Two Dice Probability Calculator
Calculate probabilities for rolling two dice. Find the likelihood of getting specific sums, determine odds, and explore all possible outcomes and combinations.
Sum you want to calculate probability for (2-12)
What is the probability of rolling a specific sum with two dice?
It depends on the sum. The most likely sum is 7 (probability 6/36 = 16.67%). Probabilities: 2 or 12 = 1/36 (2.78%), 3 or 11 = 2/36 (5.56%), 4 or 10 = 3/36 (8.33%), 5 or 9 = 4/36 (11.11%), 6 or 8 = 5/36 (13.89%), 7 = 6/36 (16.67%).
Why is 7 the most likely sum when rolling two dice?
There are 6 ways to roll a 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). This is more than any other sum. The distribution is symmetric around 7, with extreme sums (2, 12) having only one combination each. More combinations = higher probability.
How many total outcomes are possible with two dice?
There are 36 total outcomes (6 × 6). Each die has 6 faces, and they are independent, so multiply: 6 × 6 = 36. These include all ordered pairs from (1,1) to (6,6). Each outcome is equally likely with fair dice.
What is the probability of rolling doubles with two dice?
Doubles are: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6 outcomes. Probability = 6/36 = 1/6 ≈ 16.67%. This is the same as rolling any specific sum of 7. Conversely, probability of NOT rolling doubles = 30/36 = 5/6 ≈ 83.33%.
How do I calculate the odds of rolling at least a certain sum?
Count all favorable outcomes where sum ≥ target, then divide by 36. Example: At least 10 means sum = 10, 11, or 12. Outcomes: 3+2+1 = 6. Probability = 6/36 = 1/6 ≈ 16.67%. For "at most", count sums ≤ target.