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AbstractIn the calculation of point flux by Monte Carlo simulation, there is a special disadvantage in the mostly used method of next event estimation (NEE) for which theoretical variance is infinite. And, this problem has not yet been solved satisfactorily. The purpose of this paper is to provide some new ideas to solve the problem of infinite variance without introducing any bias for the mean. To eliminate the unbounded factors, the relations among the different state variables for two neighboring collisions are analyzed; then, on the basis of the integral expression of the once-more scattered flux contribution to the point detector, by changing the state variables to be sampled, six basic methods are derived - two of them are NEE and collision probability estimation, and four are new methods. Furthermore, based on one of the new methods, by variable substitution, a new method called exponent biased sample estimation (EBS) is obtained that can eliminate the [arrow over]rd- [arrow over]rm-2singularity factor and has no exponent factor, which exists in other methods. The benchmark results show that EBS is much better than NEE with the variance of one order of magnitude smaller and a figure-of-merit factor of several hundreds higher sometimes, and its calculation efficiency is higher than that of the once more collision flux estimation method. Compared with the direction biased sample estimation method, EBS has no advantage in variance, but the sample procedures are much simpler and use less CPU time.