I have mused before (I believe in this forum, but it would have been years ago) on the possibility of games where there were two winning conditions, one based on reaching a point target, and one based on board configuration. A player wins upon achieving either of the two conditions. The novel mechanism was inspired by Go ko-fights exactly as John describes them. After making a move on the board, a player is permitted to offer the opposition a deal: skip your move and earn some points instead. "I'll buy your next move for 4 points." Probably such a game would be hard to tune to make it interesting. In response to Jim Propp's original question: Permitting double moves doesn't affect the basic nature of the two classes of combinatorial games with the most complete theories, namely impartial games and partisan games. That is, "doubling" an impartial game gives another impartial game, still amenable to Sprague-Grundy analysis, and "doubling" a partisan game gives another partisan game, amenable to Berlekamp-Conway-Guy analysis. The vast ocean of games between these two extreme islands remains vast and oceanic upon doubling :) On Tue, Dec 30, 2014 at 9:24 AM, John Aspinall <j@jkmfamily.org> wrote:
In Go, ko-threats are effectively saying "I dare you to give me two moves in succession here", i.e. with the first of the two specified.
On 12/30/2014 08:02 AM, James Propp wrote:
Has anyone studied variants of standard combinatorial games (such as Nim) in which each player makes two standard moves in succession on each turn instead of just one?
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