Maths

Using the maths concepts of odds, risk and probability these 21 lessons and four assessment tasks aim to teach students the mechanics behind the different types of gambling they may come across. 

Stage 4

There are five lessons and two assessment tasks for Stage 4 Maths: 

• Lesson 1: Introduction to games of chance. Students explore basic probability by playing games of chance and will investigate how the gambling industry applies this knowledge to create a profit. 

• Lesson 2: Pigs aplenty. Students explore the concept of pushing their luck, develop a strategy to help them decide when to quit and reflect on how these strategies help people reduce their harm from gambling. 

• Lesson 3: The wide wide world of sports betting. Students will learn the difference between perfectly predictable events and less certain events and how bookmakers create odds to guarantee a profit. 

• Lesson 4: Can you beat the system? Students will calculate the average expected value of losses on a roulette wheel over time, use these values to analyse the cost of gambling on these games, study the flaws in the betting system and will reflect on gambling behaviour. 

• Lesson 5: Prediction vs. reality. Students will learn about randomness by using a coin toss and recording their observations. 

• Assessment task 1: The house always wins. Students design their own gambling game to demonstrate how the house always makes a profit. 

• Assessment task 2: Sideshow hustler. Students design a side show game that includes a skill to demonstrate how the odds always favour the game operator. 

Stage 5

There are six lessons and two assessment tasks for Stage 5 Maths. 

• Lesson 1: Lucky lottery. Students play a simple lottery game, analyse their odds of winning and how this influences the decisions they made. 
  
  
• Lesson 2: What’s the cost? To change perceptions of gambling losses, students compare the average persons losses to other average household purchases and then explore how this money could be more profitably invested over time.  
  
  
• Lesson 3: Poker machines. Using simulations students explore how poker machines work and see how losses can accumulate over time. For this lesson, please also download the appendix. 
  
  
• Lesson 4: Back to the books. With a focus on sports betting, students will explore in more detail how bookmakers set odds and how they are determined to make a profit. 
  
  
• Lesson 5: Loot boxes. Students create their own video game concept with loot boxes. They will then calculate the probability of obtaining all unique items for a complete set. 
  
  
• Lesson 6: Counter-intuitive probability. Using scenarios students will understand how random chance can be counter-intuitive. 
  
  
• Assessment task 1: Chuck-a-Luck. Using the game Chuck-a-Luck, students will calculate the probabilities of each betting option and their expected values. 
  
  
• Assessment task 2: Non-transitive dice. Students explore the outcomes of a set of non-transitive dice using probability tree diagrams, and discover their unique features. 

Stage 6

There are 10 lessons for Stage 6 Maths. 

• Lesson 1: Should you swap? Students define a problem, construct a mathematical model to run trials to collect data to compare reality and probability and then consider what lessons from the Monty Hall problem can be generalised to other gambling behaviours. 

• Lesson 2: Easter Show games of chance. Students calculate the probability of an average person scoring a shot at a basketball game and then use these probabilities to design a payout system, that can absorb losses from big wins and profits from players who pay poorly. 

• Lesson 3: Casino games - Roulette and Keno. Students analyse how the operators of lottery type games have arranged payouts so that they are always making a profit.

• Lesson 4: Lotto mania. Students simulate a lottery, and perform combinatorics calculations to determine the small probability of the exact numbers being drawn.

• Lesson 5: How does gambling on the races work? This lesson shows students how easy it is to get swept up in the excitement of a race and how bookmakers are always making a profit. 

• Lesson 6: Poker machines. Students design a poker machine payout system which guarantees a return of 85% and is fun and engaging for the player. They then simulate the machine and test the real world payout, reflecting on their feelings while they do so. 

• Lesson 7: Two-up - The fairest game of all? Students review the history and mathematics of the game and explore why it is fair. 

• Lesson 8: Lucky streaks. Students will generate their own random numbers, test their randomness and by using binomial probability and normal distribution they will test if gambling machines using random numbers are operating correctly. 

• Lesson 9: Multi-bets. Students will calculate both the payout and the odds for various multi-bets showing how an increased payout does not match the probability of a big bet. 

• Lesson 10: Sports betting. Students will take ownership of a gambling organisation, look at long term statistics of sporting matches to set initial odds and then monitor live betting to adjust the odds they are offering gamblers.