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When the pieces captured on a point represent higher value than the pieces lost in the struggle on that point, the attacker achieves an advantage on that point. Most often the number of pieces captured shows how much of an advantage the attacker has achieved, but not always. If the K is checkmated the attacker may sacrifice any number of pieces to achieve that outcome, and still end up ahead. And a Q and sometimes a Rook are of so high a value that capturing them is sufficient compensation for the loss of several men. If the pieces involved in attack and defense are of equal value, the player must count the number of threats directed against a point, in order to decide whether the attack against the upper point has succeeded in gaining the upper hand or not. Even if the attack achieves a worthwhile advantage it may not be the best strategy to make the attack immediately. The attacker may bring additional force to bear on the stationary weakness and end up with an advantage as well, but he must not strike while he maintains this advantage. And he must consider whether the reserve force which he can use against the weakness is as great or greater than the reserve force which the defender can bring up in the same time. The conception of value is therefore bound up with that force, which again implies effect and weakness. You may change the rules of chess, enlarge the board, increase the number of men, vary their degree of movement, do all this to any extent and yet the above reasoning will apply. This concept shows that we have something which is useful beyond the narrow limits of chess for the mac chess and PC. In life we have to judge men, actions, chances and risks, and this can be difficult at times. The ordinary standard is that of “usefulness,” but one has to be wary in its application. In the position White K on KR6, P on KKt7, Black K on KR1, B on KKt1, Q on KB4. The pawn checkmates and is therefore more useful to White than the Q and the B are to Black. Yet a Pawn is very much weaker than Queen of Bishop. Possibly Black in allowing this situation to arise has committed a serious mistake, or else it has been brought about by Whites sacrifice of powerful pieces. For instance, the P had been on KB6, a White Q on KB8 and a Black R on KKt8. White has played Q-KKt7 ch., and thus by the sacrifice of the Q forced the mate by the pawn. We have to distinguish between temporary and permanent values, and we have to exclude mistakes. The permanent value of a group of men is the measure of its usefulness in the hands of the master under varying conditions. Temporary value of a group of men in a certain situation is the measure of its usefulness under given conditions, again provided that the play is conducted by a master. If we follow the games of a master who plays against an equal opponent we may keep an account of the force of each of his pieces as it is shown in the course of his games and thus gain a reliable measure for the permanent value of each of the pieces. Since absolute perfection does not exist, this method can be executed only with the ideal perfect master rather than a strong player. The judgment of the master has authority. The written and printed word of the master should be consulted. Thus our own advancement can be helped by taking advice from masters. But we should not wholly rely on advice and examples and need to develop our own style from practice. If we abandon our judgment in favor of authority then we cease to have original thought. In that case the student is bound to make mistakes, because he needs judgment to understand the master. If on the other hand he stubbornly maintains his right to use his own judgment he keeps the springs of his creative thoughts alive and is one of the few that can bring innovation to the game of chess for the mac chess and PC. I therefore advise my pupils to be critical of advice imposed upon them by others, and to be diligent in attempting to arrive at game strategies developed by their own thoughts. A table of simplest values in chess was devised long ago, and l go by Leonhard Euler a mathematician, evaluation of true values. The list below shows the worth of pieces based on degree of movement. This reasoning does not apply to the promotion of a Pawn, and the Pawn therefore gains in value at the end game stage. Apart from this factor, Leonhard Euler method is sound, and the values he developed agreed with those based on experience. The following table indicates the approximately correct valuation of the pieces; Kt = 3 P's. B = Kt. R = Kt + 2 P's. Q = 2 Rs = 3 Kts. K = Kt + P. But this table is only the beginning