I'm confused, why don't you just determine the games ahead of time and release the proof that you didn't cheat?  You are asking players to trust you because way after the fact you can estimate whether you had an edge or not.  That's kind of shaky evidence when you could just as easily release the order of your outcomes and we can both determine that you didn't change any outcomes and that there is no house edge.

To be completely frank, I am skeptical of a house that claims to have no edge.  Players don't care if a casino takes 1% (or whatever percent).