Lessons In Play

Anyone who thinks about the mathematics of games should know about Winning Ways. The four books (split up from two volumes) are the bible of these games, providing a mathematical analysis to the category most of us think of abstract strategy. Go, chess, and nim are all examples, but there are lots more, some only played by math PhDs on whiteboards. The authors, John Conway, Elwyn Berlekamp, and Richard K. Guy, sketch out the ultimate in rational play, and along the way Conway realized that you could construct an entire number theory based on these systems, which he went on to publish—to the annoyance of his colleagues—as On Numbers and Games. (I should also note Beasley's The Mathematics of Games, which predates Winning Ways but only broaches some of the topics of the Conway, Berlekamp, Guy opus.)

Once you know how to analyze small games, you realize that many large strategy games eventually break down into small, manageable games. Go is too complex to analyze via Winning Ways methods, but by the end of the game, you've actually created small pockets of active play. Each is a small, analyzable game. (Berlekamp went on to explore this in Mathematical Go.)

Winning Ways started it all, and I have both the old two-volume set, picked up piecemeal from used bookstores, and the new four-volume set, updated slightly and issued a few years ago. I also have the other books I've mentioned. Puzzle geekery runs deep in my blood.

But I can't make heads or tails of Winning Ways. I've started to work through them a few times, but the authors quickly make mathematical leaps that I can't follow. I only know a few people who have worked through the books, and I wouldn't want to play nim against them.

That's why I'm so intrigued by Lessons in Play, which I've nicknamed "Winning Ways Lite." The authors set out to explain combinatorial game theory, just like Winning Ways, but they target the relative layperson like me. They don't go on to justify real numbers based on the mathematics of games: They just give a step-by-step explanation of the theories that underlie these games and mathematical constructs. I just got my copy, and I can already understand them more.

If you care about these sorts of things, check out the book. It provides a fascinating look at the math that hovers just below the surface of abstract strategy games.