Aram: random chance of getting champions and not being able to back to buy items.
Riot - too much rng aram will not be getting rank queue.
Tft - picking a champion which then can be upgraded by picking the same champion that randomly shows up in your champion pool. Which you can reroll to randomly get new champions. There is also comps you can build and to get their buffs you must have x amount of the same comps to get their buffs but each of those champions are randomly shown to you and some don't show up until later in the game.
You can also buff your champions by giving them items. Items can be earn through the caoursel which can give you an item or by neutral monsters which can randomly give you an item or nothing at all.
Riot - seems to be not base on rng at all let's give it rank queue