Resolved: Bishops are superior to knights in the game of chess.

IntroductionPro's argument is based entirely on the dogmatic "rules" and "general principles" of classical chess theory. At some point around the 1930's, this dogmatism began to change, with Nimzowitsch's seminal text on chess theory, "My System," providing the stimulus for change. In 1927, Alekhine beat the "invincible" Capablanca by playing positions with a pragmatic reliance upon involved calculations rather than on general principles. [1] Alekhine commented that "all general considerations must be entirely forgotten" and "only that which contributes to the execution of the plan selected is of any avail."Today, nearly every single point Pro argues has been disproven by contemporary chess theory and practice, where the concept of "rule-independence" dominates play at the top level. In some positions, bishops are superior, in others knights are superior. With the collapse of general rules in modern chess, saying bishops are superior to knights is misguided, as it contradicts the underlying logic of "rule-independence."The state of general rules is so suspect that Mark Dvoretsky even suggests abandoning the word "plan" (its too general), and using the phrase "next strategic operation," to emphasize the particular, local, time-limited, and pragmatic nature of modern chess play. Discussing the minor pieces (bishops and knights), chess theorist John Watson says, in the seminal "Secrets of Modern Chess Strategy," that "against all odds: championing the steeds." Watson continues, "disregarding the supposed abstract superiority of the bishops, the best modern players are familiar with many types of positions in which knights are acceptable or preferable." Watson then proceeds to analyze a huge number of positions and games where the bishop-pair is ceded for the advantage of having the knight-pair. Steve Mayer agrees, arguing in "Bishop versus Knight: the Verdict," that knights are, on balance, equal to bishops (sometimes superior and sometimes inferior). Throughout the rest of this round, I will show what modern chess play looks like, and why Pro's case is flawed. MobilityAccording to Pro, knights rule closed positions and bishops rule open positions. The reasoning is simple (and wrong): in closed positions, bishops become blocked and inactive, whereas in open positions, bishops "can attack more spaces" because of farther range. I agree that closed positions are better for knights. Pro concedes the point, and it alone should alert readers to the equality of the minor pieces: there are an equal number of closed-position games to open-position games. Thus, according to Pro's logic, knights are superior half the time.Indeed, closed positions are considered the "classical" grounds for taking knights over bishops, in which knights win by creating permanent weaknesses, blocked bishops, crippled pawn structure, and unassailable outposts. No argument here, knights rule closed positions.In modern chess play, however, it is actually the knights who dominate open positions. According to Watson, "if one's goal is to tie down a bishop-pair, it turns out that in practice, one will normally not attempt to lock up the whole pawn structure." Instead, the conventional wisom is reversed: players "control so much space that pawn-breaks are suppressed," and "the attempt to avoid such weakness grants the side with the knights a strong attack." Modern chess play reveals that, in practice, the player with the bishop-pair attempts to slow down play, close and stabilize the position, and then carefully engineer an opening of the position that will emphasize the strength of the bishops. Players with knights, on the other hand, attempt to use knights' native flexibility and tactical reach to create threats and force concessions before the bishops are ready. As Watson says, "breaking in the center, the knights' owner will be able to force enemy pawns to advance, creating permanent outposts for the knight, at which point they are no longer inferior to the bishops, even in the long run." Watson continues, "Chess opening theory is replete with examples of such pawn-breaks for the sake of gaining outposts and/or activity for the kngihts, so much so that they swamp the number of counter-examples in which the owner of the knghts scurries to close the position." Watson concludes, "the side with knights is able to exploit a temporary advantage in order to blast open the position and dynamically achieve concessions from the side with two bishops." Mayer calls the opening of the position for the knight-pair "increasing the speed of the knights," and he refers to the well-known, classic Anderssen - Paulsen (1873) game. [2] In the game, White gives up the bishop-pair; then, White transforms this material imbalance by opening the position, and using his knight-pair to force permanent weaknesses in Black's position. Pro refers to Kasparov, who "implied" that he won a game because of the "bishop pair in a closed Ruy Lopez" (my emphasis). What this suggests, then, is that bishops do better in closed positions than open positions, which completely negates Pro's logic and conclusion. In fact, if we analyze Kasparov's games, every single time Kasparov acquires the knight-pair, he immediately follows with a series of line-opening blows. Take this game [3] as example.The point is clear, as soon as one begins to examine modern chess, one sees the side with knights opening lines in just about every position where bishops are traded for knights. We also see, in modern chess practice, lines in which one side concedes the bishops in order to set up a solid centre. A pawn-break follows, opening the position and creating enough activity for the knights to equalize, or in some cases, even gain the advantage. Examples are the Slav and Caro-Kann defense, both openings used at the top level of play. The Nimzo-Indian defense -- considered one of the strongest openings for Black in response to d4 and c4 -- also takes advantage the knight-pair. Black cedes the bishop-pair after the early exchange on c3, after which Black attempts to open the position and create activity for the knights."Contention 3. The game"a) Pro concedes that knights are "developed faster than a bishop," and that the "bishop pair is worth less than half a pawn when most or all the pawns are on the board." Pro helps me make my case. Thank you, Pro.b) As I've already explained, Pro's understanding of the middlegame is based on classic middlegame manuals, outdated and simply wrong. Pro continues to argue "bishop is better in open positions," but I've already shown that is not the case. c) Pro completely misunderstands the endgame. First, knight + queen is stronger than bishop + queen, according to "Lasker's Manual of Chess." Pro concedes advantage to knights here. Second, Lasker's text (written in 1925) is outdated, and is based on classical "general principles" that have been proven wrong in modern chess. Finally, the endgame alone does not suggest the bishop is more powerful than the knight. The "general rule," in this case relevant, is that knights are better when the pawns are centralized on one side of the board, and bishops are better when the pawn isles are spread across the board. In the sum of positions, the two pieces are considered equal.We conclude: knights are superior in the opening and equal in the middlegame and endgame."The Bishop pair's material value"Pro quotes Kaufman's probabilistic analysis of a database of 300,000 games in 1999. Kaufman's methodology is suspect: it analyzes classical games (before 1930) when bishops were considered better than knights because chess players did not know how to deal with the bishop-pair. It also does not account for the games played since 1999, where chess practice has defintively proven knights equal to bishops. Moreover, Kaufman admits knights are worth "1/16" more than bishops, when considered unpaired.[1] http://tinyurl.com...[2] http://tinyurl.com...[3] http://tinyurl.com...