You hold a hard 11 (no ace counted as 11). The dealer shows a Ace. Here is the mathematically correct basic-strategy play — and why.
A dealer Ace only busts about 12% of the time — most of the time they'll finish with 17 or better. Standing on hard 11 just waits to be beaten. Even though hitting busts you 0% of the time, improving your hand is the lesser risk against a strong dealer card.
Think of it this way: your 11 almost never wins as-is against a made dealer hand. The hit isn't reckless — it's the only path to a total that can actually win.