## Yahtzee Odds and Probabilities

The Yahtzee scorecard consists of 13 scoring categories, with the possibility for multiple Bonus Yahtzees. In the unlikely event that you roll a Yahtzee on each turn, with most of those Yahtzees being in Sixes to max out your points, it is theoretically possible to achieve the ultimate high score of 1535.

The odds of approaching anything near a 1535 are astronomical. The average Yahtzeeist generally considers a final score in the 250 point range to be a success, and indeed this turns out to be the average score for the competent player. Researchers at the World Yahtzee Institute have analyzed thousands of final scores to determine the chances of achieving a particular result:

Final Score | Probability |
---|---|

>150 | 98% |

>200 | 78% |

>250 | 59% |

>300 | 16% |

>400 | 4% |

>500 | 1% |

This graph illustrates the odds of rolling a particular combination on the first roll of a turn:

Scoring Category | Probability |
---|---|

Three of a Kind | 19.3% |

Four of a Kind | 1.9% |

Full House | 3.9% |

Small Straight | 12.4% |

Large Straight | 3.1% |

Yahtzee | 0.1% |

Take a deep-dive into Yahtzee stats with the good folks at DataGentics.