Dice Roller — Cryptographically Secure Virtual Dice for TTRPGs

2D6+3 means "roll two 6-sided dice, sum them together, then add 3 to the total." The number before the D is the count of dice, the number after is how many sides each die has, and anything after + or - is a flat modifier applied to the total. Common D&D examples: 1D20+5 for an attack roll, 2D6 for a greatsword damage, 8D6 for a Level 3 Fireball spell. This notation was popularized by Dungeons & Dragons in 1974 and is now the universal standard for TTRPGs.

This calculator uses crypto.getRandomValues(), a cryptographically secure pseudo-random number generator (CSPRNG) available in all modern browsers. It is far better than Math.random() for gaming purposes and is suitable even for security-sensitive applications. While technically still pseudo-random (not quantum-random), it is practically indistinguishable from true randomness for all tabletop gaming and educational probability purposes.

The D20 (20-sided die) is the primary die used in Dungeons & Dragons 5th Edition for attack rolls, saving throws, and ability checks. A natural 20 (rolling a 20) is traditionally a critical success that automatically hits and often deals double damage. A natural 1 is a critical failure or fumble. Each face has exactly a 5% (1/20) chance of appearing on any given roll. The D20 system creates a flat probability curve where every outcome is equally likely, unlike multi-dice systems.

Multiple dice produce a bell-curve (normal) distribution where middle values are far more likely than extremes. Rolling 2D6 gives results from 2 to 12, but a 7 is six times more likely than a 2 or a 12 (1/6 vs 1/36). A single die produces a flat (uniform) distribution where every outcome is equally likely. Game designers use bell curves for skill checks where reliable, consistent results are desired, and flat distributions for random tables, loot generation, or critical confirmation where unpredictability adds excitement.

Advantage means rolling two D20s and taking the higher result — this significantly increases your chance of success. Disadvantage means rolling two D20s and taking the lower result. With advantage, the chance of rolling a natural 20 increases from 5% to 9.75%, and the average result rises from 10.5 to about 13.82. With disadvantage, the average drops to about 7.17. A common rule of thumb is that advantage/disadvantage is mathematically equivalent to roughly a ±5 modifier for middle-range target numbers, though the exact effect depends on the target DC.

The Central Limit Theorem (CLT) states that the sum of many independent random variables tends toward a normal (bell curve) distribution, regardless of the individual distributions. For dice: roll 1 die and the distribution is flat (uniform). Roll 2 dice and it becomes triangular. Roll 3+ dice and it rapidly approaches a bell curve. By 10 dice, the result is very close to a normal distribution centered at N × (S+1)/2. This is why casino craps uses 2D6 (the triangular distribution at 7 peaks at 16.67%) and why 3D6 ability score generation produces predictable, balanced characters.