of the work of valuation. Whether a player is considering upon abandoning some values in order to gain an advantage he has to compare what he intends to give up with what he hopes to gain. A frequently occurring instance is the sacrifice of a pawn for advantages gained in game play. What advantage in development maintains the balance for the loss of a Pawn? Perhaps no master has ever been able to give a fully satisfying answer to this question, though a good deal of Chess Strategy depends upon it. The experienced player answers the question by weighing the issues of the position and letting his judgment decide. A good method for creating and training your decision making is to experiment with advantages and sacrifices so as to produce a balance. Let a player, for instance, figure out which of the two minor pieces, Kt and B, is in a given case the stronger or more valuable piece. To that end, and adopting a balanced approach he will set up a balanced position; say of K, 5P and a Rook each, with nearly equal weaknesses, and he will then add a Kt to the one side, a B to the other, and see by analysis, or at least by trail an error, which side gets the advantage. If he varies the balance position in pieces and weaknesses the continued exercise will at length develop his judgment for the distinction between Kt and B to a fine point. Let the student begin with simple tasks of this kind before he attacks the more complicated ones. A few examples follow; White: K on QR1, Kt on QB3, P on QR5. Black: K on KR1, B on K3, P on KR5. White to play. 1 P-R6, B-B1; 2 P-R7, B-Kt2; 3 Kt-Q1, P-R6; 4 Kt-B2, P-R7. Black has the advantage. Add a couple of safe pawns say White on QB2, and Black on KB2, and Black wins easily. Thus, if the weaknesses of White and Black are very far apart the B is stronger than Kt. White: K on QR1, Kt on QB3, P on QKt4. Black: K on QKt1, B on K3, P on QB5. White to play. 1 K-Kt2, K-B2; 2 K-B1, K-Q3; 3 K-Q2, K-K4; 4 K-K3. White has the advantage, which would be very obvious if his K had been able to gain the point –K4. Add two pawns, White on KB2, Black on KB2, and White will probably win. If the weaknesses on either side are near each other, the Kt is stronger than the B. White: K on Q3, B on KB7. Black: K on QKt4, B on KB3, P's on QB4, QKt5, QR6. Black cannot force the win, 1 …, K-R5; 2 K-B2, P-Kt6 ch.; 3 B x P ch., K-Kt5. Black goes the only possible way by advancing some of his pawns on to White squares. 4 B-R2, P-B5; 5 B-Kt1. And that way also leads to a draw. Consequently the B supports the advance of its pawns most strongly when they are on squares of colour which are different to the squares of colour it dominates. The other way, leaving the pawns on squares dominated by the B, is the right way for defense, but it is the wrong way for attack. White: K on KR5, R on QKt1. Black: K on KKt1, R on QR3, P's on QK2 and KR3. White to play. 1 R-Kt7, K-B1; 2 R-KR7, K-K1; 3 K-Kt4, K-Q1; 4 K-B3, K-B1; 5 R-R8 ch., K-Kt2; 6 R-R7 ch. Black cannot win. The position of the White Rook on KR7 where it exerts force on two weak Black pawns is so strong that it leaves his K free to select the quarter where it is required to fight. White: K on K3, B on Q5, Kt on K4, P on QB4. Black: K on KKt3, Q on Q1, P on K4. White has a firm position, the only object for attack is the K, provided the White pieces are careful to retain their strong posts. For the attack against the K Black has K, Q, and to a slight extent the blocked P at his disposal. Blacks plan will be to attain a position where the White K is driven back and the Black K has advanced to KB5, with say, White K on K2, and Black Q on QKt6. The continuation might be: 1 …, Q-K6 ch.; 2 K-Q1, Q-Q6 ch.; 3 K-B1, K-K6; 4 K-Kt2, K-Q5; 5 K-B1. Now White hardly dares to move any piece but the King. It is therefore advisable to employ Zugzwang. 5 …, Q-KB6; 6 K-B2, Q-K6; 7 K-Kt2, Q-Q6, and now if 8 K-R2, Q-B7 ch.; 9 K-R3, Q-Kt8; 10 K-R4, Q-Kt3; 11 K-R3, K-Q6. Will Black be able to win? There are many lines of play. Some of the essential ones have not been mentioned above. The student will do well to try them out for himself, after using the method of imagining a hoped for position and aiming for it. The influence of the Q over the White pieces, firmly positioned though they are, and the nature of the advantage that she holds is, for the rest, quite clear. The conception of “Balance” often called (according to the great Chess thinker and Master, William Steinitz) “Balance of position” is more important than it would appear above. Chess is too restricted a concept to give a full meaning to that conception. The conception of balance functions in the whole of life. The values that are essential to chess, although many, are not so nicely graded as to form a continual series, therefore a perfectly balanced position does not exist for the mac chess and PC. In a symmetrical position the move would make a difference, though in practice that might amount to very little, and the game therefore might easily end in a draw. All the same the position would not correspond to the conditions of a perfect balance. Let us for the moment forget that we study chess and let us imagine what the conception of balance is. 1. In a balanced position neither side is able to gain an advantage by force. 2. In a balanced position any attempt to win an advantage, however well planned, may have to be abandoned. 3. In a nearly balanced position any attack, however well planned and intended to obtain a considerable advantage, can be stopped and even though the attacked army may be weaker than the attacker, he can still protect his pieces and even mount a worthwhile attack. The difficulty in any abstract reasoning on Chess is mainly its lack of grading in the final result. Loss, Draw or Win. This is the scale of success in chess. Life is infinitely more varied. Life goes on, it knows no permanent defeat or permanent victory and therefore one cannot detect in chess real life similarities with the concepts of Force, Value and Balance. Now the concept of an “Approximate Balance” may be used in chess, even by the perfectionist chess player. The greater force will gain the greater advantage. Let us give a few instances of how the principles set forth function in Chess; White: K on KKt3, R on QR3, P on KB4. Black: K on KKt3, R on QKt3, P on KB4. He who tries to win gets the worst of it. 1 K-R4, R to QB3; 2 R-Kt3 ch., K-B3; 3 K-R5, R-B8; 4 R-Kt6 ch., K-B2; 5 R-QR6, R-KKt8. The game is drawn, but White has to play carefully. In the initial position after 1 P-K4, P-K4; 2 Kt-KB3, Kt-QB3; 3 B-B4, B-B4, 4 P-Q3, P-Q3. White now attacks 5 Kt-Kt5. This move discloses an attempt to win, which in the balance position, is unjustified; 5 …, Kt-R3; 6 Q-R5, 0-0; 7 Kt-QB3, Kt-Q5. Black makes a counter attack, White is in difficulties. Again the initial position 1 P-K4, P-K4; 2 Kt-KB3, Kt-QB3; 3 B-Kt5, P-KB4. An unjustifiable attack. 4 Kt-QB3, P x P; 5 QKt x P, P-Q4; 6 Kt-Kt3, P-K5; 7 Kt-K5, Q-B3; 8 P-Q4. Blacks attempt has failed. Again 1 P-K4, P-K4; 2 Kt-KB3, Kt-QB3; 3 P-B3, an ambitious move, that is not called for, White wants to dominate the central places or points by pawns 3 …, P-Q4; 4 B-Kt5, P x P; 5 Kt x P, Q-Q4; 6 Q-R4, Kt-K2; 7 P-KB4. Apparently a bad position for Black, since White menaces B-B4. But it cannot be, Black has not moved, Black must have a sound defense! 7 …, B-Q2! This turns the tables on White. 8 Kt x B, K x Kt. To give an instance of the possibilities of this position; 9 0-0, Kt-B4; 10 P-QKt4, P-QR4; 11 K-R1, P x P; 12 B x Kt ch., P x B; 13 Q x R, B-B4; 14 Q x R, Kt-Kt6 ch.; 15 P x Kt, Q-R4, mates. From this actual game example it is sufficiently clear that three modes of game play are possible in chess. First is Attack, which concentrates effort on one or more weaknesses in the opponents camp with the intention of forcing the opponent to defend, and finally to gain an advantage. Second, Defense, which obstructs the efforts of the enemy, or concentrates efforts on its own weaknesses, or shifts these weaknesses, or makes some sacrifice to reduce the severity of a major onslaught. Third, Development, which does not concentrate effort, but spreads it, so as to gain in movement in readiness to attack or to defend. A move that does no good in any one of these ways is usually a wasted one. The main reason for attack is to maximize its chances. The attack has to gain the utmost advantage of which it is capable. The main reason for Defense is to minimize its risks of losing its most important pieces. The defense must make the smallest sacrifice that is possible to ward of the attack. The main reason for Development is to win in the shortest time possible. The development should be as rapid as possible, so that the state of readiness should be reached after as few moves as possible.
I should like to feel that l have made my readers eager to follow this principle, regardless of how high a level their opposing player is. They will lose many games by attempting it regardless, but if they shrug it off to experience and analyze their failures, in the end they will attain levels which they could never dream they could reach in the beginning. The above principle is applicable to all board games and to much else. The method deserves to be widely known. I call it the method of values.
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