 4, with the queen as 8 or 9, and the rook often as 5 or 6. [3] This logically adds up, since, if the bishop is ranked 3, the rook 5 or 6, since the queen is a combination of the two, it makes sense that the queen be ranked 8 or 9. The king has been ranked as a 4 by noted authorities such as Lasker and Evans, due to its limited but omnidirectional mobility, and ability to castle, and, what's more, a computer program designed to evaluate chess pieces concurred. Other than that, the king is often ranked by an arbitrarily high number, to indicate ultimate value. However, this is not practical to our debate, and thus unnecessary.Forks, Pins, and Skews, Oh My!Bishops are highly limited in forking potential due, as I have said, to their limited mobility in a crowded board, and their concern for reciprocal strike. While one can indeed attempt to protect their bishop with insurance, not all players place value on insurance, and have no qualms about taking a bishop that controls part of the board.I do concede that the bishop has an advantage of potential to pin and skew, which a knight lacks. However, this potential may be extremely hampered, as this is dependent on how clear the board is, and can be easily diverted with pawns. A knight's fork is not so easy to hamper, as the very nature of a fork is that to protect one piece, one must sacrifice the other. A knight may even fork more than two pieces at once, and can technically fork up to six pieces at once, though such occurrences are extremely rare.Quantitative EvaluationInsurance aside, each piece has a limited number of pieces that it may take without concern of reciprocity.Pawn: 2Bishop: 4* (two of these four are capable of retaliating, if adjacent)Knight: 5Rook: 4* (one of these four is capable of retaliating, if adjacent)Queen: 5* (two of these five are capable of retaliating, if adjacent, and two of these five are capable of retaliating, in certain circumstances)King: 5* (four of these five are capable of retaliating, if adjacent, in certain circumstances)Now, the knight is obviously the oddball of this bunch, being the only piece that can take 5 other pieces with no reciprocity whatsoever. This gives it a decisive advantage. Now, let us evaluate the maximum number of spaces that each piece can control simultaneously:Pawn: 2Bishop: 13Knight: 8Rook: 14Queen: 27King: 8Now one method of estimating relative value of each piece can be estimated, excepting exceptions, by dividing threat capability by risk:Pawn: .5*Bishop: 6.5Knight: 8Rook: 7Queen: 13.5*King: 8*(*exception)These values are referred to as 'attack ratio,' giving the amount of the board that can be controlled by each unit without fear of reciprocity, per average. Yes, I did invent this ranking strategy, and it's very obviously unconventional, but I seriously doubt my opponent will contest its relevance or its competence. If he will, well, I welcome it!Now, by my improvised ranking system, the knight is 1.2 times as valuable as the bishop. Not much, I'll grant, but it is able to control more of the board without threat than is the bishop.Checkmating PotentialMust this point be conceded? It is, in fact, possible to perform checkmate with naught but a pair of knights. Difficult, perhaps, but possible.If formatting will permit, this image should demonstrate how the Two Knight Checkmate is possible: If not, know that if the opposing king is on A8, and the knights are placed on C6 and either C5 or D6, the king has no viable moves, and, if there are no other pieces to move, the king is placed in indirect checkmate. This next image depicts how, if one makes use of one's king, two knights may create an alternate checkmate (Black king A1, white knights A3 and C2, white king B3): Sources[3] http://en.wikipedia.org...