One kind of infinite game discussed by logicians is determined by the choice of a subset X of the half-open unit interval [0, 1). Then each player in turn selects a bit from {0,1}, and if the countable bitstring thus created lies in X then the first player (W) wins; if not, the second player (B) wins. The Axiom of Determinacy states that every such game has a strategy for one player or the other. Meanwhile, the Axiom of Choice can be used to show there exists a subset X of [0,1) whose corresponding game has no strategy for either player. I'm hoping for a totally explicit game perhaps played by placing counters on unoccupied cells of a board, as in Hex (or Conway's Angels & Devils game). —Dan ----- On Saturday, March 3, 2018, 4:36:13 AM PST, Fred Lunnon <fred.lunnon@gmail.com> wrote: If your game has length \omega , how do you know who wins? WFL On 3/3/18, Dan Asimov <dasimov@earthlink.net> wrote:
I am curious: Do people know of interesting infinite two-player games, preferably without chance playing a role?
I'm mainly interested in discrete 2-player games with one player going first and with play alternating thereafter. Such that in some sense, except for that first player / second player thing, the challenge facing each player is as symmetrical as possible.
Though I will not rule out continuous games.