The Mathematics of Games and Puzzles: From Cards to Sudoku

As you hone your skills at games and puzzles, including 20 Questions, Mastermind, Ghost, The Tower of Hanoi, variations of Tic Tac Toe, and Cram (a cross between checkers and dominoes), you'll start seeing how mathematical ideas and concepts - including the strategy of working backward and the exploitation of symmetry - are essential to increasing your chances of winning.

Turn now to games that rely heavily on chance and betting, such as roulette and craps, and learn how to evaluate the fairness (or unfairness) of games using the ever-important concept of expected value. Once you know if a game is to your advantage or not, you can use the Kelly criterion or the Gambler's Ruin formula to help you decide your best wagering strategies.

Depending on how you play it, blackjack can be the best or the worst game in a casino. Here, Professor Benjamin shows you how to get the best of blackjack before it gets the best of you. By taking you through scenarios of increasing difficulty to strengthen your skills, and by demonstrating the secrets of simple card counting, he reveals optimal strategies.

You have a zero-sum game such as penny matching, rock-paper-scissors, and simplified poker. Discover how to use math to bluff, play unpredictably, and win these kinds of games through powerful strategies including the equilibrium strategy (which guarantees the highest expected payoff without allowing your adversary to exploit your approach).

Investigate the mathematics of Texas Hold'em, one of the most popular traditional poker games. What is the probability your hand will improve before and after more cards are revealed? How do you calculate your "pot odds" to help you determine your wagering decisions? As you enhance your mathematical poker-playing skills, you'll find the answers to these and other questions.

Mathematically trained players also have an edge in backgammon, which trains you to make decisions in highly uncertain conditions. Professor Benjamin explains the rules of the game, the basic strategies for winning, the best ways to play your opening rolls, and how math constantly enters the picture - from figuring out the safest way to move your checkers to the all-important doubling cube.