As Rudolf Spielmann explained it the chess pieces, like stocks, have two prices: the par value and the quoted rate. The par value is the value assigned by the company that issues it. The quoted price is the current market price meaning it’s the actual price you can buy or sell it for.
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.
[Event "Munich"]
[Site "Munich GER"]
[Date "1909.06.22"]
[Round "?"]
[White "Rudolf Spielmann"]
[Black "Savielly Tartakower"]
[Result "1-0"]
[ECO "B15"]
[Annotator "Stockfish 17"]
[PlyCount "43"]
[EventDate "1909.??.??"]
{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. Nc3 dxe4 4. Nxe4 Nf6 5. Ng3 {At the time this move was new and it was subsequently adopted by Alekhine. It has since been supplanted by 5.Nxf6} e5 6. Nf3 {With the move in the text, White obtains a noticeable lead in development} exd4 7. Nxd4 Bc5 8. Be3 {As Spielmann was to realize much later this is not the right con tinuation anf 8.Qe2+ is better.} (8. Qe2+ Be7 9. Be3 c5 10. Ndf5 O-O 11. Qc4 Re8 12. Bd3 b6 13. O-O-O {White stands very well. Alekhine,A-Tartakower,S Kecskemet 1927}) 8... Qb6 9. Qe2 {By indirectly guarding both b2 and d4 this move makes Q-side castling possible.} O-O (9... Qxb2 10. Bc1+) (9... Bxd4 10. Bxd4+) 10. O-O-O Nd5 {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. Qh5 Nf6 {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. Qh4 Bg4 {A well played move.} 13. Bd3 {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. Be2 {allows black to equalize after} Bxe2 14. Ngxe2 Nbd7 15. Nf5 Rae8 16. Bh6 Re4 17. Nf4 Re5 {with a very sharp position, but b;ack has sufficient defensive resources.}) (13. f3 {This is white's best reply. After} Be6 14. Bg5 Nbd7 15. Nxe6 fxe6 16. Bc4 {white is clearly better.}) 13... Bxd1 {The acceptance of the exchange sacrifice was virtually com pulsory.} (13... Nbd7 14. Bxh7+ Nxh7 15. Qxg4 {with a significant advantage.}) 14. Rxd1 {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.} Nbd7 15. Ngf5 {[%mdl 160] Hoping for Nxg7! White mounts an attack.} Ne5 {[%mdl 8192] Tartakower has completely missed the point of white's last move. The text leads to his immediate down fall.} (15... Rfe8 {leaves him safe, but hr must walk a tightrope! For example...} 16. g4 Ne5 17. Nxg7 Bxd4 18. Bxd4 Nxd3+ 19. Rxd3 Re1+ 20. Kd2 Qb4+ 21. Bc3 Qe4 22. Bxf6 Qe2+ 23. Kc3 Rc1 24. Rd2 Qf3+ 25. Rd3 {White must accept a draw by repeating move for if} Qe2 26. Nf5 Rxc2+ 27. Kb3 Qxd3+ 28. Bc3 Rxc3+ 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. Nxg7 {[%mdl 512] This sacrifice which cannot be accepted and it ultimayely leads to black getting mated.} Qd8 (16... Kxg7 17. Nf5+ Kg8 18. Qxf6 Nxd3+ 19. Rxd3 {and black cannot avoid mate.}) 17. Ngf5 {Material is not the key factor. What counts here is black's missing g-Pawn.} Ng6 18. Qh6 Ne8 {Black coners g7, but white's attack cannot be twarted.} 19. Nf3 Bxe3+ 20. fxe3 Qf6 21. Ng5 Qh8 {At first glance it appeards that black has everything covered, but ir;s white to play and win.} 22. Ne7+ {[%mdl 512] It's mate in 3, so black resigned.} (22. Ne7+ Nxe7 23. Bxh7+ Qxh7 24. Qxh7#) (22. Nxh7 {This would also win, but there is no immediate mate after} Qxh7 23. Ne7+ Kh8 24. Nxg6+ fxg6 25. Qxg6 Qxg6 26. Bxg6) 1-0