Frequently Asked Questions
Does this assume fair coins and dice?
Yes. Every flip is treated as 50 percent heads and every die face as equally likely, which is the standard textbook assumption. It does not model weighted or biased coins and dice.
What is the difference between exactly k and at least k?
Exactly k is the chance of getting precisely that many heads. At least k adds the chances of getting k, k plus 1, and so on up to the maximum, so it is always equal to or larger than the exact value.
Why are the smallest and largest dice sums so unlikely?
There is only one way to roll the minimum or maximum sum, while many combinations produce the middle sums, so totals near the middle are far more probable.
How does the coin math work?
It uses the binomial formula: the chance of exactly k heads in n flips is C(n, k) times 0.5 to the power n, where C(n, k) counts the ways to choose which flips land heads.
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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.