“Game 1: drew aegis initially; then mulligan him and got him again...”
Intersting. I’ve always assumed the specific cards you mulliganed won’t come back as replacement cards, since that’s how it worked in Hearthstone. This mechanic changes your % of replacement cards (say you mulligan 3 Lucifers: you’ll have a 3/40 chance of drawing another Lucifer instead of a 0/40 chance) so on the one hand, you know how likely it is to draw certain cards in the mulligan before a match starts, but on the other hand, you’re less likely to ditch those high cost cards. Thank you sir, I’ve learned something today.
I don't think it's safe to assume the card draw mechanism is a simple "random number" thing. We know the Goblin Mage is skewed against roaches.
So there may be other mechanisms in play that suppress or increase the likelyhood of cards showing up in your hand.
Whatever is going on, cards tends to clump for me. It's not uncommon to have 3 copies of a card by the 4th turn. I get that can happen...but it shouldn't happen multiple time a day.