I predict that rooks and bishops (and queens) are asymptotically worth infinitely more than knights and pawns. Jim Propp On Sat, Nov 24, 2018 at 3:55 PM Allan Wechsler <acwacw@gmail.com> wrote:
It seems possible that a fixed size cohort of one kind of piece might be able to defend itself against an arbitrary number of another, weaker piece, it which case the ratio would be infinite.
On Sat, Nov 24, 2018, 3:47 PM James Propp <jamespropp@gmail.com wrote:
Going back to Dan's original post, I liked the passage
It might be interesting to determine which ratios of which pieces lead to
a fairly even game.
It would be delightful to come up with some meaningful asymptotic sense in which (for instance) knights and pawns are worth infinitesimally less than rooks and bishops, but a knight is worth exactly 5 pawns and a rook is worth exactly sqrt(2) bishops.
(The numbers 5 and sqrt(2) are just random numbers that came to mind; I'm not suggesting that these are the actual values of the sorts of ratios Dan is asking about.)
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