You hold a hard 13 (no ace counted as 11). The dealer shows a 10. Here is the mathematically correct basic-strategy play — and why.
| Hit ← | -0.4253 |
| Stand | -0.5404 |
| Double | -0.8675 |
| You bust on the next card | 38.5% |
| Dealer 10 busts | 23.0% |
Hit is worth 0.1152 more per unit than Stand. On a $10 bet that is $1.15 handed over every time you get it wrong. Across the 340 situations in this chart it ranks 325th by expected value — better than 15 of them, worse than 324. 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 13 just waits to be beaten. Even though hitting busts you 38% of the time, improving your hand is the lesser risk against a strong dealer card.
Think of it this way: your 13 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.