Dice Roller Simulator

Standard dice notation follows the pattern XdY+Z:

• X: Number of dice to roll
• d: The letter 'd' for 'dice'
• Y: Number of sides on each die
• +Z: Modifier to add (optional, can be negative)

Examples:

• 2d6: Roll two 6-sided dice
• 1d20: Roll one 20-sided die
• 3d6+2: Roll three 6-sided dice and add 2
• 4d6-1: Roll four 6-sided dice and subtract 1

• d4: Tetrahedral die (1-4)
• d6: Standard cube die (1-6)
• d8: Octahedral die (1-8)
• d10: Pentagonal trapezohedron (0-9 or 1-10)
• d12: Dodecahedral die (1-12)
• d20: Icosahedral die (1-20), popular in RPGs
• d100: Percentile die (1-100)

• Drop Lowest: Roll all dice but ignore the lowest value (common in RPG character creation: 4d6 drop lowest)
• Drop Highest: Roll all dice but ignore the highest value
• Keep Highest: Roll all dice but only keep the highest value (advantage in D&D)

• Mean: Average roll value over many rolls
• Mode: Most common roll result
• Median: Middle value when results are sorted
• Standard Deviation: How spread out the results are
• Distribution: For multiple dice, results cluster around the mean (Central Limit Theorem)

• Rolling 1d6: Each outcome (1-6) has 1/6 ≈ 16.67% probability
• Rolling 2d6: Sum of 7 is most likely (16.67%), while 2 and 12 are least likely (2.78%)
• Rolling 3d6: Distribution becomes more bell-shaped (normal distribution)
• More dice = more consistent results around the mean

• Gaming: Tabletop RPGs, board games, simulations
• Education: Teaching probability and statistics
• Decision Making: Random selection with weighted outcomes
• Testing: Validating random number generators