The Mathematics of Games and Puzzles: From Cards to Sudoku

Explore some general strategies for successfully solving simple games and puzzles. 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 for knowing when to stand, when to hit, when to double, and when to split.

What happens when you’re playing a game with an intelligent adversary whose goals are opposed to yours? 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 mathematical backbone 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 proper wagering decisions? As you enhance your mathematical poker-playing skills, you’ll find the answers to these and other questions about this thrilling game. You will also learn simple and effective strategies for playing video poker.

Mathematically trained players also have a decisive 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.

The world of games is filled with scams. The trick: knowing the strategies behind how these hustles work so you can avoid being exploited (and learn some engaging insights into math at the same time). Explore the fundamentals of nontransitive properties through penny ante, Bingo, and games involving dice and cards. Then, get a lively introduction to some simple puzzles involving cups, coins, and toothpicks—and their surprisingly sneaky answers.

Try your hand at some classic puzzles that have been driving people crazy for centuries involving sliding blocks, jumping pegs, and blinking lights—each of which deals heavily with odd or even numbers. Once you’ve learned some handy mathematical concepts and tools for solving these puzzles—including mod 2 arithmetic, vector equations, and mnemonic devices—these fun and exciting games won’t seem so “impossible” anymore.

It’s one of the most famous puzzles ever invented. But Professor Benjamin has an easy-to-learn, eight-step method for solving this mind-bending puzzle quickly and accurately—every time. After examining the mathematics behind the cube and pondering how many different cube positions are possible, you’ll follow him step-by-step through an algorithm (taught to Professor Benjamin by a world-champion cube solver) that, with practice, will have you solving any Rubik’s Cube in less than three minutes.

What’s the key to solving Sudoku problems when you’re at your wits’ end? Training your mind to look for patterns and to use careful logic, just like mathematicians. This lecture is packed with helpful techniques and strategies for overcoming even the most difficult Sudoku grids. Among those you’ll learn about: crosshatching, miniboxes, naked pairs and triples, and the unique rectangle rule. These tricks can even be used to solve variations on traditional Sudoku puzzles.

Chess is more like doing real mathematics than almost any other game out there. You’ll get a quick overview of how the game is played; learn how to draw connections between math and chess; explore some classic chess puzzles and problems; tap into the power of strategies and tactics for the opening, middle, and end game; and get some insider tips that are sure to improve your game the next time you sit down in front of a chess set.

Finish this engaging series with a look back at the three categories that most games fall into (games where the last player to move wins, games where the goal is to be the first to create a structure, and games where the player who accumulates the most stuff wins). Cram, NIM, Chomp, Connect Four—play them all. Also, take a look at how computers play games—and how they’ve helped us become better players.