The other book I got was Luck, Logic & White Lies, a very different book, but also excellent.
To cut to the chase for those interested in combinatorial game theory: This book made thermographs make sense. I did not think it was possible, but here it is.
This book serves as an introduction to the mathematics of games. It seeks to show to the reader how it is that games have their power--how they manipulate chance, hidden information, and combinatorics (or, more often, a combination of the three) to create uncertainty and tension in play. It devotes a long section to each of these three sources of uncertainty.
This is kind of an obscure reference, but the book reminds me of "Master Go in Ten Days," the grandiosely-titled Go book that starts with the basic rules of the game and ends with some really pretty advanced concepts. This book is the same way with game math. In the first chapter, we are informed that there is a 1/2 chance of rolling an even number on a fair six-sided die. Three hundred pages later, we're doing combinatorial thermographs.
I'm a fairly mathy person. My parents, an engineer and a mathematician/computer scientist, could not have raised me to be otherwise, even though I'm becoming an historian anyway. As long as it's not a differential equation, I can handle pretty much all the math I ever happen to get myself in front of--some number theory here, graphs and topology there; I get by. I love the mathematics of games, naturally enough, as the intersection of two lifelong interests.
I've been trying to get all the books on combinatorial games that I can. I've long wanted something that could be an introduction to the subject--giving me some of the bacground I've missed--as well as being an accessible reference and something I can use to explain the subject to someone else. I really need to give this book some closer scrutiny, but I think this could be That Book. As I said, it assumes very little in its readership other than basic mathematical ability; it brings one along. It also does a good job of citing more specialist literature and giving one pointers about how to apply its concepts to all the games one plays. I'd have been curious to see him approach Settlers of Catan or some "modern classic."
The Mathematics of Games. So many books in this category are either long out of print, hard to find, or fairly esoteric and not something I'd recommend to just anyone. The best book I've found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner, which never takes one very far away from either the math or the games behind them. I love Winning Ways and On Numbers and Games, but they're definitely not for the faint of heart. LL&WL is the perfect book for gamers who are interested in the mathematics that underlie the choices they face and decisions they make. Just great stuff.
Alfred H. Wallace (Springfield, MO) on http://tajmahalfred.blogspot.com (Monday, January 31, 2005 resp. Monday, August 01, 2005)