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Do you keep god-tier Pokemon?
And by 'god-tier', I mean 0% IVs, lol. I think they're neat collector's items, since they're arguably rarer than 100% IVs. God-tier legends and hatches (i.e. 10-10-10) are thrown on the scrap heap for me, although in terms of rarity they're as uncommon as 15-15-15.
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I caught a 1995 Rayquaza today, came with no TMs, no rare candy, 13 golden razz, 3 revives, unnoticed number of potions. At least it was against AS/AA since only had 3 fighting it, otherwise a complete pit. In the past week I've hatched 98% Trapinch, 98% Swablu, 98% Mareep...all 15 attack. Pretty sure I've thrown a lot of good stuff away since start of the game...positive I've thrown a lot of REALLY bad stuff away.