You hold a hard 15 (no ace counted as 11). The dealer shows a 7. Here is the mathematically correct basic-strategy play — and why.
| Hit ← | -0.3698 |
| Stand | -0.4754 |
| Double | -0.7489 |
| You bust on the next card | 53.8% |
| Dealer 7 busts | 26.2% |
Hit is worth 0.1056 more per unit than Stand. On a $10 bet that is $1.06 handed over every time you get it wrong. Across the 340 situations in this chart it ranks 311th by expected value — better than 29 of them, worse than 310. 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 7 only busts about 26% 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.