Battlegrounds Initiative

I am sure this has been asked but here goes.

When people face off in battlegrounds. Would it be possible to keep track of who gets initiative with same number of minions? Next time they face off just let the person who didnt go first on the previous fight go first? Knowing this in advance, each player could set up their team better and encourage more strategy.

What if 2 players didn’t go first on the previous round and they are matched against each other?

Then the rng initiative is in play. but after it keeps track and the other player will get it next time.