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

PrefacePro's single overarching argument is that modern chess theory/practice is not superior to classical chess theory/practice, and that "classical strategy is still utilized by grandmasters." True, modern chess does use strategies from classical chess, but modern chess only does so when a particular position calls for it. The modern concept of "rule-independence" still dominates the decision-making process, and the chosen strategy is always dependent on the pragmatic analysis of positions, not on the blind application of general principles (otherwise known as the classical approach). Reading over Pro's reasoning, I have to admit I was somewhat shocked by Pro's explicit misunderstanding (assuming it was not intentional misrepresentation) of the facts. Particularly laughable was Pro's characterization of today's top players, Kasparov, Carlsen, and Kramnik, and Pro's blatant equivocation between "positional" chess and "classical" chess. KasparovWhen Kasparov compares Carlsen's "positional" style to Karpov and Capablanca, it is to differentiate Carlsen from tactical players like himself, Alekhine, and Tal. Pro takes the quote out of context to conceal the reference to tactical chess. To clarify: positional play places emphasis on strategic, long-term characteristics of the game over direct tactical attack (I take the definition from Pro's discussion of Kramnik). Notice at once that this has nothing to do with differentiating between bishops or knights, and is practically irrelevant to our debate. What's more, Pro equivocates by claiming that positional chess is the equivalent of classical chess. Ironically, it was theoretically-inclined positional players (Nimzowitzh, Reti) that first used rule-independence as the primary variable in the evaluation of positions. CarlsenPro claims Carlsen plays classical chess. Utterly absurd. In a recent interview, Carlsen says, "I don't have any clear preferences in chess. I do what I think circumstances require of me." Carlsen continues, "Having preferences means having weaknesses." [1] We couldn't ask for a better definition modern chess, directly from Carlsen himself.KramnikAgain, Pro equivocates, claiming that Kramnik's self-characterization as a positional player makes him a classical player. Pro's claim is nonsense. Kramnik is well-known as a paradigm-shifting player, the leader of the "Pragmatic School" [2], the only player to take Kasparov's world-champion title away.In response to losing, Kasparov described Kramnik's style as "pragmatic and tenacious," further evidence of Kramnik as the leading exemplar of modern chess and rule-independence. [3] As such, Kramnik's revolutionary play can hardly be called "classical," and Pro's fantasy that "positional chess" is "classical chess" is just that, a fantasy based on faulty reasoning and insistent equivocation.Alekhine and EuwePro cites Euwe's The Development of Chess Style as an example of "classical strategy," and implies that classical chess is superior to modern chess because Euwe beat Alekhine. First off, it is obvious that Pro has not read Euwe's book. Euwe's book is the first text offering a historical analysis of chess style, tracing the "shift in paradigm" from Philidor's chess theory, termed "Romantic" chess, to Steinitz's "Classical" chess, to Nimzowitsch and Reti's "Modern" chess. The development is shown as a paradigm-shift, in which earlier theories and practices are replaced by newer theories and practices in the same way science progresses. Refutations are discovered and solutions proposed. Euwe thus distinguishes the Romantic era, where "concern was not for sober truth... only for beauty" (pg. 12), from the Classical era in which "truth" was discovered through guiding "classical principles," and finally the Modern era, where refutations to these principles led to the adoption of more and more principles, with "an exception to every principle" (pg. 15). Euwe's book ends short of today's "Pragmatic" era of Kramnik, Leko, Anand, Carlsen, Aronian, but the progression is obviously towards the emancipation of chess from rules and principles in favor of pragmatic analysis that unpacks the particularity and uniqueness of every position. Think about it: why else would we play chess if we had it figured it out? Chess is an ever-evolving game that constantly defies our expectations because of its inherent complexity, each position requiring its own novel evaluation and decision-making process. To even suggest that bishops are superior to knights completely undermines the progress in chess theory, from the Romantic to the Classical to the Modern to the Pragmatic. Horowitz BishopsI did not respond to this because I thought it was implied in my discussion of the bishop-pair and knight-pair. Also, Pro's definition of "Horowitz Bishops," which is a term I have not seen in the theoretical chess literature (not once, I'd be surprised to see a reputable source behind it), is easily turned: because bishops rely on being paired for their power, as soon as a bishop is exchanged, the other bishop is stuck on one color and easily becomes inactive and powerless relative to the knight that can switch between colors. MobilitySo now, let's be generous to Pro and, for the sake of argument, grant Pro that classical chess is correct. Hypothetically, just for the sake of argument... It still does not follow, given classical strategy, that bishops are better than knights. Take mobility, for example. Every piece has an ideal position in which its mobility and activity is best exemplified. Bishops have more range and mobility than knights in a very limited set of positions (when they are unblocked by pawns and other pieces). Kights, on the other hand, can move over pieces, giving them a clear mobility advantage in closed positions. Pro concedes this point.Furthermore, a knight can attack a total of 8 squares, and can move in every direction of the board, whereas bishops can only move (in an ideal situation where they are unblocked) to 7 squares, and only in two directions, diagonally. If you really think about it, bishops are far more limited: bishops cannot go through pieces, they move to less squares, in less directions, and are stuck on one color. Mobility advantage clearly goes to knights. OpeningKnights are better, Pro conceded this point. Pro's example of the Kings Indian is actually an example in favor of knights: it is an opening where White's knights take the early advantage, but Black pins hopes on a late-game bishop (on g7) advantage when the position opens up.MiddlegameSee Round 2.EndgameSee Round 2. Turn Pro's argument: knight + queen is stronger than bishop + queen. When queens are exchanged, knights and bishops equalize. Pro's faulty logic assumes (for now reason) that bishops become stronger on exchange of queens.Material ValueKaufmann's analysis is flawed. First, it ignores "draws," which account for the majority of games. Second, victory/defeat, as a criterion of "truth," is not theory-laden. Lost games are more often attributed not to theory but to particular bad moves, and Kaufmann's analysis ignores that. Finally, his results demonstrate statistically negligible difference between bishops and knights. Pro concedes the point, so no point arguing it.ConclusionAccording to Federico Garcia, "there is no way that a non-modern player has any success in modern chess." [4] The reasoning is obvious: modern chess has developed pragmatic responses to every strategy in classical chess, so that where a classical player would be unable to handle the pragmatic strategies of modern chess, a modern player would have no problem whatsoever in dealing with a classical player. In modern chess, knights and bishops exist in unstable equilibrium, their value changing depending on the position, and the distribution of positions favoring neither. Resolution is negated.[1] http://tinyurl.com...[2] http://tinyurl.com...[3] http://tinyurl.com...[4] http://tinyurl.com...