Table of Contents

Part I: Introduction for the Educator: A Guide to Teaching Math Through Games of Chance

Pedagogical Rationale

This unit is founded on the pedagogical principle that mathematics becomes most meaningful when it is tangible, relevant, and connected to students’ interests.¹ By leveraging the high-interest context of casino games, this curriculum aims to transform abstract mathematical concepts—such as probability, combinatorics, and expected value—into powerful tools for real-world analysis. The objective is not to teach students how to gamble, but rather to provide them with the mathematical literacy required to deconstruct the systems that govern games of chance.

The core philosophy of this unit is one of critical inquiry. Students will move beyond the perception of casino games as contests of pure luck and begin to see them as meticulously designed commercial products. These products operate on predictable, long-term mathematical principles that are often masked by the psychology of short-term wins and losses. By the end of this unit, students will be equipped to analyze the underlying structure of these games, understand the financial risks involved, and apply their mathematical skills to make informed decisions in a world where probability and risk are ever-present.

Navigating the Ethical Tightrope

The use of casino games as a teaching tool requires a deliberate and responsible pedagogical approach. The subject matter is sensitive, and it is imperative that the curriculum is framed not as an endorsement of gambling, but as a critical examination of its mechanics and societal impact. The central theme of this unit is the deconstruction of a system to reveal its inherent risks, thereby serving as a powerful form of prevention education.²

Throughout these lessons, the educator must consistently reinforce that casino games are designed to be profitable for the house. The mathematical principles explored are the very mechanisms that ensure this profitability. This unit directly confronts the social and ethical dimensions of the gaming industry, including the significant harms of problem gambling, such as addiction, financial ruin, crime, and social disruption.⁵ By embedding the mathematical lessons within this ethical framework, the unit transforms from a simple applied math exercise into a vital lesson in financial literacy and critical thinking. The ultimate goal is to empower students with knowledge, enabling them to look past the marketing and understand the statistical certainties that govern games of chance. This approach embraces the inherent tension of the topic, using the allure of the games to teach the very concepts that demystify them and expose their risks.

Unit Learning Objectives

Upon successful completion of this unit, students will be able to:

Mathematical Skills:

Calculate permutations and combinations to determine the number of possible outcomes in various scenarios.
Compute the probability of simple and compound events in the context of card and dice games.
Define, calculate, and interpret the Expected Value (EV) of a probabilistic event.
Define the concepts of House Edge (HE) and Return to Player (RTP) and calculate them for various casino games.
Analyze how rule variations in games like Blackjack and Roulette affect probabilities and the house edge.
Critical Thinking & Analysis:

Deconstruct complex systems (casino games) into their fundamental mathematical components.
Evaluate the fairness and risk associated with different types of bets and games.
Differentiate between short-term luck and long-term statistical probability.
Analyze marketing materials (e.g., casino bonuses) to determine their true financial value and risk.
Financial & Social Literacy:

Explain the business model of a casino using the concepts of Expected Value and House Edge.
Identify the warning signs of problem gambling and know where to find resources for help.
Engage in an informed discussion about the social and ethical implications of legalized gambling, weighing economic benefits against social costs.

Part II: Unit 1 – The Building Blocks of Chance: Combinatorics

Lesson 1.1: The Scale of Chance – Factorials, Permutations, and Combinations

Hook Activity: The Impossibility of a Repeated Shuffle

The lesson begins with a single, shuffled deck of 52 playing cards. The educator poses a question: “Has this exact arrangement of 52 cards ever existed before in the history of the universe?” This question introduces the concept of a factorial, specifically 52 factorial, denoted as 52!. This number represents the total number of ways to arrange 52 distinct items.

The value of 52! is an incomprehensibly large number, approximately 8.06×1067.⁷ To make this tangible, the educator can share vivid analogies. Even if every star in our galaxy had a trillion planets, and each planet had a trillion people, and each of those people had been shuffling a deck of cards a trillion times a second since the beginning of time, they would not have exhausted all possible permutations.⁷ Every time a deck of cards is properly shuffled, it produces a sequence that has almost certainly never been seen before and will never be seen again, highlighting the vastness of the sample space in even simple scenarios.⁸

Core Instruction: Order vs. No Order

Following the hook, the lesson formally introduces the mathematical tools used to count large numbers of outcomes: permutations and combinations.

