In assessing the values of Qs on rectangular or square boards, I didn't like the idea that the Qs value could grow enormously if it were simply valued more on bigger boards. So, I set some limits on R and B (R+B+P=Q). For a R I took it as a standard candle - equal 5.5 on almost any size board (except very small, like 2x2). That's Euwe's value for the R on 8x8 (chess).
For a single B, I did not want it to be worth 4 pawns or more on most any size board, as in an endgame a B almost never can restrain 4 passed pawns. So, 3.99 maximum, e.g. for extremely large boards.
For Kts, being short range pieces, smaller boards are better, so N=3.5 on 8x8, N=3 on 10x10 and I worked out N=3.38 on 10x8 - the average number of squares a N can reach on 10x8 affecting the value; notice there are proportionally (compared to number of board cells) many high mobility cells for minor pieces on rectangular boards, both for N and B, thus boosting their value (Bs also hit more of the enemy P-line on rectangular 8 rank boards than say 10x10). That's why I have B=3.75 on 10x8 or 12x8 (I found having a formula for B's 'exact' value difficult). On 10x10 square board I was content to have B=3.5 still (as on 8x8), making it more valuable than N, yet Q still about 10 (exactly in fact).
Notice too that on very large boards, the value of sliders is in a way decreased by the fact that the proportion of the number of cells that a slider hits is decreased compared to board size being large (e.g. high percentage for Q on 8x8, not so much on 12x12).
Hi David
In assessing the values of Qs on rectangular or square boards, I didn't like the idea that the Qs value could grow enormously if it were simply valued more on bigger boards. So, I set some limits on R and B (R+B+P=Q). For a R I took it as a standard candle - equal 5.5 on almost any size board (except very small, like 2x2). That's Euwe's value for the R on 8x8 (chess).
For a single B, I did not want it to be worth 4 pawns or more on most any size board, as in an endgame a B almost never can restrain 4 passed pawns. So, 3.99 maximum, e.g. for extremely large boards.
For Kts, being short range pieces, smaller boards are better, so N=3.5 on 8x8, N=3 on 10x10 and I worked out N=3.38 on 10x8 - the average number of squares a N can reach on 10x8 affecting the value; notice there are proportionally (compared to number of board cells) many high mobility cells for minor pieces on rectangular boards, both for N and B, thus boosting their value (Bs also hit more of the enemy P-line on rectangular 8 rank boards than say 10x10). That's why I have B=3.75 on 10x8 or 12x8 (I found having a formula for B's 'exact' value difficult). On 10x10 square board I was content to have B=3.5 still (as on 8x8), making it more valuable than N, yet Q still about 10 (exactly in fact).
Notice too that on very large boards, the value of sliders is in a way decreased by the fact that the proportion of the number of cells that a slider hits is decreased compared to board size being large (e.g. high percentage for Q on 8x8, not so much on 12x12).