You hold a hard 13 (no ace counted as 11). The dealer shows a 3. Here is the mathematically correct basic-strategy play — and why.
| Stand ← | -0.2522 |
| Hit | -0.2912 |
| Double | -0.5824 |
| You bust on the next card | 38.5% |
| Dealer 3 busts | 37.4% |
Stand is worth 0.0390 more per unit than Hit. On a $10 bet that is $0.39 handed over every time you get it wrong. Across the 340 situations in this chart it ranks 279th by expected value — better than 61 of them, worse than 278. 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.
Showing a 3, the dealer ends up busting about 37% of the time. Meanwhile, if you hit hard 13, the next card busts you 38% of the time. When the dealer is this likely to destroy their own hand, taking that risk is a losing trade — you stand and let the math work against them.
This is one of the most common mistakes at the table: players feel 'weak' standing on 13 and draw anyway. Over thousands of hands, hitting here costs real money. The chart says stand — every time.