How this calculator works
Mark the accepted faces on one fair d6. If m faces qualify, each independent die succeeds with probability m/6, so the number of qualifying dice is binomial. The table lists every possible count. Repeated entries in a face list are counted once. The all-same event instead has six disjoint outcomes, one for each common face; it does not require choosing that face in advance.
Formula
p = m/6; P(K = k) = C(n,k) p^k (1-p)^(n-k). Sum the appropriate terms for at least or at most. P(all faces equal) = 6/6^n.
Worked example
Two dice show exactly one six in 10 of their 36 ordered outcomes, giving 5/18 or about 27.78%. Three dice all showing the same face have probability 6/216 = 1/36.
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Frequently asked questions
Is exactly one six the same as a sum of six?
No. A face count checks each die separately. For sums, use the related dice probability calculator.
Does at least include the requested count?
Yes. At least two includes two, three and every larger possible qualifying count. At most includes equality too.
Can I use loaded dice?
This page assumes independent fair d6 dice. Unequal face probabilities require a different model.