📊 Open-Ended Dice
Exploding Dice Probability Calculator (Aces / Re-roll on Max)
Calculate the probability distribution for exploding dice (when rolling the maximum face grants another roll added to the total).
⚙️ Input Parameters
Real-Time Simulation 6
4 12
10
1 30
Mathematical Formula
Geometric expansion of infinite series P(Sum = s)
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 exploding dice?
Exploding dice (also called "Acing" in Savage Worlds) are a mechanic where rolling the highest number on a die allows you to roll again and add the new number to the original result, potentially repeating indefinitely.