Yahtzee Odds and Probabilities
At its heart, Yahtzee is a numbers game and success is measured in total points. Consisting of 13 scoring categories, the Yahtzee scorecard allows for the possibility of multiple Bonus Yahtzees and this is the key strategy to maximize points. It is theoretically possible to achieve an ultimate high score of 1575 - that is 140 points in the Upper Section, 235 points in the Lower Section, and 1200 Yahtzee Bonus points. A player would achieve this feat by rolling a Yahtzee on each turn and using the ensuing Jokers to complete the Lower Section categories. Many of the Yahtzees would need to be in a certain number: the Upper Section's Ones in ones, Twos in twos, etc., and in sixes to max out Three of a Kind, Four of a Kind, and Chance in the Lower Section. The odds of approaching anything near a 1575 grand total are astronomical. The typical Yahtzee player generally considers a final score in the 250 point range to be a success, and indeed this turns out to be about the average score for the competent player, whether playing online Yahtzee or at the table.
Researchers at the World Yahtzee Institute have analyzed thousands of games to determine the odds of achieving a particular result:
The following graph illustrates the odds of rolling a particular combination on the first, second, and third roll of a turn. The Full House and Straights can not be calculated generally because of the multitude of variations that exist for each roll. This would need to be calculated on a case-by-case basis depending on each of the individual player's rolls. The figures assume that the player goes for the given scoring category from the first turn and does not deviate in their strategy. Otherwise it may take longer to achieve a given score as an initial pair may be discarded to roll for something else.
|Three of a |
|Four of a |
Yahtzee Players' Statistics
A good way to develop your own Yahtzee strategy and improve your game is to study the trends of professional players. The following statistics were compiled by analyzing the top three players’ official Yahtzee Pro Circuit games played between 2010-2020. Categories where the score can vary are represented by the players' average score per game. Those that receive a fixed score reflect the percentage of games in which the category was successfully scored:
|Three of a Kind||20.36||21.56||19.71|
|Four of a Kind||12.17||14.15||13.73|
|Yahtzees per game||0.57||0.46||0.47|
|Average Grand Total||251.88||244.21||247.15|
In the Upper Section, note that each player averaged fewer than three of the target number for Ones and Twos. These are often used as “throw-away” categories when a player is unable to record an acceptable score elsewhere on their scorecard, in the hope that they will be able to make up the difference with their Fives or Sixes. Also of interest is that none of the top-three Yahtzee pros were able to maintain an average of 63 total points for the Upper Section, the threshold needed to secure the 35-point bonus.
Learn More about Yahtzee Odds
Take a deep-dive into the mathematics behind Yahtzee odds and probabilities at these sites: