Dice Roller & Fair Coin Flipper

Roll polyhedral tabletop RPG dice (D4, D6, D8, D10, D12, D20, D100) and flip fair coins with modifier math and expected value stats.

Category: Other Utilities

How to Use Dice Roller & Fair Coin Flipper

  1. Choose your polyhedral die type (D4, D6, D8, D10, D12, D20, or D100) and number of dice (0–100).
  2. Optionally enter a positive or negative roll modifier (e.g., +3 for RPG ability checks).
  3. Set the number of coins to flip (set Dice Count to 0 if you only want coin flips).
  4. Click Process to view individual rolls, natural sum, modified total, expected average, and Heads/Tails counts.

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Frequently Asked Questions

How do I flip a coin without rolling any dice?

Set 'Number of Dice to Roll' to 0 and set 'Coins to Flip' to 1 (or up to 100). The tool will execute a pure coin-flip simulation and display the Heads and Tails breakdown.

How is the theoretical expected average of a dice roll calculated?

For N dice each with S faces and a flat modifier M, the expected value is E = N × ((S + 1) / 2) + M. For example, 2d6 has an expected average of 2 × 3.5 = 7.0, and 1d20 + 4 has an expected average of 10.5 + 4 = 14.5.

Are the dice rolls and coin flips truly unbiased?

Yes. Every die roll and coin flip uses window.crypto.getRandomValues() with 32-bit rejection sampling, eliminating modulo bias and ensuring each face (1 through S) has an exact 1/S probability.

What does Natural Max (Crit) and Natural Min (Fumble) mean?

In tabletop RPGs like Dungeons & Dragons, rolling the highest possible face on a die (such as 20 on a D20) is a Natural Critical hit, while rolling a 1 is a Natural Minimum. The summary counts how many dice hit their maximum or minimum face.

How many dice and coins can I roll at once?

You can roll up to 100 dice and flip up to 100 coins simultaneously in a single batch.