🐉 Iconic Spell
D&D 5e Fireball 8d6 Damage Distribution Calculator
Explore the bell curve, minimum (8), maximum (48), and average (28.0) damage distribution of the classic 3rd-level Fireball spell.
⚙️ Input Parameters
Real-Time Simulation 8
1 20
6
4 12
Mathematical Formula
Convolution of 8 independent uniform discrete distributions on [1, 6]
Primary Probability Result
--%
Success Probability
Fractional Odds
1 in 2.0
Failure Chance
50.0%
Client-side mathematical calculation ● 100% Deterministic
Tactical Analysis & Mathematical Context
In tabletop gaming, understanding the mathematical distribution behind your rolls allows you to make informed risk-reward decisions. Whether balancing spell slot usage in D&D 5e, evaluating an attack profile in Warhammer 40k, or weighing trade routes in Catan, knowing the exact probability mass function (PMF) turns guesswork into strategy.
Frequently Asked Questions
What is the average damage of Fireball?
An 8d6 Fireball averages exactly 28.0 fire damage. Targets that succeed on their Dexterity saving throw take half damage (average 14.0).
What are the odds of rolling max damage (48) on Fireball?
The probability of rolling eight 6s on 8d6 is (1/6)^8 = 1 in 1,679,616 (0.0000595%).
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