It is played by two players, called First and Second, who alternately take previously untaken positions.
In a strong positional game, the winner is the first player who holds all the elements of a winning-set.
An interesting corollary is that, if a certain game does not have draw positions, then First always has a winning strategy.
The second player ("Breaker") can win only by preventing Maker from holding a winning-set.
Contrary to intuition, it is possible that this new set will now destroy the winning strategy and make the game a draw.
Intuitively, the reason is that First might have to spend some moves to prevent Second from owning this extra set.
It is parametrized by two integers, n and N. In it: According to Ramsey's theorem, there exists some number R(n,n) such that, for every N > R(n,n), in every two-coloring of the complete graph on {1,...,N}, one of the colors must contain a clique of size n. Therefore, by the above corollary, when N > R(n,n), First always has a winning strategy.
[1]: 10 Consider the game of tic-tac-toe played in a d-dimensional cube of length n. By the Hales–Jewett theorem, when d is large enough (as a function of n), every 2-coloring of the cube-cells contains a monochromatic geometric line.