Methodology: where the numbers come from
Every verdict on this site is produced by one expected-value engine. This page documents exactly how it works, how it was validated, and where its honest limits are — so you can decide for yourself whether to trust it.
The engine
For any player hand against any dealer upcard, the engine computes the exact expected value of each legal action. Standing is evaluated against the dealer's full outcome distribution (17, 18, 19, 20, 21, blackjack, bust), which is derived recursively from the dealer's drawing rules — including whether the dealer stands or hits soft 17, and whether the game uses a hole card with peek (US style) or no hole card (European ENHC, where a dealer blackjack takes doubled and split bets too). Hitting is a memoized recursion over every possible drawn card followed by optimal play. Doubling is one card and a forced stand at doubled stakes. Splitting is modeled as two independent one-hand EVs with the correct post-split rules (double after split when allowed; split aces receive one card). Late surrender returns exactly −0.5 where the rules permit it.
Alongside EV, the engine computes the full win / push / lose probability of each action, which is what powers the odds tables on every hand page. These distributions satisfy strict internal invariants — probabilities sum to 1, and for even-money actions EV must equal P(win) − P(lose) to nine decimal places — which are enforced by automated tests on every build.
Validation
Three independent checks back the engine. First, a 65-cell test suite of canonical decisions across five rule sets, all matching published references. Second, the complete generated chart for 4–8 deck, S17, DAS games matches the printed basic-strategy canon cell for cell — including the separately verified H17 rows and the European no-hole-card rows, where strategy against a dealer ten and ace genuinely differs. Third, Monte Carlo simulation: 30–40 million rounds per decision dealt from a real 8-deck shoe, used to confirm the borderline cells where analytic approximations are most fragile. This process caught and fixed a real bug during development (soft dealer hands starting from A-A), which is exactly what validation is for.
Honest limits
The engine uses an infinite-shoe model, which is accurate for the 4–8 deck games that virtually all live and online blackjack uses; we deliberately do not support single-deck tables, where composition-dependent effects are too large to hand-wave. Two soft-hand cells (A-2 vs 5 and A-4 vs 4) sit so close to the line that the infinite-shoe answer differs from the finite-shoe canon by less than 0.012 EV; we render the canonical play and mark such razor-thin spots with "≈" wherever they appear. Split EVs use the standard two-hand approximation rather than full composition tracking — conservative, and consistent with how live tables (one split, no resplit) actually deal. Our house-edge figures inherit that: they land a few hundredths of a percent above textbook numbers that assume resplitting to four hands, because the games we model don't allow it.
What we will never publish
No "hot streaks", no predictors, no betting systems dressed up as math. If a number on this site can't be recomputed from the rules of the game, it doesn't get published.