In the real world, any score above 300 is a good result in Yahtzee. But what’s the absolute maximum you can score? By my calculation, it’s 1,575.
Here’s a sequence of gameplay that generates that score. Remember:
- You score an additional 100 points for every Yahtzee (five numbers the same) after the first one.
- That Yahtzee can also be used as a wild card for any other category and scores based on the values you throw. So for a maximum score you want all your “wild” Yahtzees to include sixes.
- The wild card rule still applies where a sequence of 5 matching numbers wouldn’t technically be a result that matches the category, such as a small straight or large straight.
|1||5 x 6||Yahtzee||50||Any Yahtzee would do|
|2||5 x 1||1||105||100 bonus points for each additional Yahtzee|
|3||5 x 2||2||110|
|4||5 x 3||3||115|
|5||5 x 4||4||120|
|6||5 x 5||5||160||Includes 35 bonus points for >63 at top|
|7||5 x 6||6||130|
|8||5 x 6||3 of a kind||130||Maximum points with all sixes|
|9||5 x 6||4 of a kind||130||Maximum points with all sixes|
|10||5 x 6||Full house||125||Any Yahtzee would do|
|11||5 x 6||Small straight||130||Any Yahtzee would do|
|12||5 x 6||Large straight||140||Any Yahtzee would do|
|13||5 x 6||Chance||130||Maximum points with all sixes|
As players know, the changes of getting 121 in any given round of Yahtzee are not high.
So what’s the probability of this happening? The chance of getting any one specific result in Yahtzee on a single throw is 1 in 7776. The chance of that happening 13 times in a row is roughly 1 in 3.80042E+50, as Excel would put it.
The actual odds are very slightly higher, because there are some categories (full house, small straight and large straight, plus the initial Yahtzee) where any Yahtzee will do, so you technically have 6 in 7776 odds for each of those rounds. But that doesn’t meaningfully increase the numbers for the average player. Adding that in, we get to roughly 1 in 3.41015E+48.
In other words, don’t hang round waiting.
This is an updated version of a post I first wrote in 2016.