Kevin Pacey wrote on Fri, Sep 14, 2018 06:45 PM UTC:
@ Greg
I'm curious how you estimate/calculate average mobility, if it's fairly simple to describe. I do this myself as one step when calculating my estimate for a knight's value on the (typically) rectangular or square board used for a given chess variant, by figuring out (and adding up) the number of squares a N can reach on an empty board from every single square, then calculating the average number of squares a N can reach on the board, if it were placed on each square one at a time. In Gross Chess, for example, there are a lot of squares from which a N can reach either 8 or 6 squares. Fwiw, I didn't bother to work out the exact average just yet, but estimated it must be around at least 6 squares (out of the impossible to reach 100% full mobility score, or 8, max.) for a N on an empty Gross Chess board. This seemingly isn't compatible with your 4.89 score for the N, but it does seem it could match your Average Directions Attacked figure for the N. [edit: your mobility score for a pawn in Gross Chess is a clue that you're somehow taking into account the average number/positioning of enemy and/or friendly forces on the board, too, though in that case I still don't quite get why the Vao and Cannon mobility fields are left empty in your posted table.]
[edit: Otherwise I'd note that I have a Cannon as 1/2 the value of a R (as it is in Chinese Chess), and similarly I have a Vao as 1/2 the value of a B. I'd also note that much earlier in this Gross Chess thread, Mr. Paulowich gave his own estimates for the piece values.]
@ Greg
I'm curious how you estimate/calculate average mobility, if it's fairly simple to describe. I do this myself as one step when calculating my estimate for a knight's value on the (typically) rectangular or square board used for a given chess variant, by figuring out (and adding up) the number of squares a N can reach on an empty board from every single square, then calculating the average number of squares a N can reach on the board, if it were placed on each square one at a time. In Gross Chess, for example, there are a lot of squares from which a N can reach either 8 or 6 squares. Fwiw, I didn't bother to work out the exact average just yet, but estimated it must be around at least 6 squares (out of the impossible to reach 100% full mobility score, or 8, max.) for a N on an empty Gross Chess board. This seemingly isn't compatible with your 4.89 score for the N, but it does seem it could match your Average Directions Attacked figure for the N. [edit: your mobility score for a pawn in Gross Chess is a clue that you're somehow taking into account the average number/positioning of enemy and/or friendly forces on the board, too, though in that case I still don't quite get why the Vao and Cannon mobility fields are left empty in your posted table.]
[edit: Otherwise I'd note that I have a Cannon as 1/2 the value of a R (as it is in Chinese Chess), and similarly I have a Vao as 1/2 the value of a B. I'd also note that much earlier in this Gross Chess thread, Mr. Paulowich gave his own estimates for the piece values.]