A combinatorial game is a perfect information game with no chance played by two players who take turns making moves -- the last player to move wins the game. There is an algebraic system associated with combinatorial game theory that features bizarre objects such as infinitesimals -- things that are positive, yet so small that any sum of them, no matter how many, is not bigger than any positive number. The real numbers do not have infinitesimals, but combinatorial game theory is rife with them. While their structure can be baffling at times, the ideas are very simple. We\'ll play some games -- and very TINY ones at that! You need to know nothing to understand the majority of this talk -- we\'ll introduce everything we need during the talk. Refreshments will be served.