 The paper presents Monte Carlo simulations of site percolation for three square matrices with dimensions L equals 55, 101, and 151 using 5 times 10 to the power of six iterations. The results show that the statistical distribution of the percolation threshold value is a normal distribution. The coefficients of determination for the simulation results are 0.9984, 0.9990, and 0.9993 for matrices with dimensions 55, 101, and 151, respectively. The mean values of the percolation threshold and its uncertainty are 0.5927046+, or minus 1.1 times 10 to the power of negative 5, 0.5927072+, or minus 7.13 times 10 to the power of negative 6, and 0.5927135+, or minus 5.33 times 10 to the power of negative 6, respectively. The paper also presents a new method of optimizing the determination and reducing the uncertainty of the percolation threshold estimation by selecting the dimensions of the matrix, and the number of iterations to obtain the assumed uncertainty in determining the percolation threshold, which can be used to simulate the percolation phenomenon and estimate the value of the percolation threshold, and its uncertainty in matrices with other shapes than square ones. This article was authored by Pawell-Zukowski, Pawell-Okl, Konrad Kierksinski, and others. We are article.tv. Links in the description below.