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.

Een kwadratische ontbinden in factoren

Welke voorwaarde geeft TRUE terug?

Schrijf een functie om factoriseerbaarheid te controleren

Simuleer de kans op factoriseerbaarheid

Viercijferige iPhone-toegangscodes

Vier bekende waarden

Drie bekende waarden

Wegvallen van tekenfouten

Simuleer tekenfouten: constante kansen

Simuleer tekenfouten: veranderende kansen

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

Wil je je vaardigheden in kansrekening naar een hoger niveau tillen? Deze cursus helpt je daarbij, met probleemgestuurd leren waarbij kanspuzzels centraal staan. Terwijl je stap voor stap door de oplossingen wordt geleid, krijg je zowel codeerhulpmiddelen als algemene strategieën voor het oplossen van kansproblemen die je in veel andere situaties kunt tegenkomen. De cursus is thematisch opgebouwd: we beginnen met klassiekers zoals het verjaardagsprobleem en Monty Hall, en eindigen met puzzels rond poker zoals Texas Hold'em en de World Series of Poker!

Intermediate R

Foundations of Probability in R

Ontdek hoe je kansvragen in R kunt beantwoorden met strategieën voor diverse kanspuzzels.

Kanspuzzels in R

Leer strategieën om kansberekeningen in R op te lossen door verschillende kansberekeningspuzzels te doen.

Welke voorwaarde geeft TRUE terug?

Kanspuzzels in R

Praktische interactieve oefening