The significance of sidewalls which yield velocity distributions with non-Gaussian tails and a peak near zero velocity in quasi-two-dimensional granular gases, was investigated. It was observed that the particles gained energy only through collisions with the bottom of the container, which was not evacuated. The particle motions were observed at a rate of 1000 frames per second which were recorded by a digital camera. The interactions with sidewalls were found to strongly affect the functional form of the velocity distribution. The results show that the features of the velocity distributions are well described by a discrete map model with a damped driven single particle.