I wrote a solution to this problem at my blog; the inner function is called sand
because I was throwing grains of sand instead of marbles:
(define (pi n)
(define (sand?) (< (+ (square (rand)) (square (rand))) 1))
(do ((i 0 (+ i 1)) (p 0 (+ p (if (sand?) 1 0))))
((= i n) (exact->inexact (* 4 p (/ n))))))
This converges very slowly; after a hundred thousand iterations I had 3.14188. The blog entry also discusses a method for estimating pi developed by Archimedes over two hundred years before Christ that converges very quickly, with 27 iterations taking us to the bound of double-precision arithmetic.