The error most likely didn't stop converging - its just that n^{-1/2} is a very slow convergence rate. If you want actual control of the error, and to know how

The error most likely didn't stop converging - its just that n^{-1/2} is a very slow convergence rate. If you want actual control of the error, and to know how many samples you need, you need to do some arithmetic with the central limit theorem or hoeffdings inequality.