Updated 2026-07-22 · 8 decks · S17 · DAS · methodology
Hard 7 vs dealer 4: the verdict
Basic strategy says hit. Against a dealer 4, drawing another card carries the best expectation for hard 7.
The numbers
| Action | Win | Push | Lose | EV per $1 |
|---|---|---|---|---|
| Hit | 44.5% | 6.7% | 48.8% | −0.043 |
| Stand | 39.4% | 0.0% | 60.6% | −0.211 |
| Double | 40.5% | 5.0% | 54.6% | −0.282 |
Why hit is correct
Standing here wins only when the dealer busts, and a dealer showing 4 busts just 39.4% of the time — the other 60.6% they make a hand and your total loses on its own. Hitting risks going over, but the math nets out ahead: 44.5% wins versus 39.4% for standing, and a better expected value overall.
For context, a dealer 4 finishes on 17–20 about 49.4% of the time, on 21 11.1%, and busts 39.4%. 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 $420 per 100 such hands at $25 a hand (−0.168 EV per dollar). The genuinely expensive error here is double: −0.239 per dollar, or roughly $598 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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7 against other dealer cards:
Other key hands vs a dealer 4: