We can even see negative house edge websites !
These are the faucet. I'm thinking in particular of
http://www.freebitco.inTheir business model relies on advertising, so the games are just giving BTC away.
It's very hard to get some decent amount of money. You can win more on a dice site.
If some organization find a right balance between income, profits and expenses, we can have very interesting free games.

oh that is one bad example for a negative house edge
freebitcoin is a faucet+gambling site,their dice game has one of the highest HE out of all the dice sites
it is 5% and it is there to cover the faucet expenses
also they do not have advertisment as of lately as in banner or text ads
don't think you visted their site lately
in any case, 0% house edge is sustainable in some cases (PVP,for example) but I don't trust websites like that