You hold a hard 15 (no ace counted as 11). The dealer shows a Ace. Here is the mathematically correct basic-strategy play — and why.
| Hit ← | -0.4800 |
| Stand | -0.6670 |
| Double | -0.9831 |
| You bust on the next card | 53.8% |
| Dealer Ace busts | 16.7% |
Hit is not close: it beats Stand by 0.1869 per unit. Getting this one wrong costs $1.87 on a $10 bet, every single time. It is also the 6th worst spot of the 340 hands in this chart. Expected value is per unit staked, computed for multi-deck, dealer stands on soft 17, double after split allowed. The model and the code are published as data.
A dealer Ace only busts about 12% of the time — most of the time they'll finish with 17 or better. Standing on hard 15 just waits to be beaten. Even though hitting busts you 54% of the time, improving your hand is the lesser risk against a strong dealer card.
Think of it this way: your 15 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.