What are the odds of rolling a Yahtzee?

Five dice, five matching faces, and three rolls to make it happen. If you spend an entire turn chasing a Yahtzee, the odds of success are about 4.6%, or once every 22 attempts. Getting a Yahtzee on your very first roll is even more rare, with a chance of 0.077%, which is one in 1,296.

Those figures represent entire turns, but what you truthfully care about is the probability for the specific dice sitting in front of you right now.

The math is easy enough to do by hand. When you roll a die once, it misses the face you want five out of six times. If you roll it twice, it misses both times with a probability of 5/6 x 5/6, meaning it lands on the right face with a chance of 1 - (5/6)^2. Since each die you need is independent, the total chance is that number multiplied by itself for every missing die.

The following sections explain how we reach those two main numbers.

One roll: 1 in 1,296

With five dice, there are 6 x 6 x 6 x 6 x 6 = 7,776 possible outcomes that are all equally likely. Only six of these results are five of a kind, with one for each face.

6 / 7776 = 1 / 1296 = 0.0772%

This is the number people usually refer to when they say a Yahtzee is rare. It also has very little to do with how the game is actually played, since nobody just rolls five dice once and stops.

Three rolls: 1 in 22

A standard turn consists of three rolls, and you get to retain whatever dice you like between them. This changes the question from "will five dice land the same" to "can I finish the set I'm already holding," which is a much easier task for a cup of dice.

If you play an entire turn by keeping the most common face each time, a Yahtzee lands on 4.6029% of turns. The exact math is 347,897 in 7,558,272. We reach this by looking at every possible way a turn can play out, because the best dice to keep after the second roll depends entirely on what happened during the first.

A few things are worth remembering while you're at the table:

1. A pair is the standard launch After the first roll, the best thing you'll likely be holding is a pair, which happens on 69% of turns. From there, with two rolls left, your odds of finishing are 2.9%. Three of a kind shows up on 19% of first rolls and has a 9.3% chance of finishing.
2. The last roll is the big moment. If you have four of a kind with only one roll left, you have a straight 1 in 6 chance, which is the best position you can be in.
3. Chasing it has a cost. Every roll you spend hunting a Yahtzee is a roll you aren't using to score a different category. This is why 4.6% is more of a ceiling than a guarantee.

Over a whole game

In a game of thirteen turns, a 4.6% chance per switch means you have roughly a 46% chance of getting at least one Yahtzee, provided you chased it every single time. But nobody actually plays like that, which is why most games end without a single one. Spending three rolls on a 1 in 22 shot thirteen times in a row means you're giving up a full house or a long straight every single turn.

Try it

Play Yahtzee online in Yacht, our version of the game. It uses five dice, three rolls, and the same scorecard, so every number mentioned here applies to it.