📊 Combinatorics
Roll X Keep Highest Y Dice Calculator
Calculate probability distributions when rolling a pool of X dice and keeping only the top Y results.
⚙️ Input Parameters
Real-Time Simulation 4
2 10
3
1 9
6
4 20
Mathematical Formula
Order statistics for discrete uniform distributions
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
How does keeping the highest dice affect the distribution?
Keeping the highest dice skews the distribution strongly to the right, raising both the average and the median while drastically reducing the probability of low scores.