If V is positive then the combination "may" be sound, but if it is negative, try another move instead.
1.d4 d5 2.c4 e6 3.e3 Nf6 4.Nc3 c5 5.Nf3 Nc6 6.cxd5 exd5 7.Bb5 a6 8.Bxc6+ bxc6 9.Ne5 Bb7N 10.dxc5 Bxc5 11.0-0 0-0 12.Na4 Bd6 13.Ng4 Ne4 14.b3 f5 15.f3 fxg4
16.fxe4 (D) I reached this position in a game I played the other night (G/20+10s). Obviously the sacrifice on h2 looked like the move but I decided to check everything first. My main line began with 16. ... Bxh2+ 17.Kxh2 Qh4+ 18.Kg1 g3 with mate to follow. But White has 19.Rf4 providing a shield along the f file for the fleeing King. So at this stage for V to remain positive I needed G to be above 32 points (looking 4 moves ahead), which is basically mate. As I didn't see the mate after 19.Rf4 Qh2+ 20.Kf1 Qh1+ 21.Ke2 Qxg2+ 22.Kd3 (23.Ke1 Rxf4 wins) 22. ... dxe4+ 23.Kc3 I was in a quandary. I resolved this by deciding my life wasn't ruled by numbers, chucking the piece anyway. 16. ... Bxh2+ "I expected that" said my opponent 17.Kh1 My opponent hadn't seen Rf4 as a defence 17. ... Qh4 18.Bb2 Bg3+ 0-1 But another calculating machine (Fritz) said the sacrifice was indeed sound, I just needed to play 20. ... dxe4!! and the value of my position was at least 9 points!
So I guess in this instance that Hartston's basic theory is correct.
An interesting attempt to quantify chess. But it doesn't take in to account calculating ability (or strength, for that matter). As calculating ability and/or strength increases, so does the chance a sacrifice that player decided on is sound.
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