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Stockfish - material balance/imbalance evaluation
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Tord Romstad



Joined: 08 Mar 2006
Posts: 1750
Location: Oslo, Norway
PostPost subject: Re: Stockfish - material balance/imbalance evaluation    Posted: Thu May 06, 2010 8:16 pm Reply to topic Reply with quote
Ralph Stoesser wrote:
I've read Kaufman's paper about the evaluation of material imbalance, but I wonder what exactly Tord Romstad's polynomial function does.


OK, I'll try to explain. It's nothing very fancy, really.

A material evaluation function is a function of 10 variables; P (the number of white pawns), p (the number of black pawns), N (the number of white knights), n (the number of black pawns, and by now you'll understand the meaning of the remaining variables), B, b, R, r, Q and q.

When we learned to play chess, most of us were taught a material evaluation function which is a linear polynomial in the 10 variables, something like this:

Code:
f(P, p, N, n, B, b, R, r, Q, q) = 1*(P-p) + 3*(N-n) + 3*(B-b) + 4.5*(R-r) + 9*(Q-q)


Later on, we learn a few material evaluation rules which cannot be expressed by a linear function. The most obvious example is the bishop pair: Two bishops are, in general, worth more than the double of a single bishop. However, we can still use a polynomial to model the evaluation function, as long as we allow terms of the second degree. If we decide that the bishop pair should be worth half a pawn, we can include this in the above evaluation function by adding the following term:

Code:
0.25 * (B*(B-1) - b*(b-1))



This works because the product B*(B-1) is 0 if there are 0 or 1 white bishops, but 2 if there are 2 bishops.

Similarly, other more complex material evaluation rules like the ones found in Kaufman's paper can also be modeled by second-degree polynomial terms. For instance, assume that we want to increase the value of a knight by 0.05 for each enemy pawn on the board (this is almost certainly not an exact rule from Kaufman's paper, but I'm too lazy to look up the paper now). This would correspond to a term like this:

Code:
0.05 * (N*p - n*P)


That so many material evaluation rules can be modeled by polynomials of degree 2 gave me the idea of using a completely general (apart from the obvious symmetry relations) second degree polynomial for evaluating material, and to spend lots of effort trying to tune all the coefficients (this was shortly after Joona had invented a very effective method for tuning evaluation parameters).

