Sign up to mark as complete
Sign up to bookmark this question

# Dice With Same Numbers

You roll 3 dice. If they all show the same number, you earn €16. If two of the numbers are the same as each other, you earn €14. If all numbers are different, you lose €4.

What is the expected return per roll?

What is the expected return per roll?

Solution

Let's calculate the expected return per outcome. Let's define the following:

- is the expected return when dice are the same.
- is the probability that dice are the same.

(1)

(2)

Next, consider the case where 2 dice are the same, where you earn €14. The first dice can be any dice, the second dice needs to be the same and the third dice needs to be another number. You can order this in ways. So,(3)

(4)

Finally, consider the case where no dice are the same, where you lose €4. The first dice can be any dice, the second dice needs to be another number and the third dice again needs to be another number. So,(5)

(6)

The expected return of this game is defined as:(7)

(8)

(9)

Related Questions

Title | Category | Subcategory | Difficulty | Status |
---|---|---|---|---|

100-Sided Dice | Probability and Statistics Theory | Expected Value | Hard | |

Basketball Practice #1 | Probability and Statistics Theory | Expected Value | Medium | |

Basketball Practice #2 | Probability and Statistics Theory | Expected Value | Hard | |

Dice Game | Probability and Statistics Theory | Expected Value | Hard | |

Dice Sum | Probability and Statistics Theory | Expected Value | Easy | |

Divisible Throws | Probability and Statistics Theory | Expected Value | Easy | |

Drunk Student #1 | Probability and Statistics Theory | Expected Value | Easy | |

Drunk Student #2 | Probability and Statistics Theory | Expected Value | Medium | |

Empty Boxes | Probability and Statistics Theory | Expected Value | Easy | |

Exponential Distribution #1 | Probability and Statistics Theory | Expected Value | Medium | |

First Ace | Probability and Statistics Theory | Expected Value | Easy | |

Flip 100 Coins | Probability and Statistics Theory | Expected Value | Medium | Example |

Flip 4 coins #1 | Probability and Statistics Theory | Expected Value | Medium | |

Free Ticket | Probability and Statistics Theory | Expected Value | Hard | |

Kelly Betting #1 | Probability and Statistics Theory | Expected Value | Easy | |

Kelly Betting #2 | Probability and Statistics Theory | Expected Value | Medium | |

Other Than Six | Probability and Statistics Theory | Expected Value | Easy | |

Repeating Dice | Probability and Statistics Theory | Expected Value | Easy | Example |

Shooting Star | Probability and Statistics Theory | Expected Value | Easy | |

Specific Card #1 | Probability and Statistics Theory | Expected Value | Easy | |

Three Blue Orbs | Probability and Statistics Theory | Expected Value | Medium | |

Throw a 6 #1 | Probability and Statistics Theory | Expected Value | Easy | |

Throw a 6 #2 | Probability and Statistics Theory | Expected Value | Medium | |

Throw a 6 #3 | Probability and Statistics Theory | Expected Value | Hard | |

Throw a 6 #4 | Probability and Statistics Theory | Expected Value | Medium | |

Throw Until Match | Probability and Statistics Theory | Expected Value | Medium | Example |

Toy Collection #1 | Probability and Statistics Theory | Expected Value | Medium | |

Toy Collection #2 | Probability and Statistics Theory | Expected Value | Hard | |

Uniform Distribution #1 | Probability and Statistics Theory | Expected Value | Hard |

Discussion

Please log in to see the discussion.