What is the Probability of Rolling Doubles with Dice?

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If we roll two dice at the same time, the probability that both dice land on the same number (i.e. we roll “doubles”) is 6/36 or 1/6.

To understand why this is the case, we must realize that there are 36 different ways for two dice to land.

For example:

• The first dice might land on 1 and the second dice might land on 1.
• The first dice might land on 1 and the second dice might land on 2.
• The first dice might land on 1 and the second dice might land on 3.
• The first dice might land on 1 and the second dice might land on 4.
• The first dice might land on 1 and the second dice might land on 5.
• The first dice might land on 1 and the second dice might land on 6.
• The first dice might land on 2 and the second dice might land on 1.
• . . .

And so on.

We can create the following grid to visualize each possible combination of outcomes for the two dice:

To find out the probability that both dice land on the same number, we must use the following formula:

Probability = (#Ways to Land on Same Number) / (#Total Ways to Land)

From the grid above, we can see that there are only 6 ways that both dice can land on the same number and there are 36 total possible ways for both dice to land.

Thus, the probability that both dice land on the same number can be calculated as:

• Probability = (#Ways to Land on Same Number) / (#Total Ways to Land)
• Probability = 6 / 36
• Probability  = 1/6

The probability that both dice land on the same number is 1/6 or 0.166666666.

The following tutorials explain other common topics in probability: