It's funny but just today I was playing a match in M:tG Arena and I noticed that I used a card's rarity to make a decision. The card was Worthy Knight, a 2/2 creature and I was trying to decide whether to attack into it with my own creature, a Pelt Collector (at the time also a 2/2, with a +1/+1 counter). Normally, in that situation, I wouldn't attack with Pelt Collector - I'd wait for it to grow a bit and then attack so it wouldn't just trade.
However, I wasn't sure what Worthy Knight was doing in the opponent's deck, but I noticed it was a rare (I didn't know the card, it's from the new set, Sword of Eldraine).
Now, normally that would make no difference, but there is no trading in M:tG Arena, as there is in the physical game, so rare cards are harder to come by in Arena than they are in the physical game. Given that Arena booster packs only have eight cards, when physical booster packs have 15 cards, a full set of four of any rare represents a more significant investment (of money, or time) on the part of its owner.
Based on this I figured that, if the opponent was running Worthy Knight (and likely a set of four given I'd seen it in the first turn), then it must be somehow important to their strategy. So I attacked with Pelt Collector and we traded (i.e. the two creatures killed each other in combat).
Edit: I mean, Pelt Collector is like the creature kill magnet. It seems players know it's a powerful card and do their best to get rid of it as early as possible.
Edit 2: Oh, I remember now. They just played another one next turn. They probably had it in hand from the start. I should have waited with the Collector.