You hold a hard 9 (no ace counted as 11). The dealer shows a 3. Here is the mathematically correct basic-strategy play — and why.
Hard 9 is a premium doubling hand. One card is very likely to give you a strong total, and against a 3 (which busts 37% of the time) you want maximum money on the table while you have the edge. Doubling wins you more in exactly the spots where you're a favourite.
If doubling isn't allowed (e.g. after hitting), simply hit instead — the extra card logic stays the same, you just can't add the extra bet.