M Winther wrote on Thu, Oct 23, 2008 02:53 PM UTC:
Muller, obviously you know the mathematics. But I question the relevance of
determining piece value to the decimal. The method I have used is to see
how well a piece fares in a Western piece context, e.g. how many moves
does it make compared with the other pieces (i.e. how useful it is).
Another method is when I pit the new piece(s) against a different army of
known pieces. If the result is equal after a number of games, then I
regard the piece as equally valuable as its counterpart in the other army.
So this is a practical testing method of determining piece values, which I
let Zillions do automatically.
I have found that when a piece is valued, perhaps, 2.5, or 3.5, then it
tends to converge around the piece value 3, e.g. the same as a bishop or
knight. The point is, namely, that the new piece can threaten exchange, or
vice versa. And the threatened party cannot withdraw for strategical or
positional reasons. Hence the piece values converge around the nodes of 3
and 5. Remember that also the formally higher valued piece can often
threaten exchange to achieve a positional or tactical goal.
So, they are worth the same due to practical factors, while they are
*practically* interchangeable*. Obviously, in an equal army variant both
players can exchange the new piece, and the remaining position is still
equal. Hence, the new piece is equally valuable as a light piece. To
really introduce a different valued piece, then it must by pinpointed at
4, I suppose.
I don't know if this phenomenon can be mathematically represented. It
depends on the piece congestion, i.e. size of board, and whether the
nearly equal valued pieces are long-shooting, i.e. whether they can easily
be used to make an exchange.
/Mats