Dice Probability Calculator
Calculate the probability of rolling specific numbers with one or more dice.
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Table of Contents
Dice Probability Formula
The probability of rolling a specific sum with multiple dice can be calculated using combinatorics and probability theory.
Where:
- P(sum = s) is the probability of rolling sum s
- Number of ways to get sum s is calculated using combinatorics
- Total possible outcomes = 6^n (where n is number of dice)
How to Calculate Dice Probability
To calculate the probability of rolling a specific sum with multiple dice:
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1Determine the number of dice being rolled
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2Calculate the total possible outcomes (6^n)
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3Find the number of ways to achieve the target sum
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4Divide the number of ways by total outcomes to get probability
Interpreting Results
Understanding dice probability results:
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1Probability Range:
Probabilities range from 0 (impossible) to 1 (certain).
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2Multiple Dice:
More dice increase possible outcomes and complexity.
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3Common Sums:
Some sums are more likely than others due to multiple combinations.
Practical Examples
Example 1 Single Die
Rolling a 6 on a single die.
Number of ways = 1
Total outcomes = 6
Probability = 1/6 ≈ 0.1667
Example 2 Two Dice
Rolling a sum of 7 with two dice.
Number of ways = 6
Total outcomes = 36
Probability = 6/36 = 1/6 ≈ 0.1667
Example 3 Three Dice
Rolling a sum of 10 with three dice.
Number of ways = 27
Total outcomes = 216
Probability = 27/216 = 1/8 = 0.125