Reinhard: | I am convinced - so please correct me if need be - that your engine | has implemented just that value scheme, you are talking about. ...' Well, initially, of course NOT. How could it? I am not clairvoyant. I started by 'common-sense logic' like 'Q = R + N + 1.5, and B << N probably means A << Q, and the synergy bonus probably scales proportional to piece value, so let me take A = B + N + 1'. Which translated to A = 7.5 with my 8x8 values B = N = 3.25 (taken from Kaufman's work). And with the setting A=7.5, C=9.0, I played the 'Chancellor army' against the 'Archbishop army', expecting the latter to be crushed, because of the 300 cP inferiority. (Which corresponds to piece odds, and should give 85%-90% scores.) But to my surprise, although the two Chancellors won, it was by less than the Pawn-odds score. | Then your engine will throw away underestimated pieces too cheap and | keep overestimated too dear. Thus it will start and avoid a lot of | trades in unjustified manner. This hardly occurs, because this is SELF-PLAY. The opponent has the same misconception. If I tell the engine A < R, there the engines wil NOT throw away their A for R, because the opponent will not let them, and 'save' its Rook when it comes under A attack. Trades of unlike material occur only rarely, unless the material is considered exactly equal (which I therefore avoid). So putting A=R is dangerous, and would suppress the measured A value because of bad A vs R trades. But not completely, as it would not always happen, and a fair fraction of the games would still be able to cash in on the higher power of A by using it to gain material or inflict checkmate before the trade was made. So even when you do set A=R, or A=R+P, the A will score significantly better than 50% in an A vs R (or AA vs RR) match. And when I discover that, I increase the A value accordingly, until self-consistency is reached. So my initial tests of CC vs AA, with the engine set to A=750, C=900 suggested that C-A ~< 50 cP. Then I repeated the match with A=850, and this eliminated the few bad trades that could not be avoided by the opponent. So CC beat AA now by an even smaller margin, of less than half the Pawn-odds score (in fact more like a quarter). So I set A=875. I did not repeat the test with A=875 yet, but I don't expect this 25cP different setting to cause a significant change in the result (compared to the statistical error with the number of games I play), if changing a full 100 cP only benifited the AA army 6%. The extra 25cP will not reverse the sign of any trade. So in practice, you are highly insensitive to what values you program into the engine, and iterating to consistency converges extremely fast. You should not make it too extreme, though: if you set Q < P, the side with the Queen will always squander it on a Pawn, as there is no way the opponent could prevent that, the Queen being so powerful and the Pawns being abundant, exposed and powerless. Similarly, setting A < N would probably not work even in an A vs B+N ending (with Pawns), as the A is sufficiently powerfol compared to individual B and N that the latter cannot escape being captured by a suicidal A. But if you are off 'merely' 2-3 Pawns, the observed scores will already be very close to what they should be based on the true piece values.