The Mathematics of Games and Puzzles: From Cards to Sudoku

The Mathematics of Games and Puzzles: From Cards to Sudoku
Course Trailer
Let the Games Begin!
1: Let the Games Begin!

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...

49 min
Games of Chance and Winning Wagers
2: Games of Chance and Winning Wagers

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.

45 min
Optimal Blackjack and Simple Card Counting
3: Optimal Blackjack and Simple Card Counting

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, w...

45 min
Mixed Strategies and the Art of Bluffing
4: Mixed Strategies and the Art of Bluffing

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 all...

40 min
Practical Poker Probabilities
5: Practical Poker Probabilities

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 t...

44 min
Expert Backgammon
6: Expert Backgammon

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.

44 min
Games You Can't Lose and Sneaky Puzzles
7: Games You Can't Lose and Sneaky Puzzles

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 t...

44 min
Solving "Impossible" Puzzles
8: Solving "Impossible" Puzzles

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...

45 min
Mastering Rubik's Cube
9: Mastering Rubik's Cube

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 cu...

46 min
Solving Sudoku
10: Solving Sudoku

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 ...

50 min
Mathematics and Chess
11: Mathematics and Chess

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...

45 min
Winning Ways-It's Your Move!
12: Winning Ways-It's Your Move!

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 p...

47 min
Arthur T. Benjamin

As a professor, I have always wanted to bring math to the masses. The Great Courses has helped make that dream come true.

ALMA MATER

Johns Hopkins University

INSTITUTION

Harvey Mudd College

About Arthur T. Benjamin

Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989. Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named Professor Benjamin the 2006-2008 George Pólya Lecturer. In 2012, Princeton Review profiled him in The Best 300 Professors. He is a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Professor Benjamin also served for five years as coeditor of Math Horizons magazine. An avid games player, Dr. Benjamin is a past winner of the American Backgammon Tour and has written more than 15 papers on the mathematics of games and puzzles. Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him America's Best Math Whiz.

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