In this paper, estimates of the probability of success of a multi-pass social engineering attack are considered. The purpose of the article is to identify the most critical path for the spread of a multi-way socio-engineering attack between two users. An approach is proposed for finding the most critical trajectories, an estimate of the probability of success of the passage of an attack on which will be the highest. Formally, the problem reduces to finding a path in the graph, in which the product of the weights of all edges entering the given path is maximal. The use of known algorithms in the solution of the problem was complicated by the fact that the weights of edges of the social graph are estimates of probability. This problem was solved by means of identical mathematical transformations.