Updated 2026-07-22 · 8 decks · S17 · DAS · methodology
Hard 13 vs dealer 9: the verdict
The math is in: hit. Against a dealer 9, drawing another card carries the best expectation for hard 13.
The numbers
| Action | Win | Push | Lose | EV per $1 |
|---|---|---|---|---|
| Hit | 26.9% | 7.4% | 65.7% | −0.387 |
| Stand | 22.8% | 0.0% | 77.2% | −0.543 |
| Double | 26.8% | 5.9% | 67.2% | −0.808 |
Why hit is correct
Standing here wins only when the dealer busts, and a dealer showing 9 busts just 22.8% of the time — the other 77.2% they make a hand and your total loses on its own. Hitting risks going over, but the math nets out ahead: 26.9% wins versus 22.8% for standing, and a better expected value overall.
For context, a dealer 9 finishes on 17–20 about 71.1% of the time, on 21 6.1%, and busts 22.8%. Those dealer outcomes are the same no matter what you hold — the whole game is choosing the action whose distribution fits them best.
What the mistake costs
Choosing stand instead of hit costs about $390 per 100 such hands at $25 a hand (−0.156 EV per dollar). The genuinely expensive error here is double: −0.421 per dollar, or roughly $1052 per 100 hands at the same stakes.
Does the rule set change it?
No — hit holds across every common configuration: Vegas Strip, Atlantic City with late surrender, H17 games and European no-hole-card tables all agree here.
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13 against other dealer cards:
Other key hands vs a dealer 9: