A Monte Carlo calculation of thermal utilization is described with emphasis on the statistical procedures employed. The reactor model has slightly enriched uranium fuel rods in a hexagonal lattice. The moderator is ordinary water but is treated by the code as a hydrogen gas. General principles are given for using Monte Carlo techniques and it is shown that time reducing methods are as effective as the better known variance reducing methods in decreasing the cost. Good agreement with experimental results was obtained, indicating that such thermal utilization calculations are feasible and are not sensitive to the model of the water molecule.