Yahtzee Odds: The Real Chance of Rolling a Yahtzee, and an Odds Calculator
Quick answer
The chance of rolling a Yahtzee on your first roll is 6 in 7,776, or 1 in 1,296 (0.077%). If you use all three rolls and keep your most common number each time, your chance rises to about 4.6% per turn, roughly 1 turn in 22.
| Yahtzee on the first roll | 1 in 1,296 (0.077%) |
|---|---|
| Yahtzee in one full turn (3 rolls) | 4.60%, about 1 in 21.7 |
| With four of a kind and 2 rolls left | 30.56% |
| With four of a kind and 1 roll left | 16.67% (1 in 6) |
| At least one Yahtzee in 13 all-out turns | 45.8% |
A Yahtzee, five dice showing the same number, feels like a once-in-a-game event. The numbers back that up: it's rare on any single roll, but far more reachable over a full turn than most players think. Here are the exact odds, how they're worked out, and a calculator for the dice in front of you.
Odds of a Yahtzee on the first roll
Five dice have 6 × 6 × 6 × 6 × 6 = 7,776 possible results. Only six of them are a Yahtzee: all 1s, all 2s, and so on up to all 6s.
P(Yahtzee on one roll) = 6 ÷ 7,776 = 1 ÷ 1,296 ≈ 0.077%Another way to see it: the first die can be anything; each of the other four must match it, so (1/6)⁴ = 1/1,296.
Odds of a Yahtzee in one turn (3 rolls)
You don't have to get it in one roll. The usual approach is to keep the number you have most of and reroll the others, up to three rolls in total. Following every possible roll through the turn with that strategy gives:
P(Yahtzee in one turn) ≈ 4.6029%That's about 1 turn in 21.7. Going for Yahtzee every turn, you'd expect one roughly every 22 turns.
Yahtzee odds calculator
Already rolled? Pick how many matching dice you're keeping and how many rolls you have left:
Chance of finishing a Yahtzee
| You're keeping | 1 roll left | 2 rolls left |
|---|---|---|
| 1 matching | 0.08% | 1.26% |
| 2 matching | 0.46% | 2.91% |
| 3 matching | 2.78% | 9.34% |
| 4 matching | 16.67% | 30.56% |
With a pair after your first roll, you'll finish the Yahtzee only about 2.9% of the time. Three of a kind with two rolls left gives you about 9.3%, and four of a kind with two rolls left gives you better than 30%.
Odds of other Yahtzee categories on the first roll
Counting all 7,776 results of a single roll of five dice:
| Category | Rolls (of 7,776) | Chance |
|---|---|---|
| Yahtzee (five of a kind) | 6 | 0.08% |
| Four of a kind or better | 156 | 2.01% |
| Large straight (1–5 or 2–6) | 240 | 3.09% |
| Full house (three + a pair) | 300 | 3.86% |
| Small straight or better (four in a row) | 1,200 | 15.43% |
| Three of a kind or better | 1,656 | 21.30% |
These are single-roll odds. Over three rolls, every category becomes far more likely, which is why it pays to keep the dice that move you toward the categories you still need.
Yahtzee strategy in brief
- Early in the game, chase the upper section. Scoring at least 63 there earns a 35-point bonus, which is often worth more than one lucky Yahtzee.
- Keep three of a kind and go for it. Three of a kind with two rolls left is a 9.3% Yahtzee chance, and you'll usually still fill three of a kind, four of a kind or the upper box for that number.
- Use Chance as a safety net for a bad turn rather than the first time you have a decent total.
- Sacrifice Yahtzee (score 0) late, not early. Over 13 turns you'd hit at least one Yahtzee about 45.8% of the time if you chased it every turn, so the box keeps value until the last few turns.
More dice games
- Farkle rules, scoring chart and odds
- Shut the Box: rules and a free online game
- Online dice roller for when the dice go missing
Frequently asked questions
What are the odds of rolling a Yahtzee?
On a single roll of five dice, 6 of the 7,776 possible results are five of a kind, so the chance is 1 in 1,296 (0.077%). Over a full turn of up to three rolls, keeping your best set each time, the chance is about 4.60%.
What are the odds of a Yahtzee in 3 rolls?
About 4.6029%, or roughly 1 in 21.7 turns, if you always keep the number you have most of and reroll the rest. We calculated it exactly by following every possible roll through the three rolls of a turn.
If I have four of a kind, what's the chance of finishing the Yahtzee?
With one roll left you need the last die to match: 1 in 6, or 16.67%. With two rolls left, it's 1 − (5/6)² = 30.56%.
How often will I get a Yahtzee in a full game?
A game has 13 turns. If you went for Yahtzee on every turn, the chance of at least one would be about 45.8%. In real games you chase other categories too, so most players see a Yahtzee in fewer than half of their games.
Sources
- Yahtzee — Wikipedia
- Two Basic Rules of Probability — OpenStax, Rice University. Multiplication rule; independent events