Two six-sided dice produce 36 equally likely outcomes, and the totals run from 2 to 12. Those totals are not equally likely. Seven comes up most often at 16.67%, while 2 and 12 each sit at 2.78%. The chart below gives every total, its combinations and its odds.
The two-dice probability chart
Read each row as one total. The middle column lists the ordered pairs that make it, where the first number is the red die and the second is the white die. Order matters for counting, which is why 3+4 and 4+3 are listed separately.
| Total | Combinations (die 1 + die 2) | Fraction | Probability |
|---|---|---|---|
| 2 | 1+1 | 1/36 | 2.78% |
| 3 | 1+2, 2+1 | 2/36 | 5.56% |
| 4 | 1+3, 2+2, 3+1 | 3/36 | 8.33% |
| 5 | 1+4, 2+3, 3+2, 4+1 | 4/36 | 11.11% |
| 6 | 1+5, 2+4, 3+3, 4+2, 5+1 | 5/36 | 13.89% |
| 7 | 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 | 6/36 | 16.67% |
| 8 | 2+6, 3+5, 4+4, 5+3, 6+2 | 5/36 | 13.89% |
| 9 | 3+6, 4+5, 5+4, 6+3 | 4/36 | 11.11% |
| 10 | 4+6, 5+5, 6+4 | 3/36 | 8.33% |
| 11 | 5+6, 6+5 | 2/36 | 5.56% |
| 12 | 6+6 | 1/36 | 2.78% |
The fractions all share a denominator of 36, so you can compare rows just by looking at how many pairs each total gets. The average total across a long session is 7, and the median is 7.
Why the chart is a triangle, not a flat line
A single die is flat. Every face has the same 16.67% chance, which is why one die is a fair way to pick between six options.
Two dice behave differently, and the reason is that you’re reading a sum instead of a face. A sum can be built more than one way. Twelve has exactly one recipe: both dice show six. Seven has the most recipes of any total, because whatever the first die shows, there is always a face on the second die that finishes the job. Roll a 1, you need a 6. Roll a 4, you need a 3. Roll a 6, you need a 1. Every starting face has an answer.
No other total can say that. If the first die shows a 6, you can’t reach a total of 4 no matter what the second die does. Totals near the ends of the range lose recipes, and the loss is steady: each step away from 7 drops one pair. That produces the tent shape you see when you plot the chart, sometimes called a triangular distribution.
Line the 36 outcomes up in a 6 by 6 grid with die 1 down the side and die 2 across the top, and the totals form diagonal stripes. The main diagonal is the long one. That diagonal is the 7.
Cumulative odds: at least and at most
Exact-total odds answer “what are the chances of rolling a 9?” Games more often ask “what are the chances of rolling a 9 or better?” That’s a cumulative question, and it’s the sum of every row from 9 down to the bottom of the chart.
A few worth memorizing:
- 8 or higher: 41.67%
- 10 or higher: 16.67%
- 6 or lower: 41.67%
- 4 or lower: 16.67%
- 11 or higher: 8.33%
Two things fall out of that list. Cumulative odds move much faster than exact odds as you shift the threshold, and thresholds on opposite sides of 7 mirror each other. The chance of rolling 9 or more equals the chance of rolling 5 or less, because the chart is symmetric around 7.
If you want these for dice pools other than 2d6, the probability calculator will run at-least and at-most numbers for any combination.
Reading the chart at the table
Catan. Every hex carries a number token, and the little dots printed under the number are literally the count of pairs that make it. The 6 and the 8 get the most dots and are printed in red as a warning that they pay out most often, at 13.89% and 13.89%. There is no 7 token, because the 7 has a job of its own: it moves the robber and forces every player holding more than seven cards to discard half. The most common roll in the game produces nothing.
That’s the trade to weigh when you place a settlement. A spot touching a 6, a 5 and a 9 will produce far more than a spot touching a 2, a 12 and a 3, even though both spots touch three hexes.
Craps. The come-out roll is decided by this chart. A 7 or an 11 wins immediately for the pass line, at 16.67% plus 5.56% between them. A 2, 3 or 12 loses immediately. Anything else becomes the point, and the shooter then needs to repeat that number before rolling a 7. Since the 7 outweighs every point number, the house edge on the pass line comes straight out of the shape of this chart. A point of 6 or 8 is the friendliest to the shooter, a point of 4 or 10 the worst.
Monopoly. Jail is the single most visited square, so the squares 6, 8 and 9 spaces past it catch heavy traffic on the way out. That is the orange group: St. James Place, Tennessee Avenue and New York Avenue. On the first roll out of Jail, the chance of landing on each one is 13.89%, 13.89% and 11.11%. The dark blues sit further from Jail and get visited less, which is part of why experienced players fight over orange.
Doubles, and other things the chart doesn’t show
Totals aren’t the only thing you can ask about. Doubles cut across the chart: they’re the diagonal of the grid where both dice match. A specific double like 4+4 has the same odds as any other single pair, 1/36 of the grid, but any double at all is a different question and the totals chart won’t answer it.
The same goes for questions like “at least one 6” or “the difference between the dice is 3.” Those need a different slice of the same 36 outcomes. The dice probability basics page covers how to set those up.
Three dice and beyond
Add a third die and the range becomes 3 to 18 across 216 outcomes, with a mean of 10.5 and a standard deviation of 2.96. The shape stops being a clean triangle and starts rounding into a bell. The peak stays in the middle, and the extremes get rarer much faster: rolling three sixes is 0.46%.
Want to feel it rather than read it? Roll a few hundred times on the dice roller and watch the totals pile up in the middle. Or read the full breakdown of why 7 wins.
FAQ
What is the most likely total with two dice?
Seven, at 16.67%. It has more combinations than any other total because every face on the first die has a matching face on the second that reaches 7. The totals on either side, 6 and 8, tie for second at 13.89% each.
How many outcomes are there when rolling two dice?
There are 36 equally likely outcomes, since each of the six faces on the first die can pair with each of the six faces on the second. Those outcomes collapse into a much shorter list of totals running 2 to 12, which is why some totals are far more common than others.
What are the odds of rolling snake eyes?
Snake eyes means two ones, and the odds are 2.78%, or 1/36. Double sixes carry exactly the same odds at 2.78%. Both are the rarest results on two dice because each has only one combination.
Do these numbers hold for loaded or worn dice?
No. The chart assumes each face is equally likely, which requires balanced dice. Casino dice are machined to tight tolerances and have flush, filled pips for that reason. Cheap plastic dice with drilled pips are slightly lighter on the six face, which nudges the results a little.