Dice game probabilities: Difference between revisions
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</pre>
=={{header|Common Lisp}}==
''DRAFT''
====1. Note====
We use total probability rule.
====2. Program====
<syntaxhighlight lang=lisp>(defun n-ways (n f s &optional (mem (make-array '(999 99) :initial-element -1)))
(cond ((and (= n 0) (= s 0)) 1)
((or (= n 0) (<= s 0)) 0)
((>= (aref mem s n) 0) (aref mem s n))
(t (loop for i from 1 to f
sum (n-ways (1- n) f (- s i) mem) into total
finally (return (setf (aref mem s n) total))))))
(defun winning-probability (n1 f1 n2 f2 &aux (w 0))
(loop for i from n1 to (* n1 f1)
do (loop for j from n2 to (* n2 f2)
do (if (> i j)
(setf w (+ w (* (n-ways n1 f1 i) (n-ways n2 f2 j))))))
finally (return (/ w (* (expt f1 n1) (expt f2 n2))))))</syntaxhighlight>
===== 3. Execution =====
<pre>(winning-probability 9 4 6 6)
(winning-probability 5 10 6 7)</pre>
{{out}}
<pre>48679795/84934656 ; ≈ 0.573
3781171969/5882450000 ; ≈ 0.643</pre>
That's all Folks !
''cyril nocton (cyril.nocton@gmail.com) w/ google translate''
=={{header|D}}==
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