Permutations: A permutation is an arrangement of objects in a specific order. The order in which the objects are selected matters. The formula for the number of permutations of n objects taken r at a time is:
P(n,r)=(n−r)!n!

This is used when the sequence of events is important, such as the specific order of cards being dealt from a deck.10
Combinations: A combination is a selection of objects where the order does not matter. The formula for the number of combinations of n objects taken r at a time is:
C(n,r)=(rn)=(n−r)!r!n!

This is used when only the final group of objects is important, not the sequence in which they were chosen. For example, a 5-card poker hand is a combination because the order in which the cards are received does not change the hand’s value.10

Application: Counting Poker Hands

The primary application for this lesson is calculating the total number of possible 5-card hands in poker. Since the order of the cards in a hand does not matter, this is a combination problem. Students will calculate:

C(52,5)=(552)=5!(52−5)!52!=5!47!52!=2,598,960

This number, 2,598,960, represents the total sample space for 5-card poker and will serve as the denominator for all subsequent poker probability calculations in the unit.11

Next, students will apply combinatorial logic to calculate the frequency of specific, high-ranking poker hands. This exercise demonstrates that the abstract mathematics of combinations is not merely a classroom task; it is the fundamental language used by expert players to analyze game situations. High-level players think in terms of “combos” to assess the likelihood of an opponent holding a particular hand.¹³ By learning to perform these calculations, students are learning the foundational grammar of strategic analysis.

Example Calculation (Four of a Kind):

Choose the rank: First, choose the rank for the four-of-a-kind (e.g., four Aces, four Kings). There are 13 possible ranks to choose from. This is (113).
Choose the four cards: For the chosen rank, we need all four cards of that suit. There is only one way to do this: (44).
Choose the fifth card (the “kicker”): The final card can be any of the remaining 52−4=48 cards in the deck. This is (148).
Total Combinations: The total number of ways to get a four-of-a-kind is the product of these choices: (113)×(44)×(148)=13×1×48=624.¹⁶

This process can be repeated for other hand types, such as a Flush or a Full House, reinforcing the logical steps of breaking a complex problem into smaller, countable parts.

Table 1: Frequency and Probability of 5-Card Poker Hands

The following table provides a quantitative ranking of poker hands, demonstrating why certain hands are more valuable than others—they are mathematically rarer. This transforms the game’s rules from arbitrary dictates into logical consequences of probability.

Hand	Frequency (Number of Combinations)	Probability
Royal Flush	4	0.000154%
Straight Flush	36	0.00139%
Four of a Kind	624	0.0240%
Full House	3,744	0.1441%
Flush	5,108	0.1965%
Straight	10,200	0.3925%
Three of a Kind	54,912	2.1128%
Two Pair	123,552	4.7539%
One Pair	1,098,240	42.2569%
High Card	1,302,540	50.1177%
Total	2,598,960	100.00%
	¹¹

Lesson 1.2: The Mathematician’s Card Trick – Applied Combinatorics

Activity: The Trick

This activity demonstrates that what appears to be magic is often a deterministic algorithm that can be deconstructed with mathematical logic. The teacher, acting as a “magician,” performs a card trick using nine cards.¹⁸

Nine cards are dealt face up into three rows of three.
A student volunteer silently chooses one card and tells the teacher only which row their card is in.
The teacher gathers the cards. The key is the method of gathering: the two “un-chosen” rows are picked up first, and the row containing the student’s card is placed in the middle of the stack.
The teacher re-deals the cards into three rows of three.
The student is again asked which row their card is in.
The teacher repeats the gathering process, placing the chosen row in the middle of the stack.
The process is repeated a third and final time.
After the third gather, the teacher announces that the student’s card is now in a specific position in the deck: the fifth card from the top. The teacher can then reveal the fifth card to be the chosen card.

Challenge: Deconstructing the “Magic”

Students work in small groups to determine why the trick works every time. Their task is to trace the position of the chosen card through each step of the process and explain the underlying mathematical or logical principle.

The “magic” is an algorithm that systematically reduces the possible positions of the chosen card.

