We use the reduction of a discrete traveling salesman route optimization problem to a transport type problem, for which an approximate algorithm for its solution is constructed using statistical techniques. The method of constructing a sample of cyclic decisions is used, and then statistics of the occurrence of transitions from one point to another point in a heuristically constructed route. The result of the study is the possibility of practical application of the developed algorithm for solving symmetric and asymmetric traveling salesman problems and other selection problems, as well as for educational purposes in statistics when studying the sampling method and building various kinds of indicators on its basis.