Chance, explained
These calculators assume fair coins, fair six-sided dice and a standard 52-card deck with no replacement. Results are shown as a percentage and a "1 in N" chance where useful.
Frequently asked questions
How is the coin probability calculated?
It uses the binomial distribution: the chance of getting exactly k heads in n flips is C(n,k) · 0.5ⁿ. "At least k heads" sums that from k up to n.
How is the dice sum calculated?
The tool counts every combination that adds to the target using dynamic programming, then divides by 6ⁿ (all possible outcomes).
What does "without replacement" mean?
Each drawn card is not put back, so drawing more cards changes the odds of the remaining deck. This is the standard way card games work.