{"id":1698,"date":"2024-02-27T19:10:32","date_gmt":"2024-02-27T18:10:32","guid":{"rendered":"https:\/\/skolasachu.com\/?p=1698"},"modified":"2024-02-27T20:55:52","modified_gmt":"2024-02-27T19:55:52","slug":"the-computers-bishop-or-knight-places-known-positions-in-a-row-dots-above-and-chess-trainers-have-gained-wrinkles-on-their-foreheads-1","status":"publish","type":"post","link":"https:\/\/skolasachu.com\/en\/strelec-nebo-jezdec-pocitace-stavi-v-rade-znamych-pozic-tecku-nad-ia-trenerum-pribyly-vrasky-na-cele-1\/","title":{"rendered":"Bishop or Knight? Computers put the finishing touch on a number of well-known positions\u2026 and coaches have grown more worried (1)"},"content":{"rendered":"

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\u201eThe worst bishop is better than the best knight,\u201c a classic player supposedly said once. However, this bon mot may have a rational core, and when we examine the texts and opinions of those who are now classics for us, we at least begin to consider the problem. The following article can be understood both as a supplement to my old work Bad Bishop \u2013 Reality, Dogma or Chimera?, which received considerable attention many years ago, and also deals with new perspectives on the issue. The corrections introduced by computers may be shocking for many readers.<\/p>\n

A bit of geometry and the absolute value of pieces<\/span><\/strong><\/h4>\n

Almost every beginner\u2019s book contains a chapter or mention of the so-called absolute value of individual pieces. (Curiosities, such as Capablanca not dealing with this \u201ainferiority\u2018 at all in his books \ud83d\ude42 or that the queen\u2019s value oscillates between 9 and 10, we will leave aside for now.) Few authors, however, warn beginners that the value of pieces is given in pawn units, but these are natural numbers\u2026 rounded. Steinitz <\/strong>was categorical in his works: the absolute strength of the knight<\/strong> he evaluated with a decimal number 3,05<\/strong> the pawn, the bishop<\/strong> however 3,50<\/strong>! Perhaps an innate thoughtfulness led me to the idea of how proficient the first world champion was in mathematics and whether he derived decimal values from the geometric movement of pieces on the board plus constants reflecting the bishop\u2019s main disadvantage\u2026 In any case, what we see in the working diagrams below is valid, and probably needs no further comment.<\/p>\n

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Note: my speciality is not the education and training of children under 10 years old, yet it has paid off for me to test them, for example, on propositional logic. Children have to judge without looking at an empty chessboard whether a statement is true, for example: \u201eA rook on an otherwise empty chessboard can reach anywhere in at most two moves.\u201c \u201eA knight can reach anywhere in at most six moves,\u201c and finally a \u201atrick question\u2018: \u201eA bishop can reach anywhere<\/strong> in at most two moves.\u201c \ud83d\ude42<\/em><\/p>\n

Wilhelm Steinitz wrote roughly the following about the bishop and knight issue<\/strong>: Bishop<\/strong> \u2013 masters and authorities have different opinions on the relative value of this piece. Some clearly prefer the knight in the endgame and claim that combined with the queen and rook the knight is stronger than the bishop. After careful study and analysis of typical positions and excluding some exceptions on both sides, we have come to the conclusion that the strength of the bishop<\/strong> in solving practical tasks in mathematical expression exceeds the strength of the knight<\/strong> in all three phases of the game. This also applies to most situations involving the cooperation of other pieces. The tremendous power of the bishop, especially in cooperation with the other bishop, in attack and also in defence was first systematically and thoroughly demonstrated in practice by the great German master Louis Paulsen.<\/span><\/p>\n

For defensive purposes, it is generally recommended to have the bishop on the colour of squares where we have (or will be blocked by) our pawns. Especially if they stand on different diagonals. For attacking aims, the bishop is better placed on the colour of the opponent's pawns. The advantage will be particularly evident when trying to break through the enemy pawn chain using our own pawns.<\/span><\/p>\n

The superiority of the bishop over the knight is also evident from the fact that a bishop placed on any square of the board can control at least seven squares on one or several open diagonals. In the centre of the board (squares d4, e4, d5, e5) it controls 13 squares. On the other hand, the knight's influence can be reduced to controlling only two squares if it stands in the corner. At most, a knight controls eight squares.<\/span><\/p>\n

We have already referred to the great power of two cooperating bishops earlier.<\/span><\/p>\n

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A pair of bishops \u201eerases\u201c the only disadvantage of the piece itself, namely the prohibition of entering the alternative reality \ud83d\ude42<\/em>\u00a0in the form of squares of the opposite colour. By controlling a maximum of 26 squares, they almost match the most powerful piece! Bishops standing next to each other or on neighbouring diagonals are called Horwitz bishops.<\/em><\/p>\n

They are slightly stronger than a knight with a bishop and significantly stronger than two knights. Two bishops and two pawns are considerably stronger than a rook and a knight. A bishop is stronger than three pawns.<\/span><\/p>\n

Knight<\/strong> - a knight copes well with its basic role of \u201esearching for and occupying holes or weak squares of the opponent\u201c. Especially when supported by pawns. A knight is usually only slightly stronger than three pawns. It has another interesting property: it is usually stronger than a bishop in the endgame in cases where the opponent has doubled pawns and cannot get rid of this disadvantage.<\/span><\/p>\n

Piece values in absolute numbers - knight = 3.05, bishop = 3.50<\/strong>.<\/span><\/p>\n

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The first world champion demonstrated the superiority of the bishop in many games even decades before the official title was introduced and before he wrote his fundamental works! The first classical example of demonstrating the power of the bishop over the knight strikingly resembles the following \u2013 contemporary one. Does today's young generation draw experience from these classical games? The second fragment of my favourite young super-grandmaster will at least partially answer this. The reader who takes this contribution as a serious subject for study should also notice the verbal remarks. The Prague native<\/strong> <\/em>in the above text did not make it up<\/em><\/strong>!<\/p>\n

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