The bishop is superior to the knight.

Pinning, Skewering, and Forking PotentialAs I have already conceded the points, it is hardly necessary to further discuss the issue. However, for the sake of fair play, I will make clarification: the bishop has the merit of ability to perform a pin, a skewer, and a fork, whereas a knight can perform only a fork. These three are all important tactics, giving the bishop and edge over the knight, in this scenario.I reiterate that, while a bishop has the ability to, assuming it is not adjacent (in one of the surrounding squares) to a piece in question, pin either 5 or 6 pieces (it depends on whether you want to call a pinned pawn truly pinned), and skewer 3 pieces (rook, knight, and king), it can fork only 3 pieces. All of this is, of course, overlooking insurance. This means that the bishop can fork less than half of the pieces which it can pin/skewer. The knight, on the other hand, can fork five out of six pieces. Granted, in the aspect of ultimatums, the bishop is far more versatile (an allegorically brilliant and totally unintentional truth). I will address later why the knight's limited ability to make simultaneous threats is not a disadvantage.Checkmating PotentialI won't argue with Edmar Mednis. I will say only that, by my second diagram, I demonstrate that a checkmate with two knights (and, of course, a king) is entirely possible. The issue involved is my opponent's statement, "However, it is impossible to force a checkmate with just your king and two knights," not whether or not competent players would allow such an occurrence to transpire. A skilled player might move his king into the center, when confronted with the given scenario, however, an inexperienced player is likely to perform the superficially superior, though actually inferior, action of moving toward a corner, for shelter. That aside, it is totally irrelevant as to what wild progression of events would be necessary to lead up to such a checkmate. That is not under question.My opponent is correct, that a scenario in which one player has no viable moves, such as the example of my first diagram, is a stalemate. Perhaps it would have been more prudent to say that it is an example of a win with two knights, rather than a checkmate. Of course, whether or not a stalemate should be considered a win is an entirely different (and surprisingly contentious) debate. However, I imagine my opponent would agree with Larry Kaufman, "In my view, calling stalemate a draw is totally illogical, since it represents the ultimate zugzwang, where any move would get your king taken."To answer your late comment "In light of all this, I shall clarify the point I was making: it is impossible to force a checkmate with only two knights against an opponent with a ELO rating higher than 600," this is irrelevant. Your point was not stated as thus, and bringing this up in the last round is just a ploy of desperation.Finally, I wish to point out that first my opponent has demanded that I concede that it is not possible to perform a checkmate with two knights and a king, and then, when I demonstrated how it is possible, he has changed the terms of his original point, attempting to shift the obligation for concession off of himself. However, he was the one that made an unfounded and erroneous demand, and has simply been refuted.I will not dispute the ability of two bishops to perform checkmate. Restating this is just a straw man.Simultaneous ThreatsAs I indicated earlier, I will now address the issue of the knight's limited ability to make simultaneous threats. To refresh the issue, my opponent has stated, rightly, that while bishops can perform pins, skewers, and forks, knights can perform only forks. Now, this looks very bad for knights, however, the mobility of knights must be considered. A bishop can be trapped either by threatening every space of the diagonal it may immediately occupy (for example, if a bishop is located on E1, it may be trapped by threatening D2, C3, B4, A5, F2, G3, and H4), or by enclosing it with pieces that it cannot take (for example, if D2 and F2, surrounding that same bishop, were to be threatened, and to have pieces placed thereupon, it would be unable to move without being taken). The knight, on the other hand, can be trapped solely by occupying or threatening the spaces on which it might land (for example, if a knight were located on G2, occupying or threatening E1, E3, F4, and H4 would successfully immobilize it).These mobility confinements are not a major inconvenience for a bishop during endgame, or even midgame. However, at the beginning, the bishop is sorely inconvenienced, while the knight is at its prime. This means that, for the most part, they are even throughout the game, with the knight reigning in startgame, the bishop in endgame, and both being relatively successful during midgame. Now, since it is my job, according to my opponent, to show not only how the bishop is not superior to the knight, but how the knight is superior to the bishop, I am obligated to point out that the difference is that the beginning of the game determines how the entire game is played out. The usage of the knights during the beginning of the game is a major determining factor in how the bishops may execute victory during endgame. During this part of the game, in which knights are superior, they are so because they can still perform forks, but bishops often can do little more than threaten a single piece.My EvaluationI think both my opponent and I, and hopefully the audience, understand that my invented ranking system was less intended as evidence, and more just an interesting inclusion. My opponent's suggested amendment to it is probably just as accurate and useful (that is to say, neither system is anywhere near perfect).Let us not forget, however, in the face of my improvised ranking method, that, while the bishop controls more maximum boardspace (in an open board), the knight can threaten more pieces simultaneously. I offer the following quantitative data series:Maximum Number of Occupied Spaces Each Piece can Threaten SimultaneouslyPawn: 2Bishop: 4Rook: 4King: 8Queen: 8Knight: 8This is not intended to represent a ranking of the value of each pieces (since it is held, as my opponent points out, by most, if not all, experts that the rook is the most valuable of the three flanks), rather, to simply indicate that the knight is the most versatile piece, when confronted with occupied spaces. It may be limited in mobility, but in another sense, it is liberated (in its unique ability to jump pieces).EndgameI note that, while generally not inaccurate, most of my opponent's assumptions and points are based on endgame function. While endgame is certainly important, it is the beginning of the game that allots the position of each player in endgame, and since knights are perhaps the most valuable piece in the beginning of the game, they are important to the end of it, even if they are often not around to play an active part by the end.I likewise thank my opponent, DakotaKrafick, for his most enjoyable, competent, and intriguing debate on the subject. I hope that some time we may debate again. Good day!