8

Humans use:

  • Pawn = 1
  • Knight = 3
  • Bishop = 3
  • Rook = 5
  • Queen = 9.5
  • Bishop pair = +0.5

But I would like to know what relative point values do engines use (preferably strong engines, like Stockfish, Houdini, Rybka, Komodo, ...).

If the point value that the engine assign to the pieces depends on the position of the pieces on the board (for example a White Knight on a1 is only worth 2.6 but on e5 it's worth 3.4), than I would like to know the average point values of the pieces.

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  • 1
    I'd quibble with a couple things: your value for the queen (more like 8.5) and generalizing what humans use period. I've spoken with GMs who (in a vacuum) think of rooks as more like 4.5.
    – Cleveland
    Jul 29, 2014 at 22:37
  • When I learned way back when the books said Q=10 so Q+P = 2 R
    – yobamamama
    Dec 16, 2019 at 1:24
  • I was taught queen was 9 I think
    – qwr
    Jun 14, 2021 at 16:01

5 Answers 5

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8

Rybka/Komodo/Houdini are not open source and their values aren't readily available, but the current strongest conventional engine, Stockfish, uses these values (lines 194-198):

PawnValueMg = 126, PawnValueEg = 208,

KnightValueMg = 781, KnightValueEg = 854,

BishopValueMg = 825, BishopValueEg = 915,

RookValueMg = 1276, RookValueEg = 1380,

QueenValueMg = 2538, QueenValueEg = 2682,

The "Mg" column is value during the mid-game, and the "Eg" column is for the endgame. In units where the value of a pawn is 1:

Middlegame: Knight = 6.198; Bishop = 6.548; Rook = 10.127; Queen = 20.143

Endgame: Knight = 4.106; Bishop = 4.399; Rook = 6.635; Queen = 12.894

As you might guess, these numbers are empirically tuned.

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  • Finding the "pawn value" where pawn=1 as humans do would improve the answer
    – qwr
    Jun 14, 2021 at 16:02
  • So what is used in the opening?
    – qwr
    Jun 14, 2021 at 16:03
  • 1
    @qwr opening uses Mg eval.
    – Allure
    Jun 14, 2021 at 19:11
5

These are the values used by Crafty - one of the best open source chess engines.

#  define PAWN_VALUE                             100
#  define KNIGHT_VALUE                           325
#  define BISHOP_VALUE                           325
#  define ROOK_VALUE                             500
#  define QUEEN_VALUE                           1050
#  define KING_VALUE                           40000

If you can follow the C code, then you can dig deeper by looking at the the source files that are available.

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2

I have the strong commercial chess engine Shredder Classic 4. When I open up its engine options I get the default strengths of the pieces. Without reading the documentation of this engine it seems that Shredder starts off with the traditional piece values of queen = 9.5 pts, rook = 5 pts and so on. Then there are optional sliders where I could make any type of piece worth more or less. Interestingly the default value for a "bishop pair" can also be increased or decreased by the player.

This seems to be about the best that I can do with Shredder to try to give an "average" strength of piece valuations.

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-1

A really good engine would use variable values depending on the situation and position. With position often counting more for evaluation than mere material although both are important and their weights would change too.

At the gitgo a good start is P=1, N=3, B=3 , R=5, Q=10, K=max value the computer can handle.

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  • You don't need for the king to have the "max value the computer can handle". For one, you could use arbitrary precision integers, letting it handle arbitrarily large numbers. However, that would not improve the algorithm's performance while decreasing speed substantially. All you have to do is make sure the king is worth more than all pieces summed together. The question also asked about the average values of pieces. It appears they already know piece value can change based on the situation.
    – user904963
    May 10, 2022 at 10:29
-2

In my short book “True Chess:The American Revolution” I demonstrate the values of the pieces. Pawns are worth .942 Knights 2.512 Bishops 4.082 Rooks 4.396 Queens 8.478 the King has a fighting value of 2.512. I also demonstrate this in a YouTube video entitled “Chess is an expression of Pi”. Chess engines often evaluate my positions incorrectly. The first company to use these values will probably create the dominant engine, all other things being equal. Top 99% ranking on Chess.com

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1
  • Many top engines are open source. Go ahead and fork it and insert your values and find out the results. I'm guessing programmers have adjusted the values quite a lot in search of better performance, making it doubtful your numbers will be better than something like Stockfish's.
    – user904963
    May 10, 2022 at 10:26

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