This chapter will introduce some basic principles that will be used throughout the course, such as writing loops and functions. Then, we dive into a couple of classic problems: the Birthday Problem, and Monty Hall.

Introduction to the Course

Writing a simple function

Writing a simple for loop

Setting a seed

The Birthday Problem

Simulation of a single n

Using the pbirthday function

Make a plot

Monty Hall

Win probability with "stick"

Writing a function to "switch"

Win probability with "switch"

Introduction and Classic Puzzles

In this chapter, we explore games in which dice are rolled, including Yahtzee, Settlers of Catan, and Craps. You will learn tools such as using built-in R functions to calculate combinatorics, and using functions such as replicate and the %in% operator.

Yahtzee

Probability of a Yahtzee

Probability of a large straight

Probability of a full house

Settlers of Catan

Simulate one game

Simulate 10000 games

Craps

Function to keep rolling when point is established

Function to run one round

Probability of winning the pass line bet

Games with Dice

The puzzles in this chapter were inspired by ideas encountered on the internet. In order to solve them, you will learn to combine tools such as nested for loops, and the functions round, identical, and sapply.

Factoring a Quadratic

Which condition will return TRUE?

Write a function to check factorability

Simulate the factorable probability

Four Digit iPhone Passcodes

Four known values

Three known values

Sign Error Cancellations

Simulate sign errors: constant probabilities

Simulate sign errors: changing probabilities

Inspired from the Web

This chapter explores questions in poker, including the most often televised version of Texas Hold'em. We will learn to code for win probabilities with any given number of outs, and also explore a more theoretical model of poker known as the von Neumann model. We will learn to use functions such as Reduce, runif, and ifelse.

Texas Hold'em

Calculate expected value with one card to come

Two cards to come

Consecutive Cashes

Two consecutive years

Function to evaluate set of five years

Simulate probability for a given set of five years

von Neumann Model of Poker

One round of von Neumann Poker

Function to simulate one round with betting

Simulate many iterations of von Neumann model

Congratulations!

Poker

Do you want to take your probability skills to the next level? This course will help get you there, using problem-based learning with probability puzzles as the framework. As you are guided through their solutions, you will gain coding tools and general strategies for solving probability problems that you might encounter in many other situations. Organized by theme, the course begins with classic problems like the Birthday Problem and Monty Hall, and ends with puzzles that involve poker like Texas Hold'em and the World Series of Poker!

Intermediate R

Foundations of Probability in R

Discover how you can answer probability questions in R by learning frameworks and strategies that can help you solve a variety of probability puzzles.

Probability Puzzles in R

Learn strategies for answering probability questions in R by solving a variety of probability puzzles.

Assistant Professor of Statistics Villanova University

Introduction to the game

Simulating dice rolls

The table function

Counting the number of occurrences

Let's try it!

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Games with Dice - Settlers of Catan

Settlers of Catan

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