ARAM Doesn't FEEL Random

So I have been playing a lot of ARAM recently (not because of a lack of Solo Queue, which I honestly don't give a damn about) and I have started to notice something, I have gotten Kindred three or four times in the last few days. Whenever I can, I would re-roll her. However, I sometimes I can't, and I am forced to play her. What is the problem here? Well, I saw Kindred three (maybe four, I can't remember) times. To the human mind, that doesn't seem random. Similarly, I got Leona twice, and Volibear twice (though I think someone dodged that game). I wouldn't be surprised if this isn't true randomness because, lets face it. True randomness works in a similar way. True randomness, however, doesn't feel random. Our brains seek out any and every pattern it can find/create from nothing, and so randomness, even if it is true randomness, can be perceived as a pattern.

So, what does everything I have said above mean? It means that I want ARAM to feel more random. I don't want ARAM to actually be random, that isn't as fun. No, I want ARAM to be controlled so that it feels random, which basically means that you won't get the same champion every 7-8 games at least. Even if your champion pool isn't large, and mine isn't, I want it to feel about as random as possible, which means pretty much go through a large portion of the champion pool before coming back and picking the same champion. This would make ARAM feel more random because, in game design, it is often better to make the player feel that a system is randomized than it is for the system to be truly randomized.