All people have to make risky decisions in everyday life. And we do not know how true they are. But is it possible to mathematically assess the correctness of our choice? This article discusses the model of decision making under risk on the example of project management. This is a game with two players, one of which is Investor, and the other is the Project Manager. Each player makes a risky decision for himself, based on his past experience. With the help of a mathematical model, the players form a level of confidence, depending on who the player accepts the strategy or does not accept. The project manager assesses the costs and compares them with the level of confidence. An investor evaluates past results. Also visit the case where the strategy of the player accepts the part.