You hold a hard 11 (no ace counted as 11). The dealer shows a 7. Here is the mathematically correct basic-strategy play — and why.
| Double ← | +0.4629 |
| Hit | +0.2922 |
| Stand | -0.4754 |
| You bust on the next card | 0.0% |
| Dealer 7 busts | 26.2% |
Double is not close: it beats Hit by 0.1707 per unit. Getting this one wrong costs $1.71 on a $10 bet, every single time. Across the 340 situations in this chart it ranks 51st by expected value — better than 289 of them, worse than 50. 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.
Hard 11 is a premium doubling hand. One card is very likely to give you a strong total, and against a 7 (which busts 26% 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.