Not to mention, we're talking about a game where the online site that has the most far play.
In my opinion, it's poker, because it's a game I know and the site doesn't ask so much about your stake and winnings, that's reason enough for the site not to steal from you.
The site may give you bad tickets, but again it knows whether or not to get one.
If sellcted others, clarify which game and why?
For as long as they are coded in such a way that the result is absolutely random and that the site cannot influence on it, they could all be fair.
But if you think poker is the most fair, I don't think I'll agree. I suppose you are referring to live poker. I have reservations about live poker as I cannot verify whether the person one the other side of the table is a real one. And if the other players on the table are indeed real persons, you still cannot verify whether 2-3 of them are playing together and that they know each other's cards. That would be like you against the rest of the players.