After the first sort and stack: By placing the chosen row in the middle of the nine-card stack, the volunteer’s card is guaranteed to be in one of three positions: the 4th, 5th, or 6th card in the deck.
After the second sort and stack: When the cards are re-dealt, the cards from positions 4, 5, and 6 will all land in the second row. The student will, therefore, always identify the middle row. When the teacher gathers the cards and again places this middle row in the center of the stack, the chosen card is once again guaranteed to be in the 4th, 5th, or 6th position.
After the third sort and stack: This is the crucial step. Let’s trace the exact positions. After the second stack, the card is in position 4, 5, or 6.

If it was in position 4, it is now dealt to Row 2, Position 1.
If it was in position 5, it is now dealt to Row 2, Position 2.
If it was in position 6, it is now dealt to Row 2, Position 3.
The student again identifies this row. When the teacher places this row in the middle for the third time, the card’s final position is fixed. The card that was in Row 2, Position 1 becomes the 4th card. The card from Row 2, Position 2 becomes the 5th card. The card from Row 2, Position 3 becomes the 6th card. The trick as described in 18 states the top card is the answer, which implies a slightly different stacking method (e.g., placing the chosen row on top or bottom). However, the core principle remains: the sorting process is a physical demonstration of an algorithm that narrows down possibilities until only one remains. This lesson teaches students to look for patterns and logical systems behind seemingly random or magical events.

Part III: Unit 2 – Deconstructing the Games: Probability in Action

Lesson 2.1: The Roulette Wheel – A Spin Through Sample Spaces

Core Instruction: Visualizing Probability

This lesson introduces the fundamental concept of a sample space—the set of all possible outcomes of an experiment. The roulette wheel serves as an ideal physical and visual representation of this concept.¹⁹ The instruction will focus on the two main variants of the game:

American Roulette: The wheel contains 38 pockets. These include numbers 1 through 36, a single zero (0), and a double zero (00). The sample space has 38 equally likely outcomes.¹⁹
European Roulette: The wheel contains 37 pockets. These include numbers 1 through 36 and only a single zero (0). The sample space has 37 equally likely outcomes.²⁰

Activity: Calculating Roulette Probabilities

Students will use the sample spaces of both wheel types to calculate the probabilities of winning various bets. This activity reinforces the basic probability formula:

P(event)=Total number of outcomes in sample spaceNumber of favorable outcomes

Students will calculate probabilities for:

Outside Bets: Bets on large groups of numbers, such as Red/Black, Odd/Even, or Low (1-18)/High (19-36). For a “Red” bet on a European wheel, the probability is 18/37. On an American wheel, it is 18/38.²²
Inside Bets: Bets on specific numbers or small groups, such as a “Straight Up” bet on a single number. For a bet on the number 17, the probability is 1/37 on a European wheel and 1/38 on an American wheel.²²

This exercise reveals a crucial design principle in casino games. A seemingly minor alteration in game design—the addition of the “00” pocket in American roulette—is not a trivial change. It is a deliberate engineering choice that systematically and profoundly alters the financial outcome of the game for the casino. By comparing the probabilities, students will observe that the American wheel consistently offers lower chances of winning than its European counterpart. This leads directly to an analysis of the house edge.

The addition of the “00” pocket does two things simultaneously: it decreases the numerator’s proportion in the probability of winning (e.g., from 18/37 to 18/38) while also increasing the number of losing outcomes from 19 (18 of the opposite color + one zero) to 20 (18 of the opposite color + two zeros). This dual effect is what causes the casino’s long-term advantage to nearly double, a powerful lesson in how a single variable can have a disproportionate impact on a system’s overall behavior.¹⁹

Table 2: Comparative Analysis of Roulette Variants

This table allows for a direct, side-by-side comparison that makes the mathematical and financial impact of the “00” pocket undeniable. It provides the raw data for students to analyze and serves as a foundational reference for calculating Expected Value in the next unit.

Bet Type	Payout	American Wheel (38 pockets)	European Wheel (37 pockets)
		Win Probability	House Edge
Red/Black	1 to 1	47.37% (18/38)	5.26%
Odd/Even	1 to 1	47.37% (18/38)	5.26%
Column/Dozen	2 to 1	31.58% (12/38)	5.26%
Straight Up	35 to 1	2.63% (1/38)	5.26%
Five-Number Bet	6 to 1	13.16% (5/38)	7.89%
	²⁰

Lesson 2.2: The Blackjack Table – Strategy, Skill, and Conditional Probability

Core Instruction: When Past Events Matter

This lesson introduces conditional probability, where the probability of an event is dependent on the outcome of a previous event. Blackjack is a perfect model for this, as the optimal decision for a player changes based on the information they have: their own two cards and the dealer’s visible “upcard”.²⁴ The core rules of the game are reviewed: players try to get closer to 21 than the dealer without going over (“busting”).²⁵

Activity: To Hit or Not to Hit?

Using data on the composition of a standard 52-card deck, students will calculate the conditional probability of busting on a “hit.”

Scenario: A player has a hand total of 16. What is the probability they will bust if they take another card?
Analysis: To bust, the player must draw a card with a value greater than 5 (a 6, 7, 8, 9, 10, Jack, Queen, or King).
Calculation: Assuming no other cards are known, there are 8 ranks of cards that will cause a bust. Seven of these ranks (6, 7, 8, 9, J, Q, K) have 4 cards each, and the rank of 10 also has 4 cards. That’s 8×4=32 cards that will cause a bust. The probability is 32/52, or approximately 61.5%. (Note: This calculation simplifies by ignoring the two cards already in the player’s hand. A more advanced calculation would remove those cards from the deck, further refining the conditional probability).
This exercise is repeated for various hand totals, using the “Odds of Busting” chart from 28 as a reference.

Introducing “Basic Strategy”

The lesson introduces the “Basic Strategy” chart for Blackjack.²⁵ It is crucial to frame this chart not as a list of rules to be memorized, but as the

solution set to a vast number of complex conditional probability problems. Each entry in the chart (Hit, Stand, Split, Double Down) represents the single decision that has the highest positive (or least negative) long-term Expected Value for the player in that specific situation.

This framing leads to a profound understanding of the game. The commonly cited house edge of approximately 0.5% in Blackjack is not a constant property of the game itself.²⁷ Rather, it is a theoretical minimum, a benchmark that is only achievable through the sustained and disciplined application of mathematically perfect play.²¹ For the average player who makes decisions based on intuition, superstition, or incomplete knowledge, the actual house edge they face is significantly higher. The “skill” in Blackjack is therefore not about having a feeling for the cards; it is the ability to consistently execute the probabilistically optimal decision, thereby minimizing the house’s inherent mathematical advantage.

Table 3: The Financial Impact of Blackjack Rule Variations

This table demonstrates that casinos are not passive participants; they can actively “tune” the profitability of their Blackjack games by making subtle changes to the rules. This reinforces the concept of the house edge as a product of deliberate design.

Rule Variation	Effect on House Advantage
Number of Decks
Single Deck	Base (0.17%)
Double Deck	+0.29%
Four Decks	+0.43%
Six Decks	+0.47%
Eight Decks	+0.49%
Dealer’s Action on Soft 17
Dealer Stands on Soft 17 (S17)	-0.2% (Favorable to Player)
Dealer Hits on Soft 17 (H17)	Base
Doubling Down Rules
Double Down Allowed After Split (DAS)	-0.12% (Favorable to Player)
No Double Down After Split	Base
Surrender
Late Surrender Offered	-0.07% (Favorable to Player)
No Surrender	Base
Blackjack Payout
Pays 3 to 2	Base
Pays 6 to 5	+1.4% (Unfavorable to Player)
Pays 1 to 1 (Even Money)	+2.3% (Unfavorable to Player)
	²⁵

Part IV: Unit 3 – The Unseen Advantage: Expected Value and the House Edge

Lesson 3.1: The Long Run – Calculating Expected Value (EV)

Core Instruction: The Casino’s One-Equation Business Model

This lesson introduces Expected Value (EV), one of the most critical concepts in probability theory and the cornerstone of the entire gambling industry. EV is defined as the long-run average outcome of a repeated experiment. It represents the amount a player can expect to win or lose per bet, on average, if they were to make the same bet infinitely many times.²⁴

The formula for Expected Value is the sum of the value of each possible outcome multiplied by its probability:

