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Luck, Logic, and White Lies: The Mathematics of Games

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Written by the general manager of Mega-Spielgerate, a game design company based in Limburg, Germany, Luck, Logic & White Lies: The Mathematics Of Games is a no-nonsense instructional in basic probability, geometry, and mathematics as they apply to popular games. Topics discussed include popular myths among those who the lottery, to the question of whether it is possible to reconcile chance and mathematical certainty, to testing dice, the possibilities of distribution in a roulette, modern theories as applied to the classical game of Go, whether bluffing in poker can be done without psychology, and so much more. Written in plain terms, Luck, Logic & White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills.

As this book points out, games fall into three broad categories:

1. Games of Chance
2. Games with a large number of combinations of different moves
3. Different states of information among the individual players.

And this book is broken into three main sections, one for each of these.

Before you get too turned off, yes, there is some math in this book. But it is really not heavy duty. (After all, John Nash of A Beautiful Mind won the Nobel Prize for his work on game theory and his work was not simple math.) The authors explanations of the situations described in the games are very good are very good, and the minimal amount of math is really helpful.

Virtually all of the common games from from the lottery to chess and even Monopoly, as well as the casino games such as blackjack and Roulette are discussed in detail. For anyone interested in what's really going on in games they play, this is an extremely interesting book.

The author knows whereof he speaks, he is the general manager of a game design company based in Germany.

So many books about the mathematics of games 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.

The author begins in the preface by categorizing games by the source of uncertainty: chance, vast search space (combinatorial games like Chess and Go), or imperfect information (strategic games of the sort studied by economic game theory). He counts simultaneous move selection as imperfect information.

Some chapters are much clearer than others. For example, the opening chapters on elementary probability and the explanation of the minimax theorem are excellent, but the rapid handwaving explanation of how computer programs work is completely opaque. Some chapters flowed enjoyably, while in others I had to re-read paragraphs several times to extract the argument (not always successfully).

The chapters are fairly independent, so it is easy to skip material.

The author does investigate a wide range of games, including some relatively modern (i.e., post-1950) games.

If you like to think about mathematics, this book will be a real pleasure read. Some of the math presented is practical, as well as interesting, while other examples are much less so.

I believe the book does a good job covering all aspects of the math behind games.

This is a 500 page mathematical investigation of games using probability theory, game theory, and a variety of mathematical methods. The author finds winning strategies for many games, some of them surprisingly simple. For most games, the point is less to find a trick to win but to clearly explain how the game works and to answer some interesting questions. The author's ability to present mathematics in an understandable manner is possibly unsurpassed by any other writer.

In Chapter 16, entitled, "Games of Chance", the author presents an explanation of Markov chains and how they can be applied to Monopoly and to Chutes and Ladders. The explanation is clearer here than I have found elsewhere. The result of the calculation for Monopoly is two charts detailing the best investments in Monopoly. One chart ranks the monopolies according to how much rent income they will generate for the owner. The second chart ranks monopolies according to their return on investment or ROI, expected rent divided by cost. Thus we see, for example, that the highest rent comes from the green color group, Pennsylvania, and the best monopoly measured by ROI is the orange color group, New York. The author suggests these charts may be useful for deciding what properties to buy and where to buy houses.

The problem is that the results of the Markov chain calculation are not really useful for the important decisions Monopoly players must make. Players must buy nearly every ordinary property they land on in order to advance their chances of getting a monopoly and to block opponents from getting monopolies, so properties' ROIs and rents are almost completely irrelevant to the property buying decisions. After players trade properties, almost every player has one monopoly, not two or three or four, so the problem of deciding where to build the next house is not an issue...the player must put the house on his (lone) monopoly. Only after reaching the later stages of the game, usually after one of the players has been eliminated, do players have a choice about which monopoly to build out. Even in this regard, the chart is not useful. There is too much data to memorize and Monopoly culture discourages players from consulting charts in the middle of a game. Monopoly players bring snacks and drinks, but not charts.

The truly important decisions Monopoly players must make involve trading--which monopoly to take and which monopoly to allow an opponent to take. The data from a Markov chain calculation simply do not help much. What Monopoly players need to help them make this decision is the Monte Carlo method, which the book describes but does not apply toward Monopoly. A Monte Carlo simulation involves programming a computer to play the game, play the game thousands of times, and study what happened. This is exactly what I did for my Winning Monopoly book in 1987. A more detailed review of this book-at least, the portion dedicated to Monopoly-is posted on my web site, [...]