This was a fun exposition, but the "min" part is unclear as shown because the author does not explicitly show a look-a-head plan.<p>When the computer is playing reactively i.e. only planning the next move it needs to only do a max, execute the move and wait to see what the opponent does.<p>The "min" comes in when the computer is building a tree of not only its next move, but also of its <i></i>opponent's<i></i> next move so it can plan the next-next move and so on.