If one does need multiple copies, it would seem that this method suffers from the coupon collector's problem [1] (i.e. to collect all 50 strands requires collecting 225 random strands on average), and that the retrieval rate could be improved by using a fountain code [2], which allows each strand to simultaneously encode data at multiple addresses, which would decrease the number of strands required to be sampled to only slightly more than the number of strands worth of data requested.
[1] http://en.wikipedia.org/wiki/Coupon_collectors_problem [2] http://blog.notdot.net/2012/01/Damn-Cool-Algorithms-Fountain...