You hold a hard 10 (no ace counted as 11). The dealer shows a 9. Here is the mathematically correct basic-strategy play — and why.
| Double ← | +0.1443 |
| Hit | +0.1165 |
| Stand | -0.5432 |
| You bust on the next card | 0.0% |
| Dealer 9 busts | 22.8% |
Double beats Hit by 0.0278 per unit staked. Small, but it is the same small edge in every shoe you ever play — and it compounds over a lifetime of hands. Across the 340 situations in this chart it ranks 116th by expected value — better than 224 of them, worse than 115. 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 9 (which busts 23% 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.