Why is 7 most commonly rolled with 2 dice? | Odds Explained!

Like many of you I was wondering this exact question once. It wasn’t until I developed a board game that used two dice as the main mechanism within the game that I learned the answer to it. I’ve gone into far more detail than some of you will need, but it’ll be very helpful for the rest of you.

So why is 7 the most common dice roll for two dice? Seven it the most common dice roll with two dice because it has the most number of different combinations that add up to seven. For example, a player can roll 1 and 6; 2 and 5; 3 and 4; 4 and 3; 5 and 2; and 6 and 1. They all add up to 7. No other dice total has that many combinations.

Now that you have the most basic understanding, let’s get a broader understanding and look at some examples. If you want to see some games that use dice heavily, check out our resources page here. For the rest of you, let’s get to it.

Detailed explanation

Dice are typically used in games to create random outcomes that can’t be manipulated. With one die, all sides have an equal likelihood of being rolled (without cheating). Each side has a 16.67% likelihood of being rolled, or 1/6.

The odds change significantly when a second die is added. Now there isn’t an equal likelihood of each number being rolled. The totals are added together, so the range of outcomes increases to 2-12 (instead of only 1-6). Dice totals now span a much larger range. Each outcome is now only 2.78% likely to be rolled. The problem, though, is that the numbers closer to the outside of the range have fewer dice combinations that can attain them.

For example, if you need to roll a 12 in whatever game you’re playing, there aren’t many dice combinations that can do that. In fact, there is only one combination; a 6 and a 6. No matter how hard you try, no other combination will roll you a 12. A 7, on the other hand has six different combinations that can add up to 7. As mentioned earlier, they are: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. You may be wondering why we listed several of them twice. Each die can roll each of those numbers, so each number must be listed.

The same applies to every other number that can be rolled with two dice. 7 is the most likely outcome and the odds decrease toward the periphery of the range. In the next section, we’ll discuss what the odds are for rolling a seven.

Note: Yes, each individual die has the same odds for their specific outcomes; but the dice aren’t being evaluated as individual dice. They are being added together and counted as one.

The odds of rolling a 7

Calculating the odds of rolling a seven aren’t as difficult as you may have thought. We’ll outline it in the chart below.

Dice outcome of 7	1 and 6	2.78%
Dice Outcome of 7	2 and 5	2.78%
Dice Outcome of 7	3 and 4	2.78%
Dice Outcome of 7	4 and 3	2.78%
Dice Outcome of 7	5 and 2	2.78%
Dice Outcome of 7	6 and 1	2.78%
	Total	16.67%

There are a total of 36 possible outcomes when using two dice. Six of those outcomes will yield a 7—which are listed above. Each individual outcome has the same likelihood of 2.78%. There’s no magic there. If you are looking to roll a 1 from the first die and a 2 from the second die, your odds aren’t good; but when you aggregate all of the sevens the likelihood of rolling a seven in any combination increases to 16.67%.

If you compare the likelihood of rolling a 7 with two dice to the likelihood of rolling any number with one die, you’ll see the numbers are the same. Remember that with one die, the likelihood is always 16.67% because the outcome is 1 of 6 possibilities (so 1/6= .1667 or 16.67%). Rolling a 7 with two dice is 6 possible outcomes of 36 total possibilities (so 6/36 = 1/6 = .1667 or 16.67%). All other possible results of a different 2-dice total are each less than 16.67%

Two-dice probability chart

Below is a chart that demonstrates the possible combinations when using two dice. The first column shows possible dice totals ranging from 2 to 12. The second column expresses how many unique combinations are possible given that dice total. And the third column shows the probability of that dice total being rolled.

Dice Total	Number of Combinations	Probability
2	1	2.78%
3	2	5.56%
4	3	8.33%
5	4	11.11%
6	5	13.89%
7	6	16.67%
8	5	13.89%
9	4	11.11%
10	3	8.33%
11	2	5.56%
12	1	2.78%
Totals	36	100%

As you can see in this chart, 7 has the most unique dice combinations. The next highest dice totals are 6 and 8—which have an equal probability of 13.89%. They both are only slightly less likely outcomes than a 7. The next most likely outcomes are 5 and 9 with a probability of 11.11% each. 4 and 10 come in next at 8.33% each. At 5.56%, 3 and 11 show that they aren’t rolled very often. And the two outcomes with the lowest probabilities are 2 and 12 at 2.78% a piece—they each only have one possible dice combination.

Examples in gameplay

Settlers of Catan

Settlers of Catan is an extremely popular board game that uses two dice. In Settlers of Catan players roll two dice at the beginning of each round. Outcomes earn precious resources with varying probabilities. Some resources are abundant because they are awarded from rolls of 6 or 8; while other resources are scarce only paying out on rolls of 2 or 12. All other resources land somewhere in between.

Rolls of 7 are reserved for an interesting twist. Anytime a player rolls a 7, he or she gets to move a game piece called “The Robber” to another area of the board to cause problems for other players. As we’ve already discussed, 7 is the most likely result with two dice. So roughly 17% of the time, The Robber is making his way around the game board and reeking havoc. A dice outcome of 7 was obviously chosen by the designers to ensure The Robber keeps the game interesting.

Machi Koro

Machi Koro is another game that uses dice rolling as its core game mechanism. Players can choose whether they want to roll one die or two dice. Throughout the game players buy cards that earn them money if the dice roll the required numbers. There is a lot of variability with this game because, if players choose to roll 1 die, the results can obviously only be 1-6. Players that bought cards requiring 7-12 are out of luck.

However, as soon as players start rolling two dice, everything changes. Players can calculate the odds of certain cards paying out. Obviously there are many cards to buy that require dice rolls of 6. 7 and 8. But other cards exist that require fringe results and pay higher rewards. The player earning the most wins the game by building his or her city.