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Dice Probabilities

The statistical outcomes of rolling 2 six-sided dice

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Dice Probabilities

Rolling two six-sided dice is common in some of the most popular board games, including Monopoly, Backgammon and The Settlers of Catan.

Even if you don't memorize the percentages in the chart below, it's very helpful to have a general sense of how common each roll is.

Dice Roll - Probability

2 - 2.78%
3 - 5.56%
4 - 8.33%
5 - 11.11%
6 - 13.89%
7 - 16.67%
8 - 13.89%
9 - 11.11%
10 - 8.33%
11 - 5.56%
12 - 2.78%

As you can see, 7 is the most common roll with 2 six-sided dice.

It's six times more likely that you'll roll a 7 than a 2 or a 12 -- a huge difference. And it's twice as likely that you'll roll a 7 than a 4 or a 10.

However, it's only 1.2 times more likely that you'll roll a 7 than a 6 or an 8.

Another way of looking at these numbers is that, over time, you will roll one 4 or 10 for every two 7s rolled. You'll see six 7s for every 2 or 12.

Of course, dice have a bad habit of defying expectations. Don't rely on probabilities to work out precisely according to a chart like this -- you'll often find yourself on the losing end of a game if you do.

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