EV=∑(P(outcome)×V(outcome))

where P is the probability of an outcome and V is its value (e.g., the amount won or lost).24

A positive EV indicates a profitable bet for the player in the long run, while a negative EV indicates an unprofitable one. It is a fundamental truth that all standard casino games offer a negative EV to the player.³¹ This negative EV is mathematically identical to the casino’s

House Edge (HE), just viewed from the opposite perspective. This relationship can be expressed with a single, powerful equation that summarizes the entire business model of a casino:

Player EV=−HE

The player’s expected loss is the casino’s guaranteed profit margin over the long term. Their business is not built on luck, but on applying this small, persistent mathematical advantage over millions of wagers.21

Scaffolded Activity: Calculating EV

Students will learn to calculate EV through a series of progressively more complex examples.

Simple Dice Game: An introductory, non-casino game. “A friend offers you a bet. You roll a standard six-sided die. If you roll a 6, they pay you $5. If you roll any other number, you pay them $2. What is the Expected Value of playing this game once?”

Outcomes: Win (+5) or Lose (−2).
Probabilities: P(Win)=1/6; P(Lose)=5/6.
Calculation: EV=(1/6×$5)+(5/6×−$2)=$5/6−$10/6=−$5/6≈−$0.83.
Conclusion: On average, the player will lose about 83 cents each time they play this game. It is an unprofitable venture.

European Roulette: Apply the EV formula to a $1 bet on “Red” in European Roulette, using data from the previous lesson.

Outcomes: Win (+1) or Lose (−1).
Probabilities: P(Win)=18/37; P(Lose)=19/37.
Calculation: EV=(18/37×$1)+(19/37×−$1)=$18/37−$19/37=−$1/37≈−$0.027.
Connection: This EV of -$0.027 represents a 2.7% loss for the player. This is precisely the House Edge for European Roulette.²¹ The calculation reveals the mathematical origin of the house edge.

Lesson 3.2: The Player’s Dilemma – Using EV for Strategic Decisions

Application 1: Blackjack Strategy

Expected Value is not just a tool for analyzing games; it is a tool for making decisions within them. This is demonstrated using a Blackjack scenario based on the analysis in.²⁴

Scenario: A player has a hand total of 16, and the dealer’s upcard is a 9. The player must decide whether to “Hit” or “Stand.”
Analysis: To make the optimal choice, one would calculate the EV for both actions. This involves summing the probabilities of all possible outcomes (improving the hand, busting, or pushing) multiplied by their respective payouts (+1 for a win, -1 for a loss, 0 for a push). While the full calculation is complex and relies on computer simulations, the principle is clear: Basic Strategy charts are simply pre-calculated tables of the highest EV action for every possible game state.²⁴

Application 2: The “Best Bet” in the Casino

This application explores the game of Craps to illustrate a more subtle use of game theory and EV by casinos. The rules of Craps are introduced, with a focus on two key bets: the Pass Line bet and the Odds bet.³²

The Pass Line Bet: The fundamental bet in Craps, with a house edge of 1.41%.³³
The Odds Bet: A secondary bet that can only be made after a Pass Line point has been established. This bet is famous for having a 0% house edge, meaning it pays “true odds” and is, in isolation, a completely fair bet.³³

This presents a paradox: why would a casino offer a bet with no advantage? The answer lies in the structure of the game. The “fair” Odds bet is a brilliantly designed “loss leader.” It can only be accessed after a player has already made the Pass Line bet, which carries a house edge. The casino uses the allure of the 0% edge bet to encourage players to participate in the main game and, crucially, to wager more money overall. While taking maximum odds lowers the combined house edge on the player’s total wager, it never eliminates it entirely, as the initial Pass Line bet is always in play. This is a masterful piece of game design that leverages a “fair” component to enhance the profitability of the main, unfair game.³³

Lesson 3.3: The Digital Gamble – Understanding Slot Machine Mathematics

Core Instruction: Behind the Screen

This lesson demystifies slot machines, dispelling common myths about “hot” or “cold” machines. Modern slot machines are governed by sophisticated computer programs called Random Number Generators (RNGs). Their performance is not random in the long run but is defined by three key mathematical parameters, often detailed on a Probability and Accounting Report (PAR) sheet used by the casino.³⁵

