Single-roll probabilities
These are the odds of each outcome appearing when you roll all five dice once. There are 65 = 7,776 equally likely combinations, which is where every figure below comes from.
| Outcome | Chance per roll | Odds |
|---|---|---|
| Five of a kind (Yatzy) | 0.08% | 1 in 1,296 |
| Four of a kind (exactly) | 1.93% | 1 in 52 |
| Full house | 3.86% | 1 in 26 |
| Large straight (2-3-4-5-6) | 1.54% | 1 in 65 |
| Small straight (1-2-3-4-5) | 1.54% | 1 in 65 |
| Three of a kind (exactly) | 15.4% | 1 in 6.5 |
| At least one pair | 90.7% | likely |
The odds that matter in a turn
A single roll is only the start, because you get three of them. The useful question is usually "should I chase this?" A few decision-making numbers:
- Completing a Yatzy in a turn: with optimal holding across three rolls, roughly 4.6% (about 1 in 22).
- Four of a kind to Yatzy: hold the four, re-roll one die twice, and you complete it 30.6% of the time. Usually worth the gamble.
- Three of a kind to four of a kind: hold three, re-roll two dice twice; you reach four of a kind a little under half the time, which is why a strong three of a kind is a comfortable bank.
Why this shapes strategy
Because a Yatzy from scratch is rare but a Yatzy from four of a kind is almost a coin flip, the value of a chase depends entirely on your starting point. Likewise, the upper bonus is reliable to plan for, since three of each number is simply the average, while a Yatzy never is. Put these numbers to work on the strategy page, then test them in a free game.
Frequently asked questions
What are the odds of rolling a Yatzy?+
On a single roll of five dice the chance of five of a kind is 1 in 1,296, about 0.08 percent. Across a full turn of three rolls with optimal holding, your chance of completing a Yatzy rises to roughly 4.6 percent, or about 1 in 22.
If I have four of a kind, what is my chance of making a Yatzy?+
Holding the four matching dice and re-rolling the fifth die twice, your chance of completing the Yatzy is 1 minus (5/6) squared, which is 11/36, about 30.6 percent. That is why chasing a Yatzy from four of a kind is usually worth it.
What is the average Yatzy score?+
A casual game often lands in the 150 to 200 range. With the upper bonus secured and a couple of strong lower-section results, a good player averages 220 to 270. The theoretical maximum is 374, but that requires near-perfect rolls.