True, but that doesn’t affect the win conditions of the game. All this really means is that the game cannot end in a draw and that players can effectively skip their turn at any point.
EDIT: because you still drop tokens in from the top, a vertical and a horizontally infinite properties would lead to very different strategies. For example, in a vertically Infinite board, a player could not effectively skip their turn as previously described.
The cardinality of this infinite board is the same as a board with infinite number of rows, though, so same same.
If it’s vertically infinite you can never get high enough to put a piece in so the game never starts
True, but that doesn’t affect the win conditions of the game. All this really means is that the game cannot end in a draw and that players can effectively skip their turn at any point.
EDIT: because you still drop tokens in from the top, a vertical and a horizontally infinite properties would lead to very different strategies. For example, in a vertically Infinite board, a player could not effectively skip their turn as previously described.