# Pig

The more times you roll the die, the more you add to your score. But if you roll a 1 you lose it all.

Ages: 5+
Players: 2+
Time: 10-20 Minutes
Type: number games
Location: tabletop
Ages: 5+
Players: 2+
Time: 10-20 Minutes
Type: number games
Location: tabletop

## Instructions

Pig is a game of fortune and misfortune, luck and loss, courage and caution! And also addition. Each player needs their own score card. Write your name at the top of your score card.

Then, take turns. On your turn, roll the die as many times as you like. If you roll a 2, 3, 4, 5, or 6, add that to your total, crossing off the previous total as you go.

But if you roll a 1, you lose all your points for that turn, and your turn is over!

You can choose to "hold" at any point during your turn. This means you stop rolling and circle your current total. If you roll a 1 before you hold, you lose all of your points for the turn. In that case, write your previous total and circle it.

Circling your number at the end of each turn is important because if you roll a 1, you need to know what your previous total was.

Each time you roll the die you're taking a risk. You want to increase your score by continuing to add to it, but you know that you may roll a 1 and lose everything you've gained on your turn.

The first player to reach a target number wins. A good target number is 50, but lower numbers work well for students just learning to add.

Don't forget: it's Beast Academy Playground, not Beast Academy Study Hall. Change the rules, be silly, make mistakes, and try again. The Variations and Learning Notes are here for you if you want to dive deeper, but not all of them apply to learners of every age. The most important thing is to have fun.

## Variations d

### More Players:

Pig can be played with more than 2 players. Each player needs their own score card.

### Two Dice:

Roll two dice. If neither die shows a 1, you add both dice to the total. If one of the dice lands on 1, you lose all your points for that turn and return to your previous total. If both dice come up on 1, you lose all your points for the game and start again at 0. (Since players can start over at 0 at any time in this variation, be careful not to choose too large a point total for the game.)

### Hog:

For this one, you'll need a lot of dice. Five or more is ideal. You can only roll once on your turn, but you can choose to roll as many dice as you like. (You could choose to roll only one die, or all of them, or anything in between.) If none of the dice land on 1, add all of the dice to your total. If any of the dice land on 1, add nothing to your total. In either case, your turn is over after a single roll.

## Classroom Tips d

Pig is especially useful for young students practicing addition or the number line, or older students learning about probability. Students will naturally want to figure out an optimal "holding" strategy.

Discussion Questions

• How can you use a number line to determine how far you (or your opponent) are from the target number?
• How can you use subtraction to determine how far you (or your opponent) are from the target number?
• When you roll a die, what is the probability of it landing on 1?
• If you roll 4 ten times in a row, what is the probability of rolling another 4?
• Is there a good place to "hold" your score? Why? (see Learning Notes)

• Level 2, Chapter 1: Place Value
• Level 2, Chapter 3: Addition
• Level 2, Chapter 4: Subtraction
• Level 2, Chapter 8: Strategies (+ & -)
• Level 4, Chapter 12: Probability

See Variations and Learning Notes for more ideas on how to adapt this activity and incorporate it into your classroom.

## Learning Notes d

For those just learning to add, choose a smaller target number, like 20. Each roll of the die is an opportunity to practice counting and adding. Counting on fingers at a young age is fine, and reinforces the fact that addition means "this many more." You could also use coins or any small tokens to count with. Another approach is to write out a number line, starting at 0 and ending at the target number, and use it as an aid to score-keeping:

If your total was 12, for example, and you rolled a 5, you would put your finger on 12, and then count up 5 spaces on the number line to 17.

### Probability:

When you roll a die, what is the probability that it will land on 1? There are 6 possible numbers for the die to land on, only one of which is a 1. That means the probability of a roll landing on 1 is 1/6. By the same reasoning, rolling any of the other numbers is 5/6.

But what would you think if you were playing Pig and had rolled ten times and hadn't yet rolled a 1? First of all, you'd probably think you were pretty lucky! (And you'd be right. The probability of rolling ten times in a row with no 1's is about 16%.) Second, you might think that rolling a 1 next is more likely than usual. After all, if you didn't, that would be eleven rolls in a row with no 1's, which has got to be even more unlikely than ten in a row! (And it is, in fact. The probability of rolling eleven times in a row with no 1's goes down to about 13%.)

Mathematicians call this kind of reasoning the "Gambler's Fallacy," and, as you can tell from the fact that it's labeled as a fallacy, it's actually not true. Even though long streaks with no 1's are increasingly unlikely the longer you go, the probability of each individual roll of the die remains the same!

### Strategic Thinking:

How long should you keep rolling before stopping and locking in your score? As a player, you have to decide after each roll whether you've earned enough points, or whether you'll risk everything for even more points. We'll call the number of points that is "enough" your "hold" number. Generally, you keep rolling until you've hit your "hold" number on a turn, and then you stop.

What happens if you choose a low "hold" number? You'll stop your turn after fewer rolls, so there will be fewer turns where you end up rolling a 1 and losing everything. That's good! On the other hand, you won't earn very many points each turn. That's bad.

What if you choose a high "hold" number? You'll earn more points on the turns where you're lucky enough not to roll a 1. That's good! On the other hand, since you're rolling more times each turn, you'll end up rolling a 1 more often and losing your points. That's bad.

Pig is basically a game of finding the right "hold" number. Experiment with different values as you play and see how they work out. Your hold number should also change depending on some other factors. If you're in the lead, for example, it might be better to play cautiously to try to keep that lead, but if you're behind, it might be worthwhile to take bigger risks in order to catch up. Also consider how many points you are ahead or behind by and how close you and your opponent are to the target number.

Part of the fun in this game (and part of the math of the game) is to find ways to improve your chances of winning.

## What do you think of this activity?

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Materials
• die
• paper
• pencil
Learning Goals
• counting
• probability
• strategic thinking
Common Core Standards
• MP1
• K.CC.A.3
• 1.OA.C.6
• 1.NBT.C.4
• 2.OA.B.2
• 2.NBT.B.5

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