For more on a
wide range of topics, the following expository book is excellent:
Luck, Logic & White Lies by Jorg Bewersdorff
A lot of the material comes from the first chapter of this text, which
gives a systematic approach to finding winning strategies for certain
classes of games:
Lessons in Play: An Introduction to Combinatorial Game Theory by
Albert, Nowakowski and Wolfe
As you might have guessed, logic plays a substantial role in studying
games (the section on chess). The following exposition with historical
background has a little bit to offer for everyone:
Zermelo
and the Early History of Game Theory, by Schwalbe and
Walker
Finally, if you are not satisfied with any explanation above,
Wikipedia
will provide an alternative and it will introduce to you many new,
related concepts.