How to use this calculator
A binomial model counts successes in a fixed number of independent trials. All trials must share the same success probability and have two outcomes: success or failure. Exactly k excludes every other success count; at least k includes k through n. The expected count n × p is an average over repetitions, so a fractional expectation does not mean a fractional prize.
The formula
P(X = k) = C(n,k) pᵏ (1 − p)ⁿ⁻ᵏ
Here p is a probability from 0 to 1, n is a whole number of attempts, C(a,b) counts combinations, and ∏ means multiply all the factors. The input labels define the other symbols.
A worked example
With 20 trials at 10%, exactly 3 successes has probability 19.01%; at least 3 is 32.31%.
Does this predict what I will get?
No. It describes a probability under the rules you enter. A single run can differ from the average. A displayed rounded 100% may still be slightly below certainty unless the model includes a guarantee.
Where do the rates come from?
You enter them. Check the rules and rate disclosure for your exact outcome. We do not supply odds for real products, collect account details or fetch rates from a game or seller.