The Mathematics of Games and Puzzles
From Cards to Sudoku Series

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12 episodes in this series

Episode 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…
Episode 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…
Episode 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…
Episode 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.…
Episode 5 Practical Poker Probabilities
Investigate the mathematics of Texas Hold'em, one of the most popular traditional poker games. What's the probability your hand will improve before and after more cards are revealed? How do…
Episode 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…
Episode 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. Explore the fundamentals of nontransitive properties…
Episode 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…
Episode 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…
Episode 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 episode…
Episode 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 it's is played; learn how to see connections between…
Episode 12 Winning Ways—It’s Your Move!
Finish this 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…

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This lecture applies the law of total probability and other concepts from the course to predict the long-term losses to be expected from playing games such as roulette and craps and understand what is known as the "Gambler's Ruin Problem."