Return to Player (RTP): The percentage of all wagered money that a slot machine is programmed to pay back to players over its lifetime. An RTP of 92% means that, on average, for every $100 wagered, the machine will return $92 in winnings.²⁷
Hold Percentage: The inverse of RTP. This is the portion of wagered money the casino keeps as profit. For a machine with a 92% RTP, the hold is 8%.³⁵
Volatility (or Variance): This determines the style of the payout. A low-volatility machine pays out small wins frequently, providing a longer play session. A high-volatility machine pays out large jackpots very rarely, leading to more dramatic swings of winning and losing.³⁵

Activity: Reading a PAR Sheet

Students are given a simplified, fictional PAR sheet for a hypothetical slot machine.

Machine Name: “Pharaoh’s Fortune”
Theoretical RTP: 94%
Volatility Index: High

Students will:

Calculate the theoretical hold percentage (100% – 94% = 6%).
Discuss the player experience. A high volatility and 94% RTP means that most players will lose their money, but a very small number of players will win large jackpots. The game is designed for high risk and high reward.

This analysis reveals that the complex features of modern video slots—multiple paylines, elaborate bonus rounds, engaging themes, and cinematic graphics—are primarily illusions of control.³⁷ These elements are designed to maximize player engagement and time on the device, thereby allowing the fixed mathematical model to work. They may alter the game’s volatility, changing the

experience of play, but they do not change the fundamental, negative expected value dictated by the machine’s programmed RTP.²⁷ The lesson is to see past the entertaining interface to the simple, underlying financial model.

Part V: Unit 4 – Math in the Real World: Financial Literacy and Responsible Gaming

Lesson 4.1: The “Free Money” Fallacy – The Mathematics of Casino Promotions

Core Instruction: Reading the Fine Print

This lesson applies the concepts of EV and house edge to a common real-world scenario: online casino promotions. Online casinos and sportsbooks frequently offer bonuses, such as deposit matches, to attract new customers.³⁹ However, these bonuses are almost always attached to a

wagering requirement (also called a “rollover” or “playthrough”), which stipulates that the player must bet a certain multiple of the bonus amount before any winnings can be withdrawn.⁴¹

Problem-Solving Activity: Is the Bonus “Free”?

Students will work through the following problem to analyze the true value of a typical promotion.

The Scenario: An online casino is trying to attract new players. Their promotion states you can get a 100% deposit match bonus with a $20 minimum deposit. You decide to deposit $20, and the casino gives you an additional $20 in bonus funds, for a total balance of $40. The terms and conditions state there is a 30x wagering requirement on the bonus amount. To clear the bonus, you must play a specific slot machine with a 95% RTP.
Student Tasks:

Calculate the Total Wager Required: Determine the total amount of money you must bet before you can withdraw the bonus funds.

Calculation: Bonus Amount × Wagering Requirement = Total Wager
$20×30=$600.⁴⁴

Calculate the Expected Loss: Using the concept of house edge (which is 100% – RTP), calculate your total expected loss after wagering the required $600.

Calculation: Total Wager × House Edge = Expected Loss
House Edge = 100% – 95% = 5%
$600×0.05=$30.³⁶

Write a Conclusion: Answer the question: “Is the $20 bonus truly ‘free’? Explain your reasoning using your calculations.”

This exercise leads to a critical realization: casino bonuses are often a mathematical trap. They are not gifts. They are a financial instrument designed to lock a player into a high volume of play. By forcing a player to wager a large amount ($600 in this case), the casino ensures that the game’s inherent house edge has ample opportunity to take effect. In this example, the player receives a $20 bonus but is expected to lose $30 while trying to unlock it. The bonus structure mathematically guarantees a greater expected loss for the player than the initial value of the bonus itself, revealing its true purpose as a tool for profit generation. This is a powerful lesson in reading the fine print and understanding the financial mechanics behind “free” offers.⁴³

Lesson 4.2: Knowing the Stakes – An Ethical Discussion on Gambling

Core Instruction: Weighing Costs and Benefits

This final lesson transitions from pure calculation to critical discussion, synthesizing the mathematical knowledge gained throughout the unit to facilitate an informed ethical debate. The discussion is framed using the pro/con structure presented in the research: the purported economic benefits of the gaming industry versus its documented social costs.⁵

