I definitely take the ball first. If the first possession is a match, then you have it first just needing a field goal. Put another way, no matter how many possessions you are always guaranteed to have equal or more than your opponent absent turnover. Or simply — You always want the odd possessions, 1, 3, 5.
I think “knowing what you need” is overrated. If going on fourth down makes sense, it should always make sense. If going for it does not make sense, your opponent is in a suboptimal position. That is always good.
Might they make it? Sure. Just like sometimes 16 wins against a dealer ten showing. You’d still always rather be the dealer in that case before the hand is dealt.