ARAMs Ways to make it better

I Play a decent amount of arams with my family. We are pretty casual. I have noticed that arams really arent random however. not sure what the algorithm is for this, but I own all champs and i should reasonably expect to play any champion. Not one of a fairly small group.

Also, if you could make the re roll button show us another random champ and give us the OPTION to switch to that new champ, that'd be cool.