Proponents Argue: The gaming industry generates vital tax revenue for states, creates jobs, boosts tourism, and can lead to lower welfare and unemployment rates in communities with casinos.⁵
Critics Argue: These benefits come at the cost of significant social harm, including gambling addiction, bankruptcy, crime, and domestic abuse. The industry’s business model relies on players’ losses, and it can be argued that it exploits vulnerable individuals.⁵

Discussion Prompts

Students will engage with these complex issues through guided discussion prompts:

A former gambling addict and author poses the question: “Essentially, [legislators are] admitting that they know they are creating a class of gamblers who become addicts. If you know what you’re doing creates problems, is this appropriate policy?”.⁵ Is it ethical for a government to profit from an activity it acknowledges is harmful?
Research shows that gambling behavior is often normalized through social and familial influences, starting at a young age.⁴⁵ How does the widespread marketing of gambling as “entertainment” contribute to this normalization?
Based on your mathematical understanding of Expected Value and House Edge, is “entertainment” a fully accurate description of a casino game? Why or why not? How does the math you’ve learned change your perspective on the fairness of these games?

This discussion highlights that an informed ethical debate about gambling is impossible without first understanding the underlying mathematics. The concepts of EV, HE, and RTP are not neutral terms; they are the very mechanisms that define the financial relationship between the player and the house. This mathematical literacy is a prerequisite for responsible personal decision-making and for evaluating public policy. It allows students to move beyond arguments based on emotion or anecdote and engage with the issue from a position of understanding the financial engine that drives the industry and its associated social consequences.

The lesson concludes by equipping students with practical information. The educator will provide a list of warning signs for problem gambling and share legitimate, confidential resources for seeking help. This includes information from organizations dedicated to youth gambling prevention and responsible gaming advocacy.

National Council on Problem Gambling (NCPG): Helpline at 1-800-GAMBLER.⁴⁶
Responsible Gambling Council (RGC): Offers youth-focused educational programs like “House of Wisdoms” and “GAME BRAiN”.²
McGill Youth Gambling Centre: Develops prevention tools and resources for adolescents, such as the “Hooked City” interactive game.³
GambleAware NSW: Provides free classroom resources for teachers and youth workers to educate students about gambling risks.⁴

Part VI: Culminating Unit Project: The “Design-A-Game” Challenge

To synthesize and assess the knowledge gained throughout the unit, students will engage in a creative, project-based learning challenge inspired by real-world application models.¹

Project Brief

Working in small groups, students will assume the role of casino game designers. Their task is to invent a new, simple game of chance using common materials (e.g., standard dice, a deck of cards, or a custom-designed spinner).

Requirements

Each group must prepare and deliver a presentation that includes the following components:

Game Rules: A clear, concise, and unambiguous set of rules that explains how the game is played, what bets can be made, and how a round is won or lost.
Probability Analysis: A complete mathematical breakdown of their game. This must include:

The full sample space of all possible outcomes.
The calculation of the probability for each distinct outcome.

Payout Structure: A detailed list of the payouts for all winning bets. Payouts should be expressed in a standard format (e.g., “2 to 1,” “5 to 1”).
House Edge Calculation: A step-by-step calculation of their game’s house edge for each available bet. Students must demonstrate that they have deliberately designed the payouts to be lower than the “true odds,” thereby guaranteeing a specific, long-term profit margin for the “house.” The target house edge should be between 3% and 8%.
Marketing Pitch: A brief (1-2 minute) verbal pitch explaining why their game would be appealing and entertaining to players, while also being a profitable product for a casino.

Assessment

This project serves as the summative assessment for the unit. It requires students to apply concepts of combinatorics, probability, and expected value in a synthetic and creative task. Groups will be assessed on:

Mathematical Accuracy: The correctness of their probability and house edge calculations.
Clarity and Logic: The coherence and clarity of their game rules and presentation.
Synthesis of Concepts: The ability to connect the mathematical design of their game to the financial outcome (house edge).
Presentation Quality: The overall effectiveness and professionalism of their presentation.