Lattice proteins are models resembling real proteins. They comprise an energy function and a set of conditions specifying the interaction between elements occupying adjacent lattice sites. In this paper we present an approach examining the behavior of chains of a large number of molecules. We investigate this by solving a restricted random walk problem on a cubic lattice and square lattice. More specifically, we apply the Hydrophobic-Polar model to examine the spatial characteristics of protein folds using the Monte Carlo method. This technique is the so-called Rosenbluth sampling method for solving restricted random walk problems. Specifically, by solving such walks we resolve folds. In addition, this method can be extended to solve the Hydrophobic-Polar model. In this paper, we describe this method as an algorithm that calculates the energy spectrum for the Hydrophobic-Polar model, and the related formula for estimating the number of folds. Moreover, we estimate the number of folds for each sequence using Hydrophobic-Polar model energy estimation. On test sequences the predicted protein folds were obtained with a mismatch of one unit according to the energy. We also observe that the estimated number of folds depends only on the length and not on the type of sequence. This promising strategy can be extended to quantify other proteins in nature.