In general, games like duels, in which each of two players has the goal to eliminate the enemy, are quite a popular problem from game theory. The problem becomes much more complicated when you add players. The term ""truel"" we understand the rivalry three players. They are assigned some values of accuracy the probabilities of eliminating the opponent in one shot. At each stage of the game is chosen by the active player (the selection rule active player either randomly or by prior agreement between the players about their participation). The active player chooses an opponent to eliminate or passes the course. Developed mathematical models for different formulations of the conditions of the game (random or fixed choice of the active player). For each model are analyzed based on the probability of winning in the ""truly"" of accuracy, based on randomly generated program values. Comparing analytical solution and simulation, we see that they have the same answers. For large dimensions similar games analytical method requires complex calculations, so an acceptable alternative is the simulation method. Data research nahegelegenen in political and judicial practices, as well as analytical tools for the study of the theory of evolution.

Keywords: truel, simulation, game duel three persons,Markov chain, variance of natural selection, the matrix of transition probabilities, fundamental matrix, stochastic process, the three prisoners dilemma, game theory, coalition games