Yahtzee Category Odds
Assuming you reroll purely to maximize one target category over a full turn (initial roll plus two rerolls), here’s the exact expected score — and, for the fixed-score categories, the exact probability of completing it.
Expected score per category under optimal single-category rerolling -- not what you’d actually score if forced to pick the best category after the fact, which would be higher.
Every category, in detail
What each reroll buys you, the full spread of scores you can end a turn with, and how much the first roll has already decided.
- Ones2.11
- Twos4.21
- Threes6.32
- Fours8.43
- Fives10.53
- Sixes12.64
- Three of a Kind15.19
- Four of a Kind5.61
- Full House36.2883%
- Small Straight61.5442%
- Large Straight26.1095%
- Yahtzee4.6029%
- Chance23.33
Completion odds for the four fixed-score categories; expected score for the rest.
Common Yahtzee questions
I rolled a second Yahtzee — is it worth 100, and where does it go?
Worth 100 bonus points every time, with no cap — but only if your Yahtzee box already shows 50. Take a zero there earlier and the bonus is gone for the whole game. Where it goes is not your choice under the official rule: the matching upper box if it is open, otherwise a joker in any open lower box, where Full House, Small Straight and Large Straight all pay full value. The full ruling, including the variant a lot of families play.
What are the odds of rolling a Yahtzee on the very first roll?
Exactly 0.077% — 1 in 1,296. Five dice have 65 = 7,776 equally likely ordered outcomes, and only 6 of them (all ones, all twos, … all sixes) are a Yahtzee. That’s a different, much lower number than the 4.6029% figure above — this one is a single unrerolled roll, that one assumes two optimal rerolls chasing it.
How many possible outcomes are there when you roll five dice?
7,776 ordered outcomes (65), since each of the five dice independently lands on one of six faces. Far fewer are actually distinct hands once you stop caring which physical die showed which face, but 7,776 is the number that matters for probability math like this.
Which scoring category is easiest to complete, and which is hardest?
Of the four categories with a fixed score, Small Straight is the easiest to complete at 61.5442% with optimal rerolling, and Yahtzee is the hardest at just 4.6029% — which is exactly why it pays the most.
Is a Full House or a Large Straight more likely?
Full House, and it isn’t close: 36.2883% versus 26.1095% for Large Straight — despite Large Straight paying more (40 points to Full House’s 25). Three dice matching is a much lower bar than five consecutive numbers landing in the right shape.