Lets get one thing straight: you don't play poker against the house but against other players... Maybe this is a game can be beat... but you have to play sitting down.
Actually when you put players of similar levels together and make them plays tens of thousands of hands together, all these players are going to be break-even... If not for the rake that the house takes.
This is already seen in online poker in cash games at some limits where there are a lot of regulars. And it's very often discussed (and criticized) in online poker forums, where they say that these regulars are just shifting the money all around, with the house being the only real winner.
So your oversimplification doesn't get anything straight.
When you play poker you play against other players and against the house (rake and buy-in fees).
To give you an idea: there are semi-pro who would be losing players but who are actually making quite a decent profit only thanks to the partial rake-back that the house gives them (regulars players playing lots of hands get back a % of the rake they paid, which is called the rakeback).
