What the hell is Vayne's counter play?

Trying to be a tanky tank latest few seasons been a complete b1tch, but at least when you are 300+ armor and 4k health most AD champions won't delete you in seconds, but I was just against a Vayne in a long time, she had botrk, statik and berserker boots. I was 3.4k health nunu with 250ish armour. She was chucking over 300 health per basic auto from me (having 190 AD) and I decided to just %%%% that and ran away. Seriously, why is it a sin for tanks to be tanky? I'm sort of overly sick of the instant burst bullshit that's been going on in League past few seasons
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