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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!
Introduction and Classic PuzzlesFree
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 Course50 xpWriting a simple function100 xpWriting a simple for loop100 xpSetting a seed50 xpThe Birthday Problem50 xpSimulation of a single n100 xpUsing the pbirthday function100 xpMake a plot100 xpMonty Hall50 xpWin probability with "stick"100 xpWriting a function to "switch"100 xpWin probability with "switch"100 xp
Games with Dice
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.Yahtzee50 xpProbability of a Yahtzee100 xpProbability of a large straight100 xpProbability of a full house100 xpSettlers of Catan50 xpSimulate one game100 xpSimulate 10000 games100 xpCraps50 xpFunction to keep rolling when point is established100 xpFunction to run one round100 xpProbability of winning the pass line bet100 xp
Inspired from the Web
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 Quadratic50 xpWhich condition will return TRUE?50 xpWrite a function to check factorability100 xpSimulate the factorable probability100 xpFour Digit iPhone Passcodes50 xpFour known values100 xpThree known values100 xpSign Error Cancellations50 xpSimulate sign errors: constant probabilities100 xpSimulate sign errors: changing probabilities100 xp
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'em50 xpCalculate expected value with one card to come100 xpTwo cards to come100 xpConsecutive Cashes50 xpTwo consecutive years100 xpFunction to evaluate set of five years100 xpSimulate probability for a given set of five years100 xpvon Neumann Model of Poker50 xpOne round of von Neumann Poker100 xpFunction to simulate one round with betting100 xpSimulate many iterations of von Neumann model100 xpCongratulations!50 xp
Assistant Professor of Statistics, Villanova University
Peter Chi is an Assistant Professor in the Department of Mathematics and Statistics at Villanova University. His primary research focus is centered on statistical methodologies in phylogenetics and evolutionary biology. He completed his Ph.D. in the Department of Biostatistics at the University of Washington, and has previously held faculty positions at Ursinus College, and Cal Poly San Luis Obispo. Find out more at his webpage, and follow him on Twitter @PeterBChi.