It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am pretty sure that nonterminating ones can cause many paradoxes. As this is a community wiki mode, I would be happy to see formal definitions, existence of wining strategies as well as possible collisions.

Thanks in advance for keeping my mind finite!

It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am pretty sure that nonterminating ones can cause many paradoxes. As this is a community wiki mode, I would be happy to see formal definitions, existence of wining strategies as well as possible collisions.

Thanks in advance for keeping my mind finite!