# Odds and Payoff Worksheets

Many states are making online gaming legal to increase their bottom line. As online gaming becomes a more prevalent aspect of our culture, we need to help students learn to navigate it, like it or not. The best advice I give my students is to realize that the odds are and always will be in the house’s favor. Why would you play a gaming where you are automatically at a disadvantage? These gaming establishments are built on math. How successful they can be depends on their modeling of the odds and the validity of their structured pay outs. To first entice people to place a bet and then to payout less than they take in. These worksheets help students gauge their odds and weigh the pros/cons of taking part in a game of chance.

### Aligned Standard: HSS-MD.B.5a

- Chance of a Cell Phone Step-by-step Lesson- We look at pulling a total chance from three different groups all with their own characteristics.
- Guided Lesson - This scenario hits me every time my car has 100,000 miles on it. "Should I sell it in the paper or just give it to the dealer?"
- Guided Lesson Explanation - These are actually a little overwhelming for kids at first, but they are really quite simple.
- Practice Worksheet - I really wonder where your odds are better: a casino or a carnival?
- Matching Worksheet - These are very realistic problems that I had my professional friends lead me towards creating.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

The name of the game is expected number and expected payoff here.

- Homework 1 - In Applewood 30% of families have 2 bicycles, 20% of families have 5 bicycles, 40% of families have 7 bicycles and 10% of families have 1 bicycle. What is the expected number of bicycles in a family?
- Homework 2 - Mathew wants to sell his TV. He spends $50 to advertise the sale of the TV. If the TV sells in 3 months, he earns $200. Otherwise, he loses the listing. If there is a 50% chance that the TV will sell in 3 months, what is the expected payoff?
- Homework 3 - At a carnival, Dolly sees a dice game. A ticket costs $5. The rule is that you win if you roll a sum of 8 or more with 2 die rolls. Winners receive $20. What is the expected payoff?

### Practice Worksheets

We are basically trying to determine the law of the land, mathematically.

- Practice 1 - In a school, 20% of the students have 5 lunch boxes, 30% of the students have 7 lunch boxes, 40% of the students have 3 lunch boxes and 10% of the students have 2 lunch boxes. What is the expected number of lunch boxes of a student?
- Practice 2 - Paul wants to sell his car. He spends $200 to advertise the sale of the car. If the car sells in 4 months, he earns $5000. Otherwise, he loses the listing. If there is a 60% chance that the car will sell in 4 months, what is the expected payoff?
- Practice 3 - In a city 50% of families have 5 laptops, 20% of families have 4 laptops, 10% of families have 2 laptops and 20% of families have 3 laptops. What is the expected number of laptops per family?

### Math Skill Quizzes

I had to research different types of chance games.

- Quiz 1 - A condominium complex is surveyed and asked their employment status. If they have a job, the will buy an unlimited metro pass that costs $500. If they don’t have a job, they will buy the limited metro pass for $200. The results of the survey indicated that 60% of the people are working and 40% are unemployed. In the complex, what is the expected expense for metro passes?
- Quiz 2 - In a city 50% of families have 5 air conditioners, 20% of families have 4 air conditioners, 10% of families have 2 air conditioners and 20% of families have 3 air conditioners. What is the expected number of air conditioners per family?
- Quiz 3 - At a carnival, Diana sees a balloon shooter game. The ticket cost is $3. The rule is that the person who shoots the 10 balloons from total 30 balloons wins $10. What is the expected payoff for the winner?

### What are the Games of Chance?

When you think about chances, several games come in mind. The most basic set of games are simple coin tosses and board games, where there is a set chance of a particular outcome on each turn. By definition, chance games are a set of games which strongly relates to random number generator: which people utilize to bet on for an outcome.

Nearly every game in a casino qualifies as a game of chance: such as roulette, video poker and different other table games. However, if you think that poker and blackjack are games of chances, then it is not the case. Games of chance add thrill and risk at times; which most humans love to enjoy. Do you know that our ancestors used knucklebones as dice; which makes it such a massive hit in the contemporary era today?

### The Math Behind Setting Odds

Creating a set of odds for any outcome is just a fancy way of saying probability, with a bit of a twist. Odd makers start by trying to determine the true odds of an event occurring. For example, the true odds of a coin flip landing on heads are 50%, 1/1 (fractional, or 2.00 decimally.

Once odd makers determine that true probability, they now need to build in an additional buffer of space for themselves that allows them to collect a commission. This referred to as and over round or a vig. This allows them to collect money for themselves. The over round allows them to create a business for themselves around this math. This reduces the required payout on their downside. Going back to our coin flip example, if we know mathematically there is a 50% chance of heads and half of the bettors will bet on heads, we can use the over round to reduce their potential payout. For example, a 5% over round will result in a 91% payout. For every winning bet of $100, they will receive a payout of $191.

So, assuming that the odds maker can determine a truly accurate set of odds, the over round reduces their payout while maintaining their collection numbers. This is how gambling becomes a business. Mathematically you should receive more money than you end up having to pay out. The stronger the odds, the greater your business does.