First up - infinitely many Nim boards. There are, it's true, infinitely many ways of laying out a board for a game of Nim, but once you've made that board, there are a finite number of ways of playing it. This struck me as similar to your game, in that you can lay out an infinite number of tiles, but once you do, there are only a finite number of ways I can lay out my tiles.
Second - ah, you formally score points at the end, it's true, but you can regard a game of Nim for a player as a set of transitions in and out of Nim numbers - the player gains a point when he gets to a Nim number and loses a point when he strays off it - then whoever has "more points" (although there's only one) at the end of the game wins.
I misunderstood what you meant by "know your opponents moves in advance" - I though you meant in the sense of chess vs. roshambo rather than in the sense of your game (did you give it a name?) vs. chess. I suppose in an optimally played game of Nim, one *does* know one's opponent's moves, in effect, because they'll either be a move to a Nim number or a move that will let one get to a Nim number, and the Nim number that one will get to is known, but that's clutching at straws rather.
I'm not certain, though, that there isn't some kind of relationship between the two - if it becomes more apparent to me I'll let you know, if you like.
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
timeasmymeasure
“Apart from that, Mrs. Licoln, how was the play?”
Date: 2005-12-06 06:19 pm (UTC)Second - ah, you formally score points at the end, it's true, but you can regard a game of Nim for a player as a set of transitions in and out of Nim numbers - the player gains a point when he gets to a Nim number and loses a point when he strays off it - then whoever has "more points" (although there's only one) at the end of the game wins.
I misunderstood what you meant by "know your opponents moves in advance" - I though you meant in the sense of chess vs. roshambo rather than in the sense of your game (did you give it a name?) vs. chess. I suppose in an optimally played game of Nim, one *does* know one's opponent's moves, in effect, because they'll either be a move to a Nim number or a move that will let one get to a Nim number, and the Nim number that one will get to is known, but that's clutching at straws rather.
I'm not certain, though, that there isn't some kind of relationship between the two - if it becomes more apparent to me I'll let you know, if you like.