5/10NL $20 Fixed Buyin - Possibly Mathematically Beatable?

[maxel100]

Ok, this may sound like a joke but me and a friend are having and argument about how small buyins with relativley large blinds are unbeatable games. To demonstrate his point he took an extreme senario of 5/10NL with Fixed Buyins of $20 no more or no less. He said regardless of any other factor this game would not be beatable. I disagree and heres my thoughts. First of all we can assume your opponent (dumb for buyin might i add) is has an average to low knowledge of poker. You could statisitically work out every hand that is worth pushing on and every hand that is worth folding on to create maximum EV. You just learn the right times to push and fold (all done preflop) and i believe that without your opponent knowing this you would have an edge and over a long run you would be profitable. Any thoughts? (am i compeltely wrong?)
Note that it is assumed you and your opponents will constantly be rebuying. ie rebuying right after you post and so on.