Piece Density Function

P^d = C

where

• P is the number of Pieces per side
• C is the number of Cells on the Board
• d is the density factor

For FIDE chess d is 1.500, for XiangQi 1.623, and for Shogi 1.467. The average is 1.530

Using these values with other board sizes gives the following table

Board		Pieces per Side
Geometry	Cells	FIDE	XiangQi	Shogi	Average
10x8	80	18.57	14.88	19.83	17.53
10x10	100	21.54	17.07	23.09	20.29
12x8	96	20.97	16.65	22.46	19.75
12x12	144	27.47	21.37	29.61	25.75
24x24	576	69.23	50.22	76.17	63.71
Hexagonal	1575	135.37	93.33	151.22	122.95
100x100	10000	464.16	291.49	533.13	411.51

---