Probably not relevant to any arguments about AI doom, but some notes about chess material values:
You said a rook is “ostensibly only 1 point of material less than two bishops”. This is true in the simplified system usually taught to new players (where pawn = 1, knight = bishop = 3, rook = 5, queen = 9). But in models that allow themselves a higher complexity budget, 2 bishops can be closer to a queen than a rook (at the start of the game):
Bishops are usually considered slightly better than knights; a value of 3 + 1⁄3 is typical
There is a “pair bonus” of ~1/2 point for having 2 bishops on opposite colors. (Bishops are a “color-bound” piece: a bishop that starts on a dark square can only reach other dark squares, and vice-versa. Having 2 on opposite colors mitigates this disadvantage because an opportunity that is on the wrong color for one bishop will be exploitable by the other; the “Jack Sprat” effect.)
Rooks are weaker in crowded boards (early game) where their movement options are often blocked, and stronger in open boards (endgames). 5 is an average across the whole game. I’ve seen estimates <4.5 for early-game and >6 for endgame.
(Queen is also often a bit higher than 9, especially for AI players; e.g. 9.25 or 9.5)
If you’re interested in a deeper analysis of material values, I recommend these articles by Ralph Betza. Betza is both an international master chess player and a prolific designer of chess variants, so he’s interested in models that work outside the distribution of standard chess.
Probably not relevant to any arguments about AI doom, but some notes about chess material values:
You said a rook is “ostensibly only 1 point of material less than two bishops”. This is true in the simplified system usually taught to new players (where pawn = 1, knight = bishop = 3, rook = 5, queen = 9). But in models that allow themselves a higher complexity budget, 2 bishops can be closer to a queen than a rook (at the start of the game):
Bishops are usually considered slightly better than knights; a value of 3 + 1⁄3 is typical
There is a “pair bonus” of ~1/2 point for having 2 bishops on opposite colors. (Bishops are a “color-bound” piece: a bishop that starts on a dark square can only reach other dark squares, and vice-versa. Having 2 on opposite colors mitigates this disadvantage because an opportunity that is on the wrong color for one bishop will be exploitable by the other; the “Jack Sprat” effect.)
Rooks are weaker in crowded boards (early game) where their movement options are often blocked, and stronger in open boards (endgames). 5 is an average across the whole game. I’ve seen estimates <4.5 for early-game and >6 for endgame.
(Queen is also often a bit higher than 9, especially for AI players; e.g. 9.25 or 9.5)
If you’re interested in a deeper analysis of material values, I recommend these articles by Ralph Betza. Betza is both an international master chess player and a prolific designer of chess variants, so he’s interested in models that work outside the distribution of standard chess.