In valuing a rook, I observe that a rook on the open board commands 15 squares; his own and seven others in each direction. Divide by three and you get a value of 5.
In valuing a knight, I observe that a knight on the open board commands nine squares; his own and eight others in each direction. Divide by three and you get a value of 3.
If I were to value a bishop same way, I would observe that a bishop on the open board commands 13 squares; divide by three, and I would get 4 (plus).
But most valuations have the bishop at 3, rather than 4 despite his range.
Interestingly, some experts value a bishop pair on the open board at 7-8, even though the sum of 3+3 is only 6. Some would say that the pair is worth more than 7, even valuing single bishops at 3.5. A value of eight for a pair would be in line with my theoretical value of 4, above.
Put another way, a bishop and extra pawn is almost always at a disadvantage against a rook, but two bishops and two extra pawns are not necessarily at a disadvantage against two rooks.
Could a bishop be worth only three because of its single-colored move, even if two bishops are worth eight?
Given the concern that computers beating humans has made the game less interesting, have any experts, human or computer proposed or play tested a variant whereby a bishop can change its color by making a single move in a lateral direction to a square of the opposite color? This, presumably, would increase the value of the bishop, perhaps to four.
More to the point, have the Grandmasters made any more conventional arguments in favor of an eight-valued bishop pair?