1. What is the Dice Roll Calculator?

The Dice Roll Calculator simulates rolling multiple dice of various types and calculates the sum of all rolls. It's useful for tabletop games, probability calculations, and game design.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( roll1, roll2, ... \) — Individual dice results (random integers between 1 and number of sides)
• \( N \) — Number of dice rolled

3. Probability and Dice Rolls

Details: The probability distribution of dice sums follows predictable patterns. For multiple dice, the distribution tends toward a normal (bell curve) distribution.

4. Using the Calculator

Tips: Select the number of dice (1-20) and the type of dice (4, 6, 8, 10, 12, or 20 sides). The calculator will show each individual roll and the total sum.

5. Frequently Asked Questions (FAQ)

Q1: Are the rolls truly random?
A: The calculator uses PHP's rand() function which is pseudo-random. For cryptographic security, more advanced methods would be needed.

Q2: What's the most common sum for two six-sided dice?
A: 7 is the most probable sum (6/36 probability), with 2 and 12 being the least probable (1/36 each).

Q3: Can I simulate dice with other numbers of sides?
A: The calculator currently supports standard polyhedral dice (4, 6, 8, 10, 12, 20 sides).

Q4: How does the probability change with more dice?
A: More dice create a more pronounced bell curve distribution, with extreme results becoming increasingly rare.

Q5: Can I calculate the average expected result?
A: The average roll for a die is (sides+1)/2. For multiple dice, multiply this by the number of dice.