Analyze this simple betting game with your maths student. Discuss probability - the measure of how likely it is an event will occur - as you work to figure out whether the odds of successfully rolling the 3 numbres during the three rounds of play are in the player's favor. All you need is a set of three dice, and you can get rolling! Play several times and look for patterns in the game. Is the player likely to win? Take a close-up look at each round of the game.

### What You Need:

- Three dice

### What You Do:

- Select a dealer and a player. The object of the game is for the player to roll a 1, a 2, and a 3 During 3 rounds of Rolling The dice.
- If one of these numbers is rolled after the first or second round, they should put that die aside and not roll it again.
- If the player succeeds in rolling a 1, 2, and 3, they win.
- Switch roles and play again.
- After playing several times, start a discussion about probability. Ask: What are the chances of rolling a particular number in each of the three rounds? Is the game fair? Who has the better odds, the dealer or the player?

### More About Probability:

If you're interested in the logic behind the odds, or probability, of rolling the right numbers, read on.

- First, figure out the odds of rolling just a 3. You have at least five chances of rolling a 3. How did you come up with five, you ask? Well, you might roll a 1 and a 2 in the first round, limiting your dice for the subsequent rounds to 1. So, you could roll 3 dice in the first round, 1 die in the second round, and 1 die in the third round. With at least 5 chances to roll a 3, the odds look pretty good. Now, let's look at all three numbers...
- In the first round, it's very likely you'll roll a 1, 2, or 3. Why? Because 1, 2 and 3 make up half of the total numbers on a die. Multiply 1/2 by 3 (because there are 3 dice), and chances are you will roll 1 1/2 of those numbers. (I know what you're thinking: Wait! You can't roll 1/2 of a number! Well, you're right. However, what these odds mean is you are likely to roll at least 1 of your numbers, and half the time you should roll 2 of them. This averages out to 1 1/2.)
- In the second round, the odds get a little bit tricky. Let's say you rolled just one of your numbers in the first round. This means, you have 2 dice to roll and 2 numbers to find. The odds of finding one of those remaining numbers is 1/3 (or 2/6). It is unlikely you will find either of your numbers in this round, but there is a chance. If you do find one of your numbers, you've just lowered your chances of finding the last number in the last round, with one dice, to 1/6. That is very unlikely.
- Let's consider another possible scenario: what if you rolled two of your numbers in the first round? (After all, that will probably happen 1/2 the time.) You would have 1 dice to roll and one number to find. Your odds are pretty low, as you now have a 1/6 chance in rolling that number. Keep in mind that you do get another roll in the third round, but you'll still only have a 2/6 (or 1/3) chance of rolling your desired number
- The odds do look pretty good at first, right? Nonetheless, as you progress through the rounds, you'll realise the odds aren't in your favor. Considering the probability, it's probably not a good idea to bet money on this game!

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See this activity in a set:
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