Basic strategy tells you what to do; it never tells you how often the right play actually wins. That gap is where tilt lives: a correct stand on 16 against a ten still loses more than three hands in four, and knowing the number in advance is the difference between a bad beat and a surprise. This calculator shows the exact win, push and lose probabilities for standing on any total against any dealer upcard — computed from the full dealer-outcome distribution, not rounded folklore.
Blackjack Hand Equity: Win / Push / Lose
Infinite-deck model with the US peek rule: a dealer blackjack is already excluded when a ten or ace shows. Figures are for standing on the total; the EV of hitting, doubling or splitting the same hand lives in the Decision EV Calculator.
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What the Numbers Mean
When you stand, the hand becomes pure dealer mathematics: the dealer draws to 17 or better, and your total either beats the final result, ties it, or doesn’t. The calculator resolves that draw exactly — an infinite-deck recursion over every dealer path under your chosen rule (S17 or H17), with the US peek convention applied, so a dealer blackjack is already off the table when a ten or ace shows. Win minus lose, per dollar, is the EV of the stand; the tool prints it under the bars.
Scope is deliberate: these are standing equities. The moment hitting, doubling or splitting enters the question, you are comparing actions, and that comparison — the EV of every available move side by side — is exactly what our Decision EV Calculator does. The two tools share one model family, so their numbers agree where they overlap.
Win Probability When Standing (S17)
| Stand on | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A |
|---|---|---|---|---|---|---|---|---|---|---|
| 21 | 88.20% | 88.53% | 88.88% | 89.18% | 90.28% | 92.59% | 93.06% | 93.92% | 96.26% | 92.22% |
| 20 | 75.80% | 76.50% | 77.23% | 77.86% | 80.11% | 84.73% | 86.12% | 81.92% | 59.19% | 73.33% |
| 19 | 62.83% | 63.94% | 65.09% | 66.09% | 69.49% | 76.87% | 73.26% | 46.84% | 47.12% | 54.44% |
| 18 | 49.34% | 50.89% | 52.50% | 53.87% | 58.86% | 63.09% | 37.33% | 34.84% | 35.05% | 35.54% |
| 17 | 35.36% | 37.39% | 39.45% | 41.64% | 42.32% | 26.23% | 24.47% | 22.84% | 22.98% | 16.65% |
| 12–16 | 35.36% | 37.39% | 39.45% | 41.64% | 42.32% | 26.23% | 24.47% | 22.84% | 22.98% | 16.65% |
Totals 12–16 share one row because a standing stiff hand wins only when the dealer busts — the probability is identical for all of them. Infinite-deck model, dealer stands on soft 17, dealer blackjack excluded (peek). Push and lose percentages, H17 figures and per-hand EV are in the calculator above.
Five Numbers Worth Memorizing
- 20 vs 8: wins 86.12%, pushes 6.94% — the dominating position, EV +$0.79 per $1. When it loses, the dealer drew to 20 or 21 through a 6.94% window.
- 20 vs 10: wins 59.19% but pushes a hefty 37.07% — the ten in the hole makes dealer 20 the single most likely outcome, so your monster hand ties far more often than intuition expects.
- 16 vs 10, standing: wins 22.98% — you win only when the dealer busts. EV −$0.54 per $1, which is why surrender, where offered, takes the fixed −$0.50 instead.
- 18 vs Ace: wins 35.54%, EV −$0.10 — “eighteen always wins” is a table myth; against big upcards it is a clear underdog.
- 12 vs 2: wins 35.36% standing — you are betting almost entirely on a dealer bust, and the 2 busts far less often than its lowly look suggests. The most misplayed “easy” hand in the game.
Equity as Tilt Control
The practical use of these numbers is emotional, not strategic: strategy is already solved. A player who knows that a correct stand on 19 against a ten still loses 40.81% of the time reacts to the dealer’s 20 with a shrug instead of a strategy change. Variance punished you; the play was right. Expecting exact frequencies is what lets you keep making the highest-EV move after three of them lose in a row — and per-session swings around these averages are large, which is what our session variance material quantifies.
Model Assumptions
Infinite-deck composition (the standard for strategy tables; finite-shoe figures differ by fractions of a percentage point), dealer distributions computed by exact recursion rather than simulation, peek rule applied for ten and ace upcards, and blackjack paying 3:2 in the natural’s special case. Card-counting shifts these probabilities with the count — that layer belongs to the card counting calculator.
Related Blackjack Tools
- Blackjack Decision EV Calculator — EV of hit, stand, double and split, side by side
- Blackjack Expected Value Guide — House edge by rules, hourly cost and variance
- Blackjack Insurance EV Calculator — The ace-up side bet, priced honestly
- Card Counting Calculator — How the count moves your edge