You hold a hard 15 (no ace counted as 11). The dealer shows a 10. Here is the mathematically correct basic-strategy play — and why.
| Hit ← | -0.5044 |
| Stand | -0.5404 |
| Double | -1.0090 |
| You bust on the next card | 53.8% |
| Dealer 10 busts | 23.0% |
Hit is worth 0.0360 more per unit than Stand. On a $10 bet that is $0.36 handed over every time you get it wrong. It is also the 4th 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 10 only busts about 21% 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.