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 the sequence of gameplay that generates that score. Remember that you score an additional 100 points for every Yahtzee (five numbers the same), and you can use that Yahtzee as a wild card for any other category (including ones where a Yahtzee wouldn’t technically be a result that fits, such as a straight).
| Round | Throw | Score as | Score | Notes |
|---|---|---|---|---|
| 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 |
| Total | 1,575 | |||
| Average/round | 121.2 |
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 1 in 3.80042E+50, as Excel would put it. In other words, don’t hang round waiting.
Your maths is very off.
Probability of getting 1575 is 1.38×10^-20 (https://en.wikipedia.org/wiki/Yahtzee).
Probability of getting any one specific result is 1 in 6^5 = 1 in 7776 as you stated. However, as you pointed out in your article, you can have “any Yahtzee” at certain rounds. Probability of “any Yahtzee” is only 1 in 6^4 = 1 in 1296 since there are 6 possible Yahtzees that you can throw.
I disagree that makes my maths “very off” — because even with that handful of “any Yahtzees”, it’s wildly improbable regardless. I was going to leave a comment to that effect in the post, but figured it wouldn’t matter — guess I should have. And I deliberately didn’t look up Wikipedia before I did it because I wanted to do that score calculation for myself.