Chess pieces are the same. For example, the par value of a Rook is 5 Pawns while the par value of Bishops and Knights is 3 Pawns. However, it’s the market, or relative value, that is the decisive factor. In some positions a Bishop or Knight might be worth more than a Rook. It all depends on specific positional and tactical factors.
How do you know when the sacrifice of the exchange is feasible? In The Art if Sacrifice in Chess Spielmann gives a number of guidelines and their exceptions and ends up saying you shouldn’t worry about them because, “With a little practice, (the student)will soon be able to grasp all these circumstances instinctively when they arise…” as well as a sound positional judgment.
Here’s an example of what Spielmann was talking about. The game was played in an event which, like the winner Hans Fahrni (1874-1939) has been long forgotten.
Fahrni was born in the Austrian-Hungarian empire city of Prague which today is in the Czech Republic. It's not certain when he went to Switzerland, but from there he eventually emigrated to Germany.
Rudolf Spielmann–Savielly Tartakower1–0B15MunichMunich GER22.06.1909Stockfish 17
B15: Caro-Kann 1.e4 c6 Although not very dynamic, the Caro-Kann is rock solid and often leads to good endgames for black. That's the theoretical assessment, but as this game shows, if a world class player like Tartakower can mishandle the opening like he does here, theory doesn't mean much...at least for us amateurs. 2.d4 d5 3.c3 dxe4 4.xe4 f6 5.g3 At the time this move was new and it was subsequently adopted by Alekhine. It has since been supplanted by 5.Nxf6 e5 6.f3 With the move in the text, White obtains a noticeable lead in development exd4 7.xd4 c5 8.e3 As Spielmann was to realize much later this is not the right con tinuation anf 8.Qe2+ is better. 8.e2+ e7 9.e3 c5 10.df5 0-0 11.c4 e8 12.d3 b6 13.0-0-0 White stands very well. Alekhine,A-Tartakower,S Kecskemet 1927 8...b6 9.e2 By indirectly guarding both b2 and d4 this move makes Q-side castling possible. 0-0 9...xb2 10.c1+ 9...xd4 10.xd4+ 10.0-0-0 d5 According to Spielmann this is a serious infraction of the rules of developmentm but there is nothing wrong with it and the position remains completely equal. Hiwever, 10...Re8 was also good. 11.h5 f6 This is black's real error. Because of the strong position of the white Q, which black's last move permitted, black must find the best defensive move which this move is not. He has two plausible defenses. 11...Nxe3eliminating the potentially strong B and giving white an isolated P or developing with11...Nd7 and 12...N7f6. In either case the position remains equal. 12.h4 g4 A well played move. 13.d3 White is better developed and his pieces are much more active, so he offers the exchange. Theoretically the evaluation is that the chances are completely equal. Practically though it's a different story as any slip by black is likely to have grave consequences. 13.e2 allows black to equalize after xe2 14.gxe2 bd7 15.f5 ae8 16.h6 e4 17.f4 e5 with a very sharp position, but b;ack has sufficient defensive resources. 13.f3 This is white's best reply. After e6 14.g5 bd7 15.xe6 fxe6 16.c4 white is clearly better. 13...xd1 The acceptance of the exchange sacrifice was virtually com pulsory. 13...bd7 14.xh7+ xh7 15.xg4 with a significant advantage. 14.xd1 By sacrificing the exchange Spielmann's idea is to utilize his lead in development and activity of his pieces. White has no material compensation, though he does have the two Bs and almost all his forces point menacingly at black's K. bd7 15.gf5 Hoping for Nxg7! White mounts an attack. e5 Tartakower has completely missed the point of white's last move. The text leads to his immediate down fall. 15...fe8 leaves him safe, but hr must walk a tightrope! For example... 16.g4 e5 17.xg7 xd4 18.xd4 xd3+ 19.xd3 e1+ 20.d2 b4+ 21.c3 e4 22.xf6 e2+ 23.c3 c1 24.d2 f3+ 25.d3 White must accept a draw by repeating move for if e2 26.f5 xc2+ 27.b3 xd3+ 28.c3 xc3+ 29.bxc3 And it's black's choice whether ot not he wnts to fraw ot play for the win. In Shootouts black won 5 out of 5 games. 16.xg7 This sacrifice which cannot be accepted and it ultimayely leads to black getting mated. d8 16...xg7 17.f5+ g8 18.xf6 xd3+ 19.xd3 and black cannot avoid mate. 17.gf5 Material is not the key factor. What counts here is black's missing g-Pawn. g6 18.h6 e8 Black coners g7, but white's attack cannot be twarted. 19.f3 xe3+ 20.fxe3 f6 21.g5 h8 At first glance it appeards that black has everything covered, but ir;s white to play and win. 22.e7+ It's mate in 3, so black resigned. 22.e7+ xe7 23.xh7+ xh7 24.xh7# 22.xh7 This would also win, but there is no immediate mate after xh7 23.e7+ h8 24.xg6+ fxg6 25.xg6 xg6 26.xg6 1–0
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