Possibly unpopular opinion: the RNG in TFT really isn't that bad and people are just shifting blame
Aside from item drops, which are ridiculous, the RNG in the game really isn't that bad. I am fairly certain that most of the dislike of the gamemode comes from inefficient economy management, not understanding how to min/max champ rolls, and not knowing how to play from behind. Here are a few tips that can help out.
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It's usually better to pick a T2 from the first carousel and snatch up a bunch of T1s in the beginning
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Stacking gold from interest + loss streaks is a good way to get back in the game if you get behind, as well as setting you up for first pick at the carousel.
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It's more efficient on gold to get to level 8 before trying to roll for T5 champs.
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It's way more efficient on gold to do all of your low level rolling at lower levels (you can intentionally deflate your level to keep T1 drop rates high)
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Some champions (mordekaiser/fiora/rek'sai for example) are not worth getting to 2 star, let alone 3 star (as of the current patch). It's more efficient to funnel gold onto a few carries for your team.
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If you can't find the champions you need from rolling, there is a good chance that someone else on the map is also trying to roll for those champs. Champs come from a shared pool (e.g., there are 39 of each T1 champ at the start of the game, excluding ones found in the carousel), so if two people are trying to 3 star one of the later game champions, neither of them will be able to.
Those are all the tips I can come up with off the top of my head, though there are way more.