The Mathematics of Games and Puzzles: From Cards to Sudoku

Course Description

Improve your odds of winning card games and solving puzzles, not by cheating but by tapping into the unbridled power of mathematics.

Video Lectures

01: Let the Games Begin! (49 min)

Master general strategies for solving puzzles like 20 Questions, Mastermind, Tower of Hanoi, and Cram using mathematical concepts including backward reasoning and symmetry exploitation.

02: Games of Chance and Winning Wagers (45 min)

Analyze roulette and craps using expected value to determine game fairness, then apply the Kelly criterion and Gambler’s Ruin formula for optimal betting strategies.

03: Optimal Blackjack and Simple Card Counting (45 min)

Discover mathematically proven blackjack strategies through progressively complex scenarios, including when to hit/stand and basic card counting techniques.

04: Mixed Strategies and the Art of Bluffing (40 min)

Master zero-sum games (penny matching, rock-paper-scissors, poker) using equilibrium strategies that guarantee maximum expected payoff through calculated unpredictability.

05: Practical Poker Probabilities (44 min)

Calculate Texas Hold’em probabilities including hand improvement odds and pot odds to inform mathematically sound wagering decisions.

06: Expert Backgammon (44 min)

Learn backgammon’s mathematical foundations – from opening roll strategies to checker movement probabilities and doubling cube calculations.

07: Games You Can’t Lose and Sneaky Puzzles (44 min)

Examine gambling scams through nontransitive properties in penny ante, Bingo, and dice/card games, plus classic coin/cup puzzles.

08: Solving “Impossible” Puzzles (45 min)

Conquer sliding block, peg-jumping, and light puzzles using mod 2 arithmetic, vector equations, and mnemonic devices.

09: Mastering Rubik’s Cube (46 min)

Learn an 8-step solving algorithm while exploring the cube’s mathematical complexity (43 quintillion possible positions).

10: Solving Sudoku (50 min)

Apply mathematical logic patterns including crosshatching, naked pairs/triples, and the unique rectangle rule to conquer difficult grids.

11: Mathematics and Chess (45 min)

Explore chess-mathematics connections through classic puzzles and strategic principles for openings, middlegames, and endgames.

12: Winning Ways – It’s Your Move! (47 min)

Analyze three game categories (last-move wins, structure-building, accumulation) through Cram, NIM, Chomp and Connect Four, plus computer game theory insights.