Does playing Miss Fortune (or another unit) to an open battlefield count as conquering it and cause a showdown to happen?

Ruling: Playing a unit to an open battlefield does create an open showdown (where your opponent can respond after you pass priority), and if you win the showdown you conquer the battlefield.

Sequence:

• Play unit to open battlefield
• Open showdown is created
• Pass focus/priority
• Opponent can respond with cards
• If you win the showdown, you conquer the battlefield

Nuances:

• You cannot conquer a battlefield you've already scored on that turn, even if you win a showdown
• If you held a battlefield, scored for it, moved away, then moved another unit back to it later in the same turn, you would not conquer it because conquering is part of the scoring process