The depth-slider window allows you to adjust the depth that the alpha/beta min/max algorythm uses for various parts of the program. The three parts you can adjust are the Black & Red AI Player depths and the AI Tutor depth. For the AI Players, a value of 0 indicates a human player. At any other setting, the computer will play for that color. The higher the depth, the more moves into the future the computer will consider (the better it will play). It is important to note that things get exponentially slow as you increase the play depth. Values up to about four are resonable on most machines (P133+).