Hextech Annie Availability
So based on data from a test of the PBE server including opening 10,000 hextech chests, it would take 272 hextech chests to have enough Rare Gems to create Hextech Annie (can only be obtained with 10 gems, 368 gems in 10K chests). Otherwise, you'd have to purchase promo chests from Riot to collect enough gems. Just a reminder, this is not a ploy to give free skins to players who don't pay money: This is a marketing tactic to get more people to spend on microtransactions for larger numbers of smaller gifts.