Although I doubt this is what Jim had in mind . . .
[...]
So according to AC, there is some W(A) + W(B) for which there exists no strategy for either player.
I suspect this means that the outcome does not depend on what either player does. But I'm not absolutely sure of that.
No, it just means that neither player can force a win, even though the game cannot end in a draw. The way to `construct' such a game is by (uncountable transfinite) induction: 1. Well-order the set of all player-1-strategies and player-2-strategies by the initial ordinal of cardinality 2^aleph_null. 2. For each strategy in a list, insist that a particular sequence of moves `beats' it. Since at any stage we have fixed < 2^aleph_null outcomes, we can always do this. By the end of all time, we have a game where for any strategy that player n makes, player 3-n can make a sequence of moves to win. Sincerely, Adam P. Goucher
--Dan
On Nov 13, 2014, at 8:00 AM, James Propp <jamespropp@gmail.com> wrote:
What are fun examples of combinatorial games that (like Conway and Paterson's game of Brussels Sprouts) appear to be games of strategy but whose outcome doesn't depend on what either player does? . . .
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