# 3 Dice Probability Chart (With Probabilities)

When you roll 1 dice, there are 6 possible numbers the dice could land on: 1, 2, 3, 4 5, or 6.

When you roll 2 dice, there are 6 * 6 = 36 possible combinations of numbers the dice could land on.

When you roll 3 dice, there are 6 * 6 * 6 = 216 possible combinations of numbers the dice could land on.

For example:

• The first dice may land on 1,the second may land on 1 and the third may land on 1.
• The first dice may land on 1,the second may land on 1 and the third may land on 2.
• The first dice may land on 1,the second may land on 1 and the third may land on 3.
• . . .

And so on.

It turns out that there is only 1 way for the sum of the dice to be 3:

• First Dice = 1, Second Dice = 1, Third Dice = 1

However, there are 3 ways for the sum of the dice to be 4:

• First Dice = 1, Second Dice = 1, Third Dice = 2
• First Dice = 1, Second Dice = 2, Third Dice = 1
• First Dice = 2, Second Dice = 1, Third Dice = 1

And there are 6 ways for the sum of the dice to be 5:

• First Dice = 1, Second Dice = 1, Third Dice = 3
• First Dice = 1, Second Dice = 2, Third Dice = 2
• First Dice = 1, Second Dice = 3, Third Dice = 1
• First Dice = 2, Second Dice = 1, Third Dice = 2
• First Dice = 2, Second Dice = 2, Third Dice = 1
• First Dice = 3, Second Dice = 1, Third Dice = 1

We can create the following chart to visualize the probability that the sum of the three dice is equal to a particular number:

We can see that the probability distribution is symmetrical.

The most likely sum of the three dice is 10 or 11 while the least likely sum of the three dice is 3 or 18.