The following scheme code calculates the chance of succeeding at a skill challenge in fourth edition D&D at a given DC by a character with a certain skill. It assumes that you must get succ successes before getting fail failures.

(define fourth-ed-skill-contest
  (lambda (dc skill succ fail)
    (letrec ((pds (/ (+ 20 (- dc) skill) 20))
             (n (+ succ fail -1))
             (fact (lambda (n) (if (= 0 n) 1 (* n (fact (- n 1))))))
             (cn (lambda (n k) (/ (fact n) (* (fact k) (fact (- n k))))))
             (msum (lambda (i accum)
                     (if (>= i fail) accum
                         (let ((iprob (* (cn n i) (expt pds (- n i)) (expt (- 1 pds) i))))
                            (msum 
                            (+ i 1) 
                            (+ accum iprob)))))))
      (msum 0 0))))

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