# Blog

## Liar’s Dice

By

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Here’s a fun game that will reward you when you don’t tell the truth. Have a go at liar’s dice!

### You will need

• At least two people
• Five dice for each player
• An opaque (not see-through) cup or bowl for each player

### Set-up

1. At the start of the game, sit everyone at a table, and give each of them a cup and five dice.
2. Choose someone to have the first turn.

### Starting a round

1. Get everyone to put their dice into their cup and shake them around.
2. On the count of three, everyone turns their cup upside-down, covering their dice. Each player can look under their cup to see what they rolled, but they are not allowed to look at other people’s dice.

The aim of this game is to guess what numbers have been rolled by everyone. You can see your numbers, but you can’t see everyone else’s, so you might need some luck, and you might need to lie a bit!

1. The first player names a roll (a number from 1-6) and a guess of how many dice on the table came up with that roll.
2. The next player has two options:
• They can make their own guess, or
• They can call the previous player a liar.
1. If they make their own guess, they have to make it bigger. They can guess more dice (so a guess of twelve ‘3’s is bigger than ten ‘6’s). Or they can guess the same number of dice with a bigger roll (eight ‘4’s is bigger than eight ‘3’s). Then play goes to the next person around the table.

2. If they call the previous player a liar, the round is over. Everyone reveals their dice and they are counted. If there are enough dice showing the right face (having too many is fine!) then the challenging player loses the round. If there are not enough dice showing the guessed roll, the guess was a lie and the liar loses the round.
3. When the round ends, the player who lost loses one of their dice.
4. If a player has no dice, they are eliminated from the game.
5. When there is only one player left, they are the winner!

### The end of a round

1. When the round ends, the player who lost loses one of their dice.
2. If a player has no dice, they are eliminated from the game.
3. When there is only one player left, they are the winner!

### What’s happening?

There’s a lot of luck in liar’s dice, and even the best players can lose. But doing a bit of maths can help you play a lot better. Each die has six sides, so they have a one-in-six chance of showing a particular face. For example, you’re playing with three other players, and they have 15 dice between them. If you want to know how many ‘2’s they rolled between them, you can imagine that as two groups of six dice, and three extras. They probably rolled at least two ‘2’s.

You can make a quick estimate by counting up the dice and putting them in groups of six. But there are more precise ways of calculating the chances. Statisticians call this the ‘expected return’ and it uses some tricky maths, but it gives us the best possible estimate of what might happen.

It is important to note that your rolls don’t affect everyone else’s. If you roll five ‘2’s, you didn’t ‘use up’ all the ‘2’s. There’s still a good chance everyone else rolled two ‘2’s between them. And just because you didn’t roll any ‘6’s, doesn’t mean everyone else must have rolled more to even it out. Your rolls and everyone else’s rolls are completely independent.

Some rules for the game, including lots of variants to make the game more interesting

Try making some dice that actually lie

If you’re after more maths activities for kids, subscribe to Double Helix magazine!

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