You hold a hard 10 (no ace counted as 11). The dealer shows a 2. Here is the mathematically correct basic-strategy play — and why.
| Double ← | +0.3589 |
| Hit | +0.1825 |
| Stand | -0.2928 |
| You bust on the next card | 0.0% |
| Dealer 2 busts | 35.4% |
Double is not close: it beats Hit by 0.1764 per unit. Getting this one wrong costs $1.76 on a $10 bet, every single time. Across the 340 situations in this chart it ranks 73rd by expected value — better than 267 of them, worse than 72. 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 10 is a premium doubling hand. One card is very likely to give you a strong total, and against a 2 (which busts 35% 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.