What are the odds of rolling a Yahtzee on the first roll?

The probability of rolling five of a kind on a single roll is exactly 6/7776 = 1 in 1296, or about 0.077%. With three rolls and optimal re-rolling, the cumulative probability rises to roughly 4.6%.

How is the "optimal play" probability calculated?

For each category, the calculator assumes you keep the best set of dice after each roll and re-roll the rest. The multi-roll probabilities are computed by summing over all possible kept-dice states weighted by their frequency.

Why does the Large Straight have better first-roll odds than a Full House?

A Large Straight (1-2-3-4-5 or 2-3-4-5-6) has 2 x 5! = 240 favorable outcomes out of 7776, while a Full House has 300 favorable outcomes — so Full House is actually slightly more likely on the first roll.

Does this account for joker rules?

No. The probabilities shown are for standard Yahtzee rules where each category requires its specific combination. Joker rules (using Yahtzee as a wild) are not modeled here.

What does "1 in X" mean?

"1 in X" means you would need to attempt this category X times on average before succeeding once. A lower X means a more achievable category.

Yahtzee Odds Calculator

Name: Yahtzee Odds Calculator
Availability: InStock
Author: Nham Vu

Select a Yahtzee scoring category and see the exact probability of achieving it on each roll attempt.

Select Category

Number of Rolls

Selected Category

Yahtzee

Five of the same number on all five dice.

Key Fact

Favorable outcomes (1 roll)

—

out of 7,776

Total possible rolls

7,776

6⁵ combinations

Example Winning Combinations

Summary

Select a Yahtzee scoring category and see the exact probability of achieving it on each roll attempt.

How it works

Select the Yahtzee category you want to roll.
The calculator instantly shows the probability of achieving it on the first roll.
It then shows the cumulative probability if you play optimally through roll 2 and roll 3.
Probabilities are displayed as both percentages and "1 in X" odds.
Use the breakdown panel to see which dice combinations count toward each category.

Use cases

Understand how rare a Yahtzee (five of a kind) really is.
Compare the difficulty of scoring a Large Straight vs. a Full House.
Settle debates about Yahtzee strategy with hard probability data.
Learn which categories to target first for maximum scoring efficiency.
Teach probability concepts using a familiar dice game.
Analyze house-rule variants to see how they change the odds.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu