Expected Value Worksheet

Students hear "the house always wins" long before anyone shows them why. This worksheet shows them why, using the same math that also explains why long-term investing works in the opposite direction.

Expected value is a simple formula — probability of winning times the payout, minus probability of losing times the cost — but it's rarely put in front of students next to something they actually recognize, like a slot machine or a roulette wheel. This worksheet does exactly that. Students calculate the expected value of a $10 bet across three familiar gambling games: a coin flip, roulette, and a slot machine. Each game has a different win probability and a different payout, and the math reveals the same pattern every time: the expected value comes out negative. Play any of these games long enough and you lose money on average, no matter how it feels on a given night.

That's the setup. The real payoff is the discussion that follows, where students connect the math to a bigger question: if gambling has a built-in negative expected value, why do people keep playing, and what does that say about betting on a stock versus betting on a slot machine? The worksheet closes with a short written reflection asking students to state, in their own words, what they learned about the difference between gambling and investing.

This is deliberately quantitative. Students aren't just told gambling is a bad long-term bet — they calculate exactly how bad, game by game, with real numbers. That's a stronger lesson than a warning, because the student did the math themselves.

The gambling angle is not incidental. Online gambling and sports betting apps market directly to teenagers and young adults, often using the same app-based, gamified interfaces that make social media addictive. A student who understands expected value has a mental tool for recognizing when an app is designed to take their money over time, regardless of how any single bet turns out. That's a more durable defense than a rule like "don't gamble," because it explains the mechanism instead of just stating a conclusion.

The comparison to stocks matters just as much as the gambling math. Long-term investing in a diversified portfolio has historically produced a positive expected return over time, which is the mirror image of what students calculate for coin flips, roulette, and slots. Put the two side by side and students see that the difference between gambling and investing isn't about being lucky or unlucky — it's about which side of the expected value equation you're standing on. That reframing is worth more than any warning label, because it gives students a reason rooted in math rather than a rule to simply obey.

This sample comes from the Dangers of Online Gambling module, which sits inside a broader unit on financial decision-making under risk and uncertainty.

Expected Value of Stocks Versus Gambling

In this activity, students will compare the expected value of investing in stocks versus gambling, reinforcing the importance of long-term financial decision-making.

Instructions

1. 1. For a few minutes, think about the question “If you had $100, would you rather

gamble it or invest it?” Discuss with your group briefly about the risks and potential rewards of your various ideas.

REMEMBER: Expected Value (EV) = (Probability of Winning x Award) - (Probability of Loses x Cost)

1. Fill out the following table to calculate the expected value of different gambling

activities.

1. Discuss your findings with the group.

○What surprised you most about the calculations? ○Why do casinos and online gambling platforms make so much money? ○How can this knowledge influence your financial decisions in the future?

1. In 3-4 sentences, summarize what you learned about gambling vs. investing and how

you would apply this knowledge to real-life financial decisions.

Teacher notes

The table in this worksheet is intentionally sparse — students only get win probability and, for the coin flip, the payout. Filling in the rest requires them to reason about payout structures for roulette and slots, or research typical values, rather than plugging numbers into a formula someone else already set up. Decide ahead of time whether you want groups to look up realistic payout figures or work from reasonable assumptions, and be consistent across the class so the discussion questions land on comparable numbers.

Question 3's second prompt — why casinos and gambling platforms make so much money — is where students often make the leap from "this game has bad odds" to "the entire business model depends on negative expected value at scale." That's the conceptual bridge this worksheet is built to create, and it's worth slowing down on.

Keep the discussion focused on the math rather than on judgment about gambling as a behavior. The worksheet works because it's quantitative and neutral in tone — students draw their own conclusions from the numbers rather than being told what to think.

This worksheet is one piece of a broader unit on financial decision-making, which frames risk and expected value as tools students can apply well beyond this one comparison.

See how the rest of this unit works in a live demo