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Brilliant

Casino Probability

via Brilliant

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Overview

Learn how to beat the house! Or, if that's not possible, at least learn how much of an edge they have.

In this course, you'll analyze three specific casino games: blackjack, craps, and poker. And, while you're learning how to master these games, you'll also strengthen your skills working with many foundational probability topics including probability trees and conditional probability.
Some prior knowledge of probability at the level of the Probability Fundamentals course is useful for tackling this material. Additionally, a strong foundation with algebra is assumed as a prerequisite.

Syllabus

  • Introduction: "Casino games such as roulette, blackjack, baccarat, slot machines and so on, are stacked in favour of the house." – Victoria Coren Mitchell, professional poker player
    • Cards: Warm up your probability skills with some card-based puzzles.
    • Dice: Get some probability and expected value practice with dice.
    • Avoid the Scam: Analyze two real casino games; how much do they favor the house? Do the math and find out!
  • Blackjack: "Blackjack is very scientific. There's always a right answer and a wrong answer. Do you take a card, increase your bet, bet big or bet small. There's absolutely a right and wrong answer." – Charlie Ergen, businessman and billionaire
    • The Rules of Blackjack: To play Blackjack, first you need to know the rules.
    • Infinite Decks: Infinite decks simplify the math so that's how we'll begin.
    • Blackjack Strategies: Practice your skill at blackjack with actual play scenarios.
    • Optimizing Profit: Work out the math behind doubling down, splitting pairs, and insurance.
  • Casino Craps: "Life is a big craps game. I've got to tell you, it's all been fun." – Kirk Kerkorian, casino owner and billionaire
    • The Rules of Craps: Learn the basic rules behind Pass and Don't Pass.
    • Any Time Bets: Study the mathematics of the Field, place bets, Big 6 and Big 8.
    • The Pass and Don't Pass Lines: Work out how much you'll win on Pass and Don't Pass.
    • Betting Strategy: Compile what you've learned into an optimal betting strategy.
    • The House Advantage: How much advantage does the House have in the best scenario?
  • Poker: "Investing in a poker game and investing in stocks, at least the way I do it, it's a very similar skill set." – David Einhorn, investor and billionaire
    • Basic Card Probabilities: Get down the basic probabilities in drawing cards out of a deck.
    • Poker Hands: Learn and find probabilities with the hierarchy of winning hands.
    • The Rules of Texas Hold'Em: Apply your skills to one of the most popular Poker variants.
    • Strategy: Fold or bet?

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