The microgeometry of the equilibrium friction surface of wear-resistant gas-thermal coatings is discussed. To describe the steady-state profile of powder coatings during sliding friction, a theoretical probabilistic approach is used to statistically justify the hypothesis of the normal distribution of heights of the equilibrium friction surface of materials on the basis of the de Moivre-Laplace theorem. The limiting Poisson law and computer simulation of the powder environment with the probabilistic-geometric system is used to study the profile of the equilibrium friction surface of wear-resistant powder coatings. The findings obtained can be applied to build the support curve of the friction surface of wear-resistant powder coatings.