Make refund tokens unlocked at level 30, 40, 50.
Everybody has the story of how they just started playing league and immediately blew their 3 refunds on champions that they didn't like. I feel if you got the hang of the game a lot more and actually got to think about what to refund. Also by not having all 3 of them unlocked at the same time, nobody is going to refund 3 champions at once on a whim.
Even at that, maybe 40, 50, 60 would be better so you get a real grip on the game first. Of course, if players have already spent their 3 refunds they will not earn more refunds through reaching these levels.
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New players will hate it, but they'll regret it less afterward. Like how I regret refunding TF in the first week because I liked playing him less than Veigar and wanted to buy Anivia. I play none of these champions anymore. I actually ended up refunding Anivia and buying her back a week+ later. If I had those tokens later on, I would've refunded Tryndamere which I would not regret since I'm absolute garbage at him. Maybe my level 50 token would be used on Azir who I still suck at as well.