🎲 GURPS & Retro
3d6 Probability & Bell Curve Distribution Calculator
Complete probability distribution for 3d6 (sums 3 through 18), as used in GURPS, classic RPGs, and Hero System.
⚙️ Input Parameters
Real-Time Simulation 10
3 18
Mathematical Formula
Trinomial expansion over 216 permutations
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 are the most common rolls on 3d6?
Sums 10 and 11 are the most probable outcomes on 3d6, occurring in 27 out of 216 permutations each (12.50%). Rolling between 9 and 12 happens 48.15% of the time.
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