We never managed to make it work as well as I hoped, though.
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Subject Author Date/Time
Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 05, 2010 4:39 pm
      Re: Stockfish - material balance/imbalance evaluation Marco Costalba Wed May 05, 2010 4:48 pm
            Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 05, 2010 5:37 pm
                  Re: Stockfish - material balance/imbalance evaluation Marco Costalba Wed May 05, 2010 5:47 pm
      Re: Stockfish - material balance/imbalance evaluation Jan Brouwer Wed May 05, 2010 5:49 pm
            Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Wed May 05, 2010 7:25 pm
                  Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 05, 2010 8:02 pm
                        Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Wed May 05, 2010 10:10 pm
                              Re: Stockfish - material balance/imbalance evaluation Milos Stanisavljevic Wed May 05, 2010 10:30 pm
                                    Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Wed May 05, 2010 10:47 pm
                                    Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 05, 2010 11:27 pm
                                          Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Thu May 06, 2010 1:23 am
                                                Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Thu May 06, 2010 9:07 am
                                                      Re: Stockfish - material balance/imbalance evaluation Sven Schüle Thu May 06, 2010 9:31 am
                                                            Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Thu May 06, 2010 9:52 am
                                                                  Re: Stockfish - material balance/imbalance evaluation Sven Schüle Thu May 06, 2010 10:48 am
                                                                        Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Thu May 06, 2010 12:08 pm
                                                                              Re: Stockfish - material balance/imbalance evaluation Tord Romstad Thu May 06, 2010 8:24 pm
                                                      Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Thu May 06, 2010 1:19 pm
                                                Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Fri May 07, 2010 9:34 pm
                                                      Re: Stockfish - material balance/imbalance evaluation Marco Costalba Sat May 08, 2010 12:48 pm
                                                            Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Sat May 08, 2010 1:47 pm
                                                            Re: Stockfish - material balance/imbalance evaluation Marcel van Kervinck Sat May 08, 2010 2:01 pm
                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Thu May 06, 2010 11:40 am
                              Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Wed May 05, 2010 10:42 pm
      Re: Stockfish - material balance/imbalance evaluation Joona Kiiski Wed May 05, 2010 7:54 pm
            Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 05, 2010 8:28 pm
            Re: Stockfish - material balance/imbalance evaluation Larry Kaufman Sun May 27, 2012 7:31 pm
      Re: Stockfish - material balance/imbalance evaluation Tord Romstad Thu May 06, 2010 8:16 pm
            Re: Stockfish - material balance/imbalance evaluation James Coit Thu May 06, 2010 10:13 pm
            Re: Stockfish - material balance/imbalance evaluation Vratko Polák Thu May 06, 2010 11:38 pm
            Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Fri May 07, 2010 12:15 am
                  Re: Stockfish - material balance/imbalance evaluation Marco Costalba Fri May 07, 2010 5:39 am
                        Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Fri May 07, 2010 8:09 am
                              Re: Stockfish - material balance/imbalance evaluation Marco Costalba Fri May 07, 2010 8:25 am
                                    Re: Stockfish - material balance/imbalance evaluation Sven Schüle Fri May 07, 2010 9:48 am
                                          Re: Stockfish - material balance/imbalance evaluation Sven Schüle Fri May 07, 2010 10:31 am
                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Fri May 07, 2010 10:54 am
                                          Re: Stockfish - material balance/imbalance evaluation Miguel A. Ballicora Fri May 07, 2010 10:31 pm
                                                Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sat May 08, 2010 1:33 pm
                                                      Re: Stockfish - material balance/imbalance evaluation Marco Costalba Sat May 08, 2010 2:29 pm
                                                            Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sat May 08, 2010 4:24 pm
                                                                  Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sat May 08, 2010 7:54 pm
                                                                        Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sun May 09, 2010 3:19 pm
                                                                              Re: Stockfish - material balance/imbalance evaluation Marco Costalba Sun May 09, 2010 4:47 pm
                                                                                    Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sun May 09, 2010 7:51 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Sun May 09, 2010 10:47 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sun May 09, 2010 11:22 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Mon May 10, 2010 4:58 am
                                                                                          Re: Stockfish - material balance/imbalance evaluation Sven Schüle Mon May 10, 2010 7:39 am
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Mon May 10, 2010 10:22 am
                                                                                          Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Mon May 10, 2010 5:04 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Mon May 10, 2010 9:35 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Tue May 11, 2010 11:19 am
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Tue May 11, 2010 1:51 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Tue May 11, 2010 9:38 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Wed May 12, 2010 5:05 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Robert Hyatt Wed May 12, 2010 6:14 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Wed May 12, 2010 6:39 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Thu May 13, 2010 12:51 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 12, 2010 8:13 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 12, 2010 9:15 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Marco Costalba Wed May 12, 2010 9:34 pm
                                                                                          Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Wed May 12, 2010 10:02 pm
                                                            Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Sat May 08, 2010 4:53 pm
                                                                  Re: Stockfish - material balance/imbalance evaluation Ralph Stoesser Sat May 08, 2010 7:03 pm
            Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 6:10 pm
                  Re: Stockfish - material balance/imbalance evaluation Milos Stanisavljevic Wed Jul 28, 2010 6:24 pm
                        Re: Stockfish - material balance/imbalance evaluation grzegorzs Thu Aug 05, 2010 5:36 pm
                  Re: Stockfish - material balance/imbalance evaluation Dann Corbit Wed Jul 28, 2010 6:43 pm
                        Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 7:43 pm
                              Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 7:44 pm
                                    Re: Stockfish - material balance/imbalance evaluation Joona Kiiski Wed Jul 28, 2010 7:55 pm
                                          Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 8:30 pm
                                                Re: Stockfish - material balance/imbalance evaluation Milos Stanisavljevic Wed Jul 28, 2010 9:30 pm
                                                      Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 10:11 pm
                                                            Re: Stockfish - material balance/imbalance evaluation Milos Stanisavljevic Wed Jul 28, 2010 10:31 pm
                                                                  Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Wed Jul 28, 2010 10:57 pm
                                                            Crazy talk Ben-Hur Carlos Langoni Wed Jul 28, 2010 11:07 pm
                                                                  Re: Crazy talk Vincent Diepeveen Wed Jul 28, 2010 11:36 pm
                                                Re: Stockfish - material balance/imbalance evaluation Ben Stoker Wed Jul 28, 2010 10:07 pm
                                                      Re: Stockfish - material balance/imbalance evaluation Vincent Diepeveen Sun Aug 08, 2010 1:54 pm
                              Re: Stockfish - material balance/imbalance evaluation Robert Hyatt Wed Jul 28, 2010 8:27 pm
                                    Re: Stockfish - material balance/imbalance evaluation Dann Corbit Wed Jul 28, 2010 9:30 pm
                              Re: Stockfish - material balance/imbalance evaluation Wylie Garvin Tue Aug 10, 2010 10:00 pm
      Re: Stockfish - material balance/imbalance evaluation Tu Ngoc Trung Sun May 27, 2012 2:22 am
            Re: Stockfish - material balance/imbalance evaluation Ferdinand Mosca Sun May 27, 2012 10:01 am
                  Re: Stockfish - material balance/imbalance evaluation Tu Ngoc Trung Mon May 28, 2012 3:19 am
            Re: Stockfish - material balance/imbalance evaluation Eelco de Groot Mon May 28, 2012 4:19 am
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