[math-fun] Another chess variant
I just saw this a couple of days ago on YouTube: The idea is to pit K of one piece against L of another in the context of avoiding checkmate. Two different pieces, one for each player, are chosen, like K white queens and L black knights. The W and B kings are in their usual starting positions; the rest of the squares on the board are filled up with (say) the K W queens and L B knights. Like (lowercase = B, uppercase = W): n n n n k n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q K Q Q Q (Of course the numbers K of W and L of B pieces need not be of form 8J + 7.) It might be interesting to determine which ratios of which pieces lead to a fairly even game. —Dan
'Solid chess' might be interesting to play: it's identical to normal chess except both players begin with 3 rows of pawns instead of 1. My intuition is that it will make it much harder to memorise openings, and therefore place more emphasis on the middlegame/endgame (which should be similar to those of ordinary chess). Has this variant been studied before? Best wishes, Adam P. Goucher
Sent: Friday, November 23, 2018 at 7:48 PM From: "Dan Asimov" <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Another chess variant
I just saw this a couple of days ago on YouTube: The idea is to pit K of one piece against L of another in the context of avoiding checkmate. Two different pieces, one for each player, are chosen, like K white queens and L black knights. The W and B kings are in their usual starting positions; the rest of the squares on the board are filled up with (say) the K W queens and L B knights. Like (lowercase = B, uppercase = W):
n n n n k n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q K Q Q Q
(Of course the numbers K of W and L of B pieces need not be of form 8J + 7.)
It might be interesting to determine which ratios of which pieces lead to a fairly even game.
—Dan
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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.) Jim Propp
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.)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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.)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (4)
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Adam P. Goucher -
Allan Wechsler -
Dan Asimov -
James Propp