What are the odds of winning the jackpot on a slot machine?
Why?
- Provides context for probability and combinatorics topics
- Engage students in discussion on ethics of gambling and the Toronto Casino Debate
Being in Niagara Falls yesterday got me thinking about casinos and gambling, an interesting topic for debate and a common way of illustrating concepts in probability.
Also, the debate on whether or not Toronto should allow a casino to built or not provides context for a discussion of the topic in a classroom setting.
My internship supervisor and I were wondering what the actual odds of winning at a slot machine were. What does an 80% payout mean? It turns out payouts are deceiving. A 80% payout doesn't mean you will win 80% of the time but the value you can expect to walk away with is 80% of what you started with. In probability, an expected value of 100% (or 1) is considered a fair game because the player and the casino have equal chances of winning.
According to this website, Nevada law states that the minimum payout can be 75%. It is rarely this low however because casinos compete for players by increasing the payout. 90-95% are more common. In addition to the games being mathematically unfair, they are built so that it is more likely that the machine will stop in the blank spaces on either side of the jackpot symbol to make it feel like the player is close to winning.
The Curriculum...
As an activity in class, students could calculate the odds of winning a jackpot on a slot machine with (for example) 3 reels and 20 positions (symbols + spaces in between symbols) on each reel.
Then, questions get more complicated when trying to find out the expected value (or payout) of a machine based on the probabilities of landing on each symbol and the payout of each symbol. This website provides the background for some of that math.
These questions touch on various concepts central to the Grade 12 Data Management course (probability, random variables, combinations, expected values, probability distributions).
21C...
As an extension and problem-solving exercise would be to devise a slot machine that would provide a fair (100%) payout. Students with experienced in programming could write a program to simulate the machine.
A lot of the time in Data Management, gambling and game related probability problems are given to students. I think it is important to put these questions in context by critically thinking about and discussing the ethics and psychology of gambling. The Toronto casino debate is potentially an entry point for the topic.
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
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