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Nine or Ten?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Racing Odds

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Non-transitive Dice

Age 11 to 14 Challenge Level:

Here are three dice that are used to play a game for two players:
 

 

 


The red die has the numbers {1, 1, 6, 6, 8, 8}
 
The green die has the numbers {2, 2, 4, 4, 9, 9}
 
The blue die has the numbers {3, 3, 5, 5, 7, 7}


Each player chooses a different die.
They roll their dice.
The winner is the person whose die shows the bigger number.

Alison and Charlie are playing the game. Charlie wants to go first so Alison lets him.

Was that such a good idea?
 
Can you advise Alison on which die to choose once she knows which die Charlie has selected?


 

Notes and background
 
Dice of this sort are known as non-transitive dice. You can read more about transitivity in this article or have a go at creating your own in Dicey Dice. This spreadsheet might be useful if you want to create your own.

After you've had a go at the problem, you may be interested to read more about dice in the Plus articles Curious dice and Let 'em roll.

You may be familiar with another non-transitive game known as 'rock, paper, scissors'.