Updated 2026-07-22 · 8 decks · S17 · DAS · methodology
Hard 13 vs dealer 4: the verdict
The verdict is stand. Against a dealer 4, hard 13 does best by letting the dealer take the risk of busting.
The numbers
| Action | Win | Push | Lose | EV per $1 |
|---|---|---|---|---|
| Stand | 39.4% | 0.0% | 60.6% | −0.211 |
| Hit | 34.0% | 4.7% | 61.4% | −0.274 |
| Double | 34.0% | 4.7% | 61.4% | −0.548 |
Why stand is correct
A dealer showing 4 busts 39.4% of the time, and that bust chance is doing the work here: standing wins 39.4% of hands without ever risking your own bust. Drawing a card would improve the total sometimes, but the bust risk and the hands you’d ruin cost more than they gain.
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 hit instead of stand costs about $158 per 100 such hands at $25 a hand (−0.063 EV per dollar). The genuinely expensive error here is double: −0.337 per dollar, or roughly $843 per 100 hands at the same stakes.
Does the rule set change it?
No — stand 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 4: