Pick the number of dice and a target sum to get the exact probability — plus the winning combinations and odds.
What Is Dice Probability?
A dice probability calculator counts exact outcomes: with 2 dice, sum 7 has 6 ways out of 36 → 16.67%. Seven is the most likely sum (six combinations: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1) while 2 and 12 have one each. The tool enumerates every outcome — no formulas to misremember, just counting.
How to Use
- Pick the number of dice (1–3).
- Enter the target sum.
- Click “Calculate Probability”.
Formula
P = winning combinations ÷ 6^n.
Worked Example
2 dice, sum 7: 6 ways ÷ 36 = 16.67%. Odds: 6 to 30.
How It Works, In Plain Words
Start with what can actually happen. One die has 6 faces, so two dice have 6 × 6 = 36 equally likely outcomes, and three dice have 6 × 6 × 6 = 216. That total is the 6^n in the formula, where n is the number of dice you pick in the first input. The second input, the target sum, is the total you care about. The tool then counts — literally enumerates — every combination of faces and tallies how many of them add up to your target.
Probability is that count divided by the total, turned into a percentage: P = winning combinations ÷ 6^n. For the worked example, six combinations of two dice make 7 — 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — so 6 ÷ 36 = 16.67%. The odds line reframes the same count: 6 winning combinations against the 30 that lose, written “6 to 30”. Sums near the middle have the most combinations, which is why 7 beats 2 and 12, with one combination each.
Real-World Uses
A board-game player deciding whether a move is worth the risk uses this before rolling: if a plan only works on one exact sum, the calculator shows how thin that hope is compared with a plan that succeeds on the most likely sum, 7. A teacher uses it to make probability concrete — pupils predict the most likely sum, roll real dice, tally the results, and watch the class counts drift towards the exact figures the tool gives. A game designer balancing a home-made game uses it to set fair rewards: prizes attached to rare sums can be generous, while prizes on common sums must be modest, or the game bankrupts its banker.
Benefits
- Exact enumeration — no approximations;
- Ways, probability and odds together;
- 1–3 dice supported;
- Great for board games and teaching probability.
Features of Our Tool
- Instant results in your browser;
- No sign-up, no download, 100% free;
- Works on mobile, tablet and desktop;
- Clear step-by-step explanation below the tool;
- Private — your entries never leave your device.
Common Mistakes
- Thinking all sums are equally likely — 7 is 6× more likely than 2;
- Confusing “odds” with “probability” (6 to 30 vs 6 of 36);
- Assuming dice have memory (gambler’s fallacy).
Common Mistakes to Avoid
The classic mistake is treating every sum as equally likely. With two dice there are eleven possible sums but they are far from equal — 7 has six combinations while 2 and 12 have one each, making 7 six times more likely than either. Second, mixing up odds and probability: “6 to 30” compares wins with losses, while probability compares wins with all 36 outcomes — quoting one as the other misstates your chances. Third, the gambler’s fallacy: dice have no memory, so a long run without a 7 does not make one “due”. Fourth, forgetting that combinations are ordered — 1+6 and 6+1 are two different outcomes, and counting them as one understates the middle sums.
FAQ
What is the probability of rolling 7 with 2 dice?
16.67% (6 of 36).
What is the most likely dice sum?
7 — with six combinations, more than any other sum.
What are the odds of rolling 7?
6 to 30.
What is the probability of snake eyes?
1 of 36 = 2.78%.
Do dice have memory?
No — each roll is independent; past rolls don’t change the odds (gambler’s fallacy).
Why is 7 the most common sum with two dice?
Because more face combinations produce it than any other sum — six: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. Sums near the edges have fewer combinations, down to one each for 2 and 12, so the middle sum wins most often.
Does this calculator use simulation or exact counting?
Exact counting. The tool enumerates every possible combination of faces — all 36 outcomes for two dice — and counts the ones matching your target, so the probability is exact rather than estimated from trial rolls, which would only approximate it.