How to evaluate pieces in Chess/Shogi

I played chess in tournements a long time ago so I know a little. Chess was invented a long, long time ago. People say it's perhaps 1000 years old based out of India, but nobody really knows. Pieces in chess do not have values. Any piece can capture any piece, but the "betterness" of a piece lies in how it moves around the board. Chess pieces have values, but they're just as reference so an ignorant player won't sacrifice a good piece for a bad piece that he thinks is a good trade.

King = checkmate him, and win!
Queen = 8
Rook = 5
Bishop = 3
Knight = 3
Pawn = 1

I don't know how the geneius who invented chess thought of the values, I guess he's just... a genuis!

I think a good starting point is to consider how many spaces on the board a piece controls.

In the middle of the board a pawn controls 2
a bishop 14, (fewer as it approaches the edges)
A knight 8
A rook 16
a king 9
a queen 30
(these values may not be correct)

Obviously this isn't the only criteria, as bishops and knights are usually considered equal, thanks to the mobility of the knight, and the bishop often being blocked in. and color limited. But just given those values you could rank the pieces pretty accurately.

The numerical evaluations of chess pieces was devised by Samuel Lloyd the great american puzzlist of late 19th cent. He was not a great chess player but he was fairly decent, some of his games survive. Anyhow this guy was fantastic at creating puzzles he created that little game with sliding pieces, like 15 square pieces that slide on a board that's 4x4. ANd you try to align the numbers 1 through 15. Remember that one it was like the Rubik's cube of his day?

Or the disappearing indian trick? Have you ever seen that? It's like using the salami technique. It's worth looking up and studying the stuff this guy created, even for modern designers.

THe queen is valued at 9, not 8 as someone said above. I'm pretty certain of this, you almost never sacrifice a queen for R and Bishop it never seems to be a very good trade if you study games of masters. And a Queen for a 2 Rooks is usually very good if you can pull it off although there are some exceptions s that can be found in games.

to come up with a general formula that I found on chessvariants.org:

http://chessvariants.org/newideas.dir/construction.html

http://chessvariants.org/unequal.dir/genericchesssystem.html

This page might also be interesting, it has some fun ideas for 'powers':

http://chessvariants.org/d.betza/chessvar/wand.html

One thing to beware of is the 'weenie swarm' tactic: a large group of pawns can beat a group of better pieces of the same value. So you might want to put a limitation on the total number of pieces, or the number of pawns, that a player can have at a time. Or you might want to give some advantage to a piece which takes a weaker piece: perhaps it can